Microworld particles, their origin, properties and application in research and technology

1. Nuclear and radiation physics
1.0. Physics - fundamental natural science
1.1. Atoms and atomic nuclei
1.2. Radioactivity
1.3. Nuclear reactions, nuclear energy
1.4. Radionuclides
1.5. Elementary particles and accelerators
1.6. Ionizing radiation

1.5. Elementary particles and accelerators

In interpreting the properties of atoms in Chapter 1.1, we have learned that neither an atom, nor even its nucleus, are elementary building blocks of matter, but are composed of even smaller particles - electrons, protons, neutrons. In the study of radioactivity, we also recognized some other particles - positrons, neutrinos. Are these subatomic particles really already internally "monolitic" - elementary and fundamental? Or do they have their internal structure, composed of "even smaller" particles? (A more detailed discussion is below in the section "Are elementary particles really elementary?").
  In this chapter we will try a brief but systematic trip to the varied and wonderful world of elementary particles. We will proceed inductively in the interpretation. After introductory passages on the common properties of particles, their classification and patterns of interactions, we will move from basic, known and widespread particles and their simple properties (straight from experiments), through "more exotic" particles and more complex mechanisms of interactions, to unitary symmetries and attempts to clarify the internal structure of particles. We will also mention hypothetical and model particles, some of which have not yet been directly discovered, or their role in nature is not yet fully understood.
  We will first outline the systematics of elementary particles and then analyze the properties and interactions of individual specific types of particles, including the formation of particles in high-energy interactions. And also antiparticles - their origin and annihilation, their role in nature, possibilities of use. We will also think about what the individual particles have in common and how we have progressed towards a unified understanding of particle and field physics - unitary field theory. Finally, we describe how we investigate the interactions of particles at high energies on particle accelerators.
  Behind all this knowledge about elementary particles is hidden the enormous effort and colossal volume of work of thousands of physicists, technicians and workers - designers of complex acceleration systems and detection apparatus.
  But before that, let's make a few general remarks and discussions about particles as such :
Terminological note - elementary ? :
The name "elementary" or "basic" should mean that it is a further indivisible object, without internal structure; it is thus the simplest material object acting as a separate physical entity. However, in the course of the scientific knowledge of the microworld, it has been shown several times that particles previously considered to be basic (elementary) have an internal structure and consist of even "smaller", more basic or "more elementary" particles. According to earlier opinions "indivisible atom" (hence its name), has a complex structure of the electron shell and the atomic nucleus. Protons and neutrons in atomic nuclei have also been considered indivisible, but next research (in a standard particle model) has shown that they consist of quarks (as do other hadrons). Opinions on the "elementality" of particles can thus vary depending on the current state of physical knowledge (a more detailed discussion is in the passage below "Are elementary particles really elementary? ').
  Therefore, since many particles are "folded", the "elementary" may be misleading. However, this is the established name, like the name "atom", which has long been not "indivisible". In recent years, often the word "elementary"omits and speaks only of "particles".
Are there any elementary particles at all? "Ball" model.
Our idea of existence - that "something exists" - is based on our daily experience of observing the macroworld of the surrounding nature. There are, for example, stones - we can see, touch and weigh by hands, or throw them. There are different species of plants and animals with specific looks and properties. There are cells in organisms that can be observed under a microscope, including their internal structure (see eg §5.2., Section "Cells - basic units of living organisms") and study their biochemical manifestations. However, in a microworld of subatomic or even subnuclear dimensions, it is more complicated.
  Particles of the microworld we can't see even with the strongest microscope - they are much smaller than the wavelength of visible light. Even if we reduced ourselves in the imagined sci-fi concept to "dwarfs" the size of a picometers and observed with radiation of much shorter wavelengths, we would not see any localized particles. Quantum uncertainty relations "blur" the velocity determination with accurate position measurement, and the particle velocity measurement in turn blurs its position. We would perhaps only see blurred tufts of fluctuating fields. From this usual point of view, we could make a "heretical" claim that "elementary particles do not exist "!
  However, in more detailed physical research, we come to the realization that there is a "something" hidden that carries physical forces, such as an electric charge, something that transmits energy trought space, that causes mutually influences - interactions - of material bodies. In classical physics it is a physical field, in quantum physics the quantum of fields. We call this "something" the elementary particles (the word "elementary" discussed above). We can not imagine it in any concrete way and that is why model them as small spheres (small balls) - eg. electrons draw a red protons as blue, neutrons as gray spheres, neutrinos as perhaps green; it is a matter of convention. These bullets, having a certain mass, charge and other physical characteristics, are, according to the usual laws of (relativistic) mechanics move through space at a certain speed and the associated kinetic energy. With a certain probability (see "Effective cross-section" below), they can "collide" - interact - with other spheres (particles), while other spheres - particles of the same or different properties - fly out of this place. However, during the actual internal course of the interaction, the "ball model" cannot be used, there are often quite complex quantum-field processes (see "Feynman diagrams" below).
  The ball model is very successful - in co-production with physical mechanisms of electromagnetic, strong and weak interactions can explain or represent practically all phenomena with particles of the microworld in atomic, nuclear, radiation and particle physics. This "ball illustration", possible supplemented by the wave nature, therefore we draw in most of the pictures of our treatise "Nuclear Physics and the Physics of Ionizing Radiation".
Who ordered the "exotic" particles ?
To understand the structure of matter around us, we will suffice with the few particles mentioned above (§1.1 and 1.2) - photons, electrons, protons, neutrons (in mor complex phenomena also neutrinos, mesons, quarks u and d ). Nevertheless, in the interactions of particles (whether artificially induced or in cosmic rays) we encounter many other particles, which - at is seem - they have no role to play in building of matter. Nothing of them are composed, they are not able to create bound structures, they usually disintegrate immediately after their formation. The metaphorical question arises "who ordered them?" - what is the meaning and role in the functioning of our world? (This question was first raised by I.I.Rabi in connection with the discovery of the muon). The answer to this question is trying to find a unitary field theories and particle physics in co-production with astrophysics and cosmology.
  Unitary field theories attempt to find laws and mechanisms that allow or imply the existence of these particles - as a quantum of excited fields or geometric structures (§B.6 "Unification of fundamental interactions. Supergravity. Superstrings."). Astrophysics and cosmology show, that all these particles were probably once in the earliest stages in the universe, they already played their role in the "cooking" of matter and then disappeared (see eg §5.5 "Microphysics and cosmology. Inflationary universe." of the mentioned books); without them the universe would not be as it is, perhaps there would be no mass at all..?.. Some of these particles perhaps still form a mysterious "dark matter" in space (see eg § 5.6 "The Future of the Universe. The Arrow of Time. Dart matter, Dark energy."). And we are now trying to re-create and explore these particles in order to understand the early universe and be able to answer the questions more surely, how matter was formed and what is its internal properties ...

Indistinguishability of elementary particles
Bodies and particles in classical mechanics do not lose their "individuality" during their motion, even if they are the same particles with the same physical properties (from a macroscopic point of view). Such particles forming a given physical system can be "marked" or "numbered" at a certain initial time and then, while monitoring their movement, we can, at least in principle, identify each of the particles in the system at any time - the particles are distinguishable here.
  In the analysis of motion and behavior of particles in quantum mechanics the situation is completely different in this respect. Due to corpuscular-wave dualism and the uncertainty principle, particles, such as electrons, have no trajectories in the sense of classical kinematics. If we determine the position of a particle at a given moment, its momentum becomes indeterminate; then in the following moments it is not possible to determine any specific values of the particle coordinates. Therefore, if we try to locate electrons at a certain moment and imaginarily "number" them, then at another point in time when locating an electron at a certain point in space, we can no longer determine which of the considered electrons got to this point. In quantum mechanics, there is no possibility to continuously monitor the motion of individual particles and thus distinguish them. Microparticles are manifested only by their interactions with other particles. Thus, in quantum mechanics, the same particles completely lose their individuality - their physical properties are identical, they are indistinguishable from each other.
Spin, symetry of wave function and statistical behavior of particles 
The quantum-mechanical behavior of sets consisting of the same type of particles is based on this principle of indistinguishability of particles. Since the particles are the same and indistinguishable, the physical states of the system obtained by exchange (swapping, transposition) the two particles "1" and "2" must be equivalent; from a quantum point of view, the probability density ú yú ² of this system must remain the same when the particles are interchanged: úy ("1", "2" y ("2", "1") ú ² , ie either y ("1", "2") = y ("2", "1"), or y ("1", "2") = - y ("2", "1") - the wave function of the system can only change by a sign. Thus, there are two possibilities: 1. The wave function is either symmetrical and does not change with any permutation of particles; 2. Or, the wave function of the system is antisymmetric - it changes sign when each pair of particles is transposed. Which of these options is realized depends on the type of particles - it is related to their spin (§1.1, passage "Spin"). Below, according to this criterion, we divide particles into bosons with a symmetric wave function (integer spin) and fermions with an antisymmetric wave function (half-number spin) - passage "Fermions-Bosons". By analyzing the wave functions of a system of the same particles, it can be shown that in a set of identical fermions, two particles (or more particles) cannot be in the same quantum state - the so-called Pauli exclusion principle applies. While in a set of bosons there may be an unlimited number of particles in the same quantum state.
  The analysis of the relationship between the spin of particles and their statistical behavior in a set of particles decays into three sub-problems :
1. Relationship between the spin and symetry of the wave function
Spin is an intrinsic angular momentum of particles, analogous to the rotational angular momentum of a particle during its rotation around its axis (but it cannot be explained quantitatively in this way!), rather related to symmetries with respect to spatial rotation (within quantum mechanics, spin is described in §1.1., passage "Spin"). From the point of view of quantum field theory (secondary quantization), a spin field is interpreted as a measure of symmetry in the plane wave of the field: a field has spin s (spin number s), if its plane wave is invariant to rotation by an angle of 2p/s around the propagation direction. Thus, the spin of a particle indicates the rotational symmetry of the wave function relative to the rotation in space. For particles with integer spin, most often s=1, the wave functions are invariant to rotation by an angle of 360^o; the wave functions are symmetric with respect to the transposition. ..., the particles behave like bosons. For particles with a half-numbered spin 1/2, the wave functions are antisymmetric. ....... ......, the particles behave like fermions.
Note: This is just a brief heuristic outline of the relationship between the particle's spin and the symmetry of the wave function. In a more detailed derivation, analysis using relativistic quantum field theory is used.
2. Relationship between symetry of wave function and occupancy of quantum states
Consider two identical particles a, b with the wave functions y(....... y(........ ......; the wave function for a system composed of these two particles will then be Y(....... = ..... If the functions y(....... y(..... are antisymmetric with respect to the transposition of particles y(....... = - y(...., the resulting wave function Y(...... a pair of particles located in the same quantum state will be equal to zero - the probability is zero here. Two particles with an antisymmetric wave function cannot be in the same quantum state, applies to them so-called Pauli's exclusion principle. For particles with a symmetric wave function with respect to transposition, all combinations of state functions will have positive signs, so the resulting wave function y will also be positive and non-zero - any number of particles of this kind can be in the same quantum state.
3. Own statistic behavior of particle sets
By statistical behavior (abbreviated as "statistics") of particles we mean the average distribution of their states - according to velocities, kinetic energies - in a large set of these particles. This analysis is dealt with by a special field of statistical physics, in practice mostly in conjunction with thermodynamics. In the simplest case of a sufficiently large set of non-interacting particles in thermodynamic equilibrium, behaving according to the laws of classical (non-quantum) physics, analysis by methods of statistical mechanics shows that the average (expected) number of particles <N (E)> with energy E is given by Maxwell- Boltzmann distribution <N (E)> = 1 / e^-E/kB^.T, where T is the absolute temperature [^oK] and k_B is the Boltzmann constant (giving the conversion coefficient between the average kinetic energy of the particles in the gas and the thermodynamic temperature of the gas k_B = 1.380649×10^-23 J/^oK).
  In the case of the above-mentioned quantum properties (point 2.), the distribution function N(E) will depend on the occupation rules of quantum states. In quantum statistical physics, the distribution function according to the occupancy possibilities of quantum states of particles is specified to the form :
           < N(E) >  =  1 / (e^-E/kB.T ± 1)   ,
where in the denominator the positive sign "+" applies to fermions - Fermi-Dirac statistical distribution and the negative sign "-" to bosons - Bose-Einstein distribution.
Note: In the thermodynamics of gases formed by atoms or molecules with a certain chemical composition, the denominator of distribution functions also has the so-called chemical potential m : e^-(E-m)/kB^.T, expressing energetic changes in chemical reactions that may occur during atomic collisions. For elementary particles, an analogy of this situation could arise if the particles had sufficient kinetic energy to interact with transmutations and the formation of new particles.
  In the Fermi-Dirac distribution of particles that satisfy Pauli's exclusion principle, there are also situations where the same energy corresponds to some different states - the so-called degeneration of energy levels occurs. In the numerator of the distribution law, instead of "1", there is a degeneration factor g, which indicates the number of different states corresponding to a certain same energy level: <N(E)> = g / (e^-E/kB^.T + 1). Degeneration of energy levels occurs mainly due to some kind of symmetry in the system, such as motion in a centrally symmetric field.
  An important property of the Fermi-Dirac distribution of particles in a set of fermions is the possibility of the formation of so-called degenerated matter or degenerated gas. In a set of non-interacting fermions - the ideal Fermi gas - particles enclosed in a finite volume can acquire only discrete energy values (quantum states). Pauli's exclusion principle prevents identical fermions from occupying the same quantum states. At high densities of matter, all energy levels of fermions are occupied up to a certain maximum energy, which corresponds to a certain maximum momentum; this condition is called degeneration, it is a degenerate fermion gas. Each additional fermion in a given volume must occupy a new higher energy level and thus have a higher momentum. The pressure here therefore increases significantly faster than corresponds to the equation of state of an ideal gas.
  The statistical behavior of electrons, protons and neutrons according to the Fermi-Dirac distribution, with degeneration, is of great importance in stellar astrophysics, where it co-determines the equilibrium state of stars against gravity, disturbance of this equilibrium and collapse of stars on white dwarf and neutron star (§4.1 "The role of gravity in the formation and evolution of stars" and §4.2 "The final stages of stellar evolution. Gravitational collapse. The formation of a black hole." in the monography "Gravity, black holes and space-time physics").
  The outlined analysis of the relationships between spin, symmetry of wave functions and statistical behavior of sets of particles, can be summarized in the resulting theorem :

Physical parameters of particles; quantum numbers
The properties of elementary particles are characterized by suitable physical parameters, some of which are also known from classical physics, others are purely quantum and have no classical analogy. These parameters of elementary particles, which are mostly quantized, ie take on discrete values, are called quantum numbers.
¨ Rest mass, lifetime
These are the basic unquantized characteristics of particles. Rest mass of particles is rarely expressed in grams, but most often in energy units electron volts eV, keV, MeV *) - in connection with Einstein's relation E = m.c² equivalence of mass and energy. It is sometimes given in multiples of the electron mass. Life time, resp. the half-life of particles is expressed in seconds and their decimal fractions (10 ^-xx sec.); for stable particles it is considered to be ¥ .
*) More precisely, the energy expression of mass is in MeV/c², but c² is often omitted.
¨ Size, dimensions and shape of elementary particles? - problematic!
In everyday life and in the physics of macroscopic phenomena, the spatial size of bodies, their shape and individual dimensions are of great importance. In the microworld, however, this is problematic. In the case of particles of the microworld, due to the wave nature and quantum relations of uncertainty, the concept of spatial "size" loses its meaning - it cannot be defined and measured. These particles are not some tiny "material bodies" with a solid surface, as we know from our usual experience from the macroworld, but rather spatially distributed "densities of fields" of a wave nature. They have no specific boundaries. Only some of them can be defined some "effective size" of particles in interactions - using the range of forces and the so-called effective cross section (see below "Interactions of elementary particles", section "Effective cross section of particle interactions"). From scattering experiments in particle bombardment - in determining how "close to each other" particles penetrated. However, such an "effective size" may be different for the same particle in various types of interactions. These problems with particle size are circumvented by a physical agreement that elementary microworld particles will in principle be considered to be zero-sized points, while effective cross-sections being considered for interactions...
Physical efforts to determine the size of elementary particles 
In the early days of the study of the microworld, atomic and nuclear physicists worked hard to determine the size ("radius") of newly discovered particles - the electron and the proton. For an electron with mass m _e and elementary charge e, three very different values were reached in the analysis from different points of view :
- The classical (non-quantum) or Thomson radius of the electron is based on the model that the electron is a sphere on whose surface the electric charge of value e is uniformly distributed. The radius of electron r _e is taken to be the radius of the sphere such that the electrostatic potential energy of this charge corresponds to the rest mass of the electron m_e according to the relativistic relation of the equivalence of mass and energy E = m_e. c². Comes out: r_e = e²/4pe_o m_e c² = 2.818x10^-13 cm. It's such a radius that all resting electron mass m_e had an electrical origin (was formed by electrostatic potential energy; this approach is also analyzed in §1.6, passage "Nonlinear Electrodynamics" monograph "The gravity, black holes and spacetime physics").
- Bohr radius of the electron comes from the fact that the majority of electrons bound in atoms, so the size of the electron would be natural to deduce from the dimensions of the atom. According to Bohr's quantum model (§1.1 , part "Bohr model of the atom") has the lowest (basic, unexcited) orbit of an electron in a hydrogen atom radius r₁ =4pe_o h/m _e e² = 0.529 x10 ^-8 cm. This value is considered here as the radius of the electron r_e .
- The Compton wavelength of an electron is the smallest distance to which an electron can be constrained ("compressed") according to quantum uncertainty relations: l_c ~ h / m_e c » 10^-9 cm. If we try to compress the electron to a smaller size, then according to the uncertainty principle, its momentum becomes so large that its kinetic energy exceeds the rest energy of the electron m_e c². In this case, there will be enough energy to form a new electron-positron pair. Compton length is therefore the smallest distance, on which two electrons can penetrate without the formation of new particles ...
  From the current point of view, these values are only of model and historical significance and are not considered "real" dimensions of the electron. For electrons, in the end, no plausible value of "size" could be determined, the higher the kinetic energy, the deeper they approach each other during the interaction - as if they were points with zero size (<10^-16 cm)..?.. Similar to that expected for other leptons *). From the point of view of corpuscular-wave dualism, the effective size of an electron, its "wavelength", would depend on its velocity (§1.1, passage "Particle-wave dualism").
*) At neutrinos, which show only a weak interaction, the effective "size" is assumed to be significantly lower than for electrons, about 10^-16 cm. No direct measurements are feasible here.
  For protons and neutrons, their effective "size" for strong interactions was set at about 1.6x10^-13 cm, according to the measured range of these nuclear forces (see §1.1, passage "Strong nuclear interaction"), as a "residual" manifestation of a strong interaction between quarks inside protons and neutrons. Similarly for other hadrons (pions, kaons, hyperons). For electromagnetic interactionthe "size" of a proton is measured by the scattering of accelerated electrons. Another method is hydrogen spectrometry: accurate measurement of energy levels (difference in energies between ²S_1/2 and ²S_1/2 orbitals - hyperfine structure caused by Lamb shift due to quantum fluctuations of virtual electron-positron pairs in the electric field of a proton); this method resulted in a value of 0.88x10^-13 cm. These measurements were modified in a new experiment where hydrogen atoms were exposed to a beam of low-energy muons, whereas some of the muons were captured, replacing electrons in the hydrogen atom. Such a muon due to its higher weight (it is about 200 times heavier than an electron) orbits significantly closer to a proton, so differences in energy levels are "more sensitive" to the structure of the proton. Here a slightly lower value of the proton radius of 0.84x10^-13 cm was reached. Protons, like other hadrons, are not "elementary" particles, but are composed of quarks, so the so-called quantum chromodynamics (see "Imprisoned quarks" below) has something to say about their structure and "size", at the fundamental level then unitary field theory ("Unification of fundamental interactions. Supergravity. Superstrings." in the monograph "Gravity, black holes and space-time physics").
  For photons, as quanta of electromagnetic waves, their effective "magnitude" depends on the wavelength of the radiation. Photons of gamma radiation are effective only picometres dimensions, visible light photons hundreds of nanometers, in the case of radio waves we could absurdly imagine the many-meter dimensions of "photons" - here, however, photons can not prove at all ...
¨ Electric charge
An extremely important parameter of particles is their electric charge, which is quantized and therefore, instead of in coulombs, is expressed in multiples of the magnitude of the elementary charge of the electron |e| with the sign *) - the electron then has a charge -1, proton +1, hyperon W charge -2, neutron and other uncharged particles of course 0. Antiparticles to charged particles have charges of opposite sign (and the same absolute size). In all known interactions, the law of conservation of electric charge is strictly fulfilled: the sum of the charges of the particles before the interaction is the same as the sum of the charges of the particles flying out after the interaction.
*) Below we will also encouter the charge ¹/₃ e or ²/₃ e in quarks.
¨ Spin, magnetic moment
Another important quantum characteristic of particles is their spin or spin number s, expressing the own angular momentum of a particle in multiples of the Planck constant h. Except to the zero spin s=0 (occurring in the mesons p and K), the smallest possible spin is the value s = 1/2 (electrons, protons, neutrons, neutrinos, muons have such a spin). Spin s = 1 have photons, s = 3/2 heavy hyperons W, spin s = 2 at gravitons. Closely related to the spin of corpuscular particles is their magnetic moment, given in multiples of the elementary Bohr magneton e.h/4p m_e , resp. nuclear magneton e.h/4p m_p (discussed in more detail in §1.1, passage "Quantum momentum, spin, magnetic moment"). The spin number of the particles further determines the quantum-mechanical statistical behavior in the sets of particles - see "Bosons - Fermions" below.
Note: Spin - rotation ?
According to classical mechanics, the spin of particles is usually interpreted as their rotational momentum. However, this property of elementary particles has a specific quantum nature and cannot be satisfactorily explained by classical mechanical concepts (spin cannot be quantitatively explained, for example, by the rotation of a particle around its own axis!) .
¨ Parity
is the quantum number, characterizing the behavior of the wave function of quantum mechanical object - nuclei or elementary particles - relative to a spatial mirror reflection, i.e. the coordinate transformation x ® -x, y ® -y, z ® -z, t ® t. If the while doing so the wave function describing the state of the particle does not change, the parity is positive: P = 1, or "+". If the wave function of the system changes sign during this transformation, the parity is negative: P = -1, or "-". It can be shown that the parity of a system with an orbital momentum l is (-1) ^l. Analysis of elementary particle interactions shows that the parity of the proton and neutron is positive, while the parity of photons and mesons p^{+, -, o} is negative. The parity is sometimes given as the index at the top right of the quantum momentum J of the system, such as the nucleus, J^P: either J⁺ or J^-. For elementary particles then as an index for the spin number: s^P - eg 0^-, (1/2)⁺ and so on.
  Overall, parity P is not a very important quantum number. However, parity has its theoretical significance in connection with symmetry properties and conservation laws in particle interactions - see below the section "CPT symmetry of interactions" in the section "Four types of interactions". Parity is maintained at a strong and electromagnetic interactions, but with weak interactions are not conserved (discussion and experimental verification see below "CPT symmetry interactions"; the hypothesis of the so-called mirror matter, discussed below in the section "Hypothetical model particles", passage "Shadow Mirror Matter - Cathoptrons?" is based on the failure to preserve parity).
¨ Lepton and baryon number
In order to classify elementary particles, particles are assigned a lepton number L, which for leptons is L = ± 1 (depending on whether it is a particle or an antiparticle), for other particles L = 0, and the baryon number B, which for baryons is B = ± 1 (again "+" for particles, "-" for antiparticles) and for particles other than baryons is B = 0. The lepton and baryon number is preserved for practically all types of interactions *) - the sum of leptons and baryons (respecting the signs) before and after the interaction is the same.
*) The only exception is with the gravitational interaction involving black holes: when particles are absorbed below the horizon of a black hole, all their individual characteristics are lost except mass, electric charge and orbital momentum ("black hole has no hair"); the particle seems to "dissolve" in the total gravitational field of the black hole - see §4.5 "Theorem "black hole has no hair"", in "Gravity, black holes and spacetime physics". Lepton and baryon number is not preserved even during the quantum evaporation of black holes - §4.7 "Quantum radiation and the thermodynamics of black holes" in the same monograph.
¨ Another quantum numbers isospin, strangeness, and hypercharge will be introduced below in connection with mesons K, hyperons, and unitary symmetries of elementary particles - see the passage "Unitary symmetries and multiplets of particles".

Intermediate and virtual particles
According to the ideas of quantum field theory, the mutual force action of two particles takes place in such a way that these particles exchange (transmit and receive) so-called intermediate particles, which are quantums of the respective field. Each particle subject to interaction is surrounded by a "cloud" of respective intermediate particles, which remain virtual, until there is an act of interaction.
  To explain the mechanisms of interactions and mutual transformations of elementary particles, not only observed "real" particles entering into interactions or radiated as a result of the interaction are used, but often also certain "auxiliary" particles mediating certain stages of interaction, that are not directly observed. Such virtual particles *) "exist" only for a very short time, which is shorter than the time required to measure their energy according to uncertainty relations. Commonly known and proven particles, such as photons, can serve as virtual particles, but often hitherto unknown and unproven particles are often used - model and hypothetical particles (they are mentioned below). Virtual particles cannot be directly detected, but can manifest themselves in real measurable phenomena because they interact with real particles and fields; such latent interactions can cause, for example, spontaneous emission of real particles or anomalies depending on the effective cross sections of the interactions on energy. Interactions using intermediate particles are represented by so-called Feynman diagrams.
*) Virtual = imaginary, apparent, unreal, potential, physically absent. It originally comes from lat. virtus = man, masculinity, virtue, but has undergone a significant etymological change.

The "temperature" of the particles ?
In the science of heat - kinetic theory of heat, thermals, thermodynamics - temperature is closely related to the velocity or energy of particles. The temperature of a normal substance environment is given by the speed of oscillating or chaotic movement of particles of which a substance is composed - atoms and molecules. Root-mean-square speed v_k² of the motion of particles is related to the thermodynamic temperature T [^oK] the relation
            ¹/₂ m_o v_k²  =  ³/₂ k_B.T   ,
where k_B = 1.38.10^-23 J . K^-1 is Boltzmann's constant and m_o is the rest mass of particules of matter (in the simplest case of an ideal monoatomic gas). Thus the temperature is proportional to the mean kinetic energy of the particles E_k = (1/2) . m_o v_k ² .
  This kinetic concept of temperature is generalized from the material environment to the environment composed of particles other than molecules and atoms - to the physical sets of various microparticles and their bound combinations *). The kinetic energy of the particles E_k is then measured here in electron-volts [eV] and the Boltzmann constant has the value k_B= 8.617.10^-5 eV.K^-1 (the carrier of kinetic energy in ionized matter and sets of particles are mostly electrons). In principle, therefore, we can equivalently measure the energy state of particle sets either by the mean kinetic energy E_k of the particles in [electron volts], or by the thermodynamic temperature T in [degrees of Kelvin].
*) It would certainly be misleading to say that "the particle has a temperature of xxx °K"; the particles have no "temperature" quantity. More precise is the formulation "a given set of particles has a thermodynamic temperature of xxx °K". The temperature in such a collection of particles has obviously not be measured by conventional thermometer inserted into the system (with the attainment of thermal equilibrium), but on the basis of the radiation emission or directly by measuring the energy particles by means of detectors.
  Room temperature T = cca 300 ^oK corresponds to the kinetic energy of the electrons E_k = about 26 millielectronvolts. The high-temperature plasma required for efficient thermonuclear fusion of deuterium and tritium must be heated to about 150 million degrees (regardless of Kelvin or Celsius), which represents a kinetic energy of particles of about 12 keV (see §1.3, section "Atomic fusion"). nuclei "). And in quark-gluon plasma a huge thermodynamic temperature higher than 10¹² degrees is reached for a short moment (see the passage "Quark-gluon plasma -"5th state of matter" " below), the kinetic energy of the particles reaches the order of TeV.

Classification of elementary particles
Elementary particles are sorted and divided into groups according to their significant properties, expressed by physical parameters and quantum numbers. The most fundamental characteristic of each subject *), and therefore also the elementary particle, is its weight - more precisely the resting mass m_o.
  According to the special theory of relativity, the actual mass m (inertial mass, characterizing according to 2. Newton's law F = m.a the resistance of the body to acceleration) depends on the speed of motion of the body v : m = m_o/Ö(1-v²/c²), where m_o is the rest mass, determined in the inertial frame of reference in which the body is at rest. The resulting mass m is greater the faster the particle moves; for v ® c grows above all limits. Therefore, no particle whose rest mass is non-zero can move at the speed of light (or superlight speed). According to a special theory of relativity, the total energy of a particle (the sum of rest and kinetic energy) is equal to E = (m_o/Ö(1-v²/c²)).c² = m.c² - Einstein's equation expressing the equivalence of mass and energy.
*) Another basic characteristic of objects in the macroworld - spatial size (dimensions, volume), has no significance for elementary particles ! Due to corpuscular-wave dualism and the uncertainty principle, no certain size can be assigned to particles in the microworld (discussed in more detail above in the section "Size, dimensions and shape of elementary particles? - problematic!"). In the model ideas, however, we can consider some "effective" particle sizes, given by the interaction properties of these particles (eg the proton has a dimension of » 1.6.10^-13 cm in terms of strong interaction). On this ideas based the so-called effective cross section of particle interaction (see below).
  According to the rest mass, we divide the particles into four groups :

• Particles with zero rest mass
  In atomic and nuclear physics they are mainly quantum of electromagnetic radiation - photons, in subnuclear physics also model particles gluons mediating strong interaction. In the general theory of relativity and quantum gravity, then possibly even a quantum of gravitational waves - gravitons (gravitational waves are proven only indirectly in astronomy, the first direct detection was achieved only recently - see "The first direct detection of a gravitational wave by LIGO"; there is no hope for experimental detection of gravitons in the foreseeable future). From the point of view of quantum field theory, particles with zero rest mass mediate - as exchangeable intermediate particles - long (unlimited) range interactions (electromagnetic photons, gravitons of gravitational interaction, gluons of strong interaction between quarks).
  Note: It may seem paradoxical to speak of "rest mass" for particles that, in principle, can never be at rest. However, in the special theory of relativity, the rest mass of a particle is defined as the invariant size (4-dimensional length, independent of the frame of reference) of a 4-vector momentum of a particle - see relation (1.101´) in §1.6 "Four- dimensional spacetime and special theory of relativity" book " The gravity, black holes and the physics of space-time". Photons have zero rest mass, but their inertial (relativistic) mass depends on the frequency: m = h.n/c². When braked, the photon gives up all its energy and disappears, unlike a particle with a non-zero rest mass, which gives off only its kinetic energy and after braking it still exists with its rest mass.
  
• Leptons - light particles with low rest mass (Greek leptos = thin, fine, weak, thin, thin *)
  These include mainly electrons e^- and positrons e⁺ with rest mass m_e = 9.1.10^-28 g = 511 keV ( in nuclear physics, it is customary to express mass in connection with the relation E = m.c² in energy units electron volts). Then there are neutrinos (electron n_e , muon n_m , tauon n_t) and antineutrinos with a resting weight of about 2 eV.
    Today, the muon m^- (referred to as the "heavy electron"), which has a mass of »206 m_e and even the tauon t^- with a mass of »3484 m_e , referred to as the "superheavy electron", also belongs to the category of leptons; and, of course, their charge-coupled antiparticles.
  *) Original designation leptons, as light particles, is now losing its original literal meaning, due to the inclusion of muons and tauons. The role of leptons as the basic building blocks of matter, along with quarks, will be outlined below in the section "Standard Model of Elementary Particles". According to this standard model, leptons (together with their antiparticles) form the so-called generations. The first generation consists of an electron with an electron neutrino. The second generation includes the muon with its muon neutrino, the 3rd generation tauon with the tauon neutrino. It is assumed that the next generation, made up of even heavier electron analogues, does not exist. Analogous 3 generations are distinguished in quarks.
    According to current knowledge, leptons do not have an internal structure, the standard model considers them as point particles (another approach is considered in superstring theory). All leptons are subject to a weak interaction, charged leptons also to electromagnetic interactions.
    
• Baryons - heavy particles (Greek. Baryos = heavy)
  These include primarily proton p⁺ with a mass m_p = 1836 m_e = 938 MeV/c² and the neutron n⁰ having slightly larger mass m_n = 1838 m_e (and of course their antiparticle). Protons and neutrons are collectively referred to as nucleons - the building blocks of the atomic nucleus. The baryons then include even heavier particles - hyperons. These are formed by collisions of high-energy particles and disintegrate very quickly - their lifetime is of the order of »10^-10 seconds. Known hyperons L^o (mass 2183 m_e), S^{+, - , o} (mass » 2330 m_e), X^{o, -} (mass »2580 m_e), W^- (mass »3273 m_e).
    The only stable baryons are protons (so far we omit the hypothesis of proton decay) , in suitable connection with protons in atomic nuclei also neutrons. Others are unstable, decaying into nucleons and pions. Baryons are "equipped" with all kinds of interactions - strong, weak, electromagnetic (if electrically charged) - and of course gravitational, which we do not consider here. In terms of interaction, they belong to hadrons.
    
• Mesons - medium-heavy particles (Greek mesos = medium, between something - their mass lies between an electron and a proton)
  The lightest of them is a meson m^-,+, muon *) with mass m_m = 206 m_e, then a positive meson p⁺, pion, and a negative p^- weighing 273 m_e, neutral pion p^o weighing 264 m_e. Finally, they are K-mesons K^{+, -} (mass 966 m_e) and K^o (weight 974 m_e).
  *) Note: The muons m are here namely of weight included between mesons, but by the characteristics of their interactions and structures are now inserted between leptons! They are formed in processes involving weak interactions, are unstable and decay into electrons and neutrinos (see below).
    Mesons p and K are formed in processes involving a strong interaction and are unstable - they decay by weak interaction into muons and neutrinos (K-mesons also by strong interaction into pions); disintegration modes and lifetimes are listed below. Like baryons, the mesons p and K are hadrons, interacting generally with all 4 types of interactions.

The origin of particle rest masses
The above-mentioned diametrically different rest masses of different types of particles used to be a purely empirical matter in the past. Now the standard particle model tries to explain them by basically two mechanisms :
1. For basic, elementary structureless particles - photons, leptons, neutrinos, quarks, intermediate bosons - their mass depends on the values of the coupling constants of the interaction of the respective fields with the ubiquitous Higgs-Kibble scalar field (whose quanta are Higgs bosons). For fermions, this interaction is also called the Yukawa coupling (it is modeled by the Yukawa potential with an exponential dependence).We can imagine it in a simplified way, that a particle "draggs" with it a certain part of the energy-momentum of the Higgs field (according to the size of the coupling constant), which effectively makes it appear more massive (according to Newton's 2nd law), puts up a greater resistance to acceleration, and carries a higher kinetic energy at the same speed.
  Photons and gluons do not interact with the Higgs field at all, so they have zero rest mass. "Ordinary" electrons interact with the Higgs field only relatively weakly (coupling constant g ~ 3.10^-6), they have a rest mass of 511keV. Their related leptons, muons ("heavy electrons") interact more strongly (coupling constant ~ 6.10^-4) and have a rest mass 200 times greater, 105.6 MeV. And tauons ("super-heavy electrons") interact with the Higgs field very strongly (coupling constant ~ 1.10^-2) and therefore have a rest mass of 1777 MeV, more than 3000 times greater than electrons! Quarks "d" with a coupling constant ~ 2.6.10^-5 have a mass of 4.6 MeV, "s" quarks with a coupling constant ~ 5.10^-4 have a mass of 94.6 MeV, "b" quarks with a coupling constant ~ 5.10^-2 have a mass of 4.3 GeV. The bosons W^+,-, Z⁰, causing a weak interaction, have a particularly strong interaction with the Higgs field (coupling constant g ~ 1), which leads to their high masses of 80-90 GeV and a very short range of the weak interaction.
Note: Even this approach remains basically phenomenological: the empirically measured masses of M particles are only transformed into values of the coupling constant g with the Higgs field according to the simple formula M = g .V_v/2^1/2, where V_v is the "expected" value of the Higgs vacuum potential V_v = (2^1/2. G_F)^-1/2 ~ 246 GeV (G_F is the reduced Fermi constant of the weak interaction). The standard model cannot yet predict specific values of masses or binding constants.
  This mechanism is often associated with the rather unintuitive concept of "spontaneous symmetry breaking" - it is discussed in more detail in §B.6 "Unification of fundamental interactions. Supergravity. Superstrings.", passage "Symmetry in physics and their breaking" of the book "Black hole gravity and the physics of spacetime".
2. For "composite" particles, hadrons - protons, neutrons, hyperons, pions, kaons, ... - the rest mass of their structural components - quarks - is only a small part of the total mass, around 1%. Most of a hadron's mass comes from the kinetic energy of the internal motion of its quark components. E.g. proton has a mass of 938MeV, while the rest mass of the "u" quark is 2MeV and the "d" quark is 5MeV.

The spectrum of rest masses of particles - is it limited or infinite ?
The rest masses of various types of particles are very different, their values form a wide "spectrum". From photons with zero or neutrinos with a slight rest mass, through light electrons (about 0.5 MeV), mesons (around 140-500 MeV), to heavy baryons with rest masses of 1-1.7 GeV. The heaviest known particles are bosons W^+,-, Z^o of weak interactions weighing about 80-90 GeV and Higgs bosons with rest mass 120 GeV approx. The question arises as to whether the mass spectrum is already ending here, or are there even heavier particles? In the 1960s and 1970s, the so-called Hagedorn hypothesis was discussed of existence an infinite number of particles of ever higher masses that could gradually appear as ever more powerful accelerators were constructed. Current particle physics is rather skeptical about this, it could possibly only be excited states of quark-gluon combinations..?.. - only future experiments can decide.

According to the way of interaction between elementary particles, a special group is singled out :

• Hadrons - particles showing a strong nuclear interaction (Greek hadros = strong, heavy, thick, robust)
  These include protons, neutrons, mesons p and K, hyperons. The origin of the strong (nuclear) interaction stems from model subnuclear particles of quarks and gluons (see below). Hadrons are therefore particles with a quark structure - baryons are composed of three quarks, mesons of two. Hadrons are therefore not "elementary" in the true sense of the word, but their direct decomposition into quarks is quite problematic - see the section "Quark structure of hadrons" below.
  Note : The name "hadron" was first introduced L.B.Okun of the Physics Institute in Moscow in 1962.

According to lifetime, we can divide elementary particles into :

• Stable particles with an infinitely long lifetime.
  These include the electron e^-, the positron e⁺, the photon, the proton p⁺ *), the neutrino n (apart from the oscillation phenomenon of neutrinos, which cannot be considered as decay).
  *) According to some so-called grandunification theories, the proton would not have to be a completely stable particle, but should decay with a half-life T_1/2 > »10³³ years. This idea is largely speculative, because during the existence of the universe, perhaps not a single proton has decayed..?. Only in the case of an open universe with infinite time evolution, the decay of protons could perhaps in time scales »10¹⁰⁰ years to contribute to the so-called heat death of the universe (see §5.6 "The future of the universe. The arrow of time." in "Gravity, Black Holes and space-time physics") ....
    
• Long-lived particles .
  This includes the neutron n⁰, which, if free (outside the atomic nucleus), decays by the b^- - transformation: n^o ® p⁺ + e^- + n_e´ with a half-life T_1/2 @ 13 minutes. With some reservations, we can also include the muon m^- with a lifetime of 2.10^-6 sec (decays into an electron and a neutrino: m^- ® e^- + n_e´ + n_m).
    
• Particles with a short lifetime .
  These are all other real particles, which are formed for a short time by the interactions of high-energy particles and then immediately disintegrate, their lifetime is in the range of about 10^-8 -10^-20 sec. We can name some: mesons p⁺ and p^- with lifetime 2.6.10^-8 sec, p^o (»10^-16 sec), K⁺ (1.2.10^-8 sec), K⁰ (»10^-10 sec), hyperons L^o (2.5.10^-10 sec), S⁺ (8.10^-11 sec), S^- (1.5.10^-10 sec), S^o (»10^-20 sec), group of hyperons X^{o, -} and W^- with lifetimes of the order of 10^-10 sec.
    
• Ultra-short-lived particles - so-called resonances
  Form during some interactions of high-energy particles (such as p^+,- + p⁺ ® p^+,- + p⁺, or the interaction of a proton with an antiproton to form several p- mesons) and immediately decay, their lifetime is about 10^-23 to 10^-20 seconds. They are actually manifested only by a significant resonant maximum in the energy dependence of the effective cross-section of the given interaction, or by densities and peaks on Dalitz diagram of the energies of secondary particles (see the section "Analysis of the dynamics of particle interactions" below). We distinguish baryon resonances and meson resonances (such as meson r or some types of mesons K*). Resonances are often not even considered special particles, they are called quasiparticles. Rather, they are only temporarily excited states of two or more baryons or mesons that decay as soon as they fly beyond the boundaries of the region of strong nuclear interaction in which they originated. Due to the extremely short lifespan, they probably have no significance for the structure and properties of matter. However, their study is important for better penetration into the subnuclear structure of hadrons, their quark structure and understanding the properties of strong interactions within quantum chromodynamics (QCD).

Fermions - Bosons
In the passage "Indistinguishability of particles" - "Spin, symmetry of the wave function and statistical behavior of particles" we have shown how the spin of particles determines the statistical behavior of sets of particles.
Thus, according to spin, and consequently also according to quantum-mechanical statistical behavior in sets of particles, elementary particles are divided into two large groups :

• Fermions - particles with a "half- numbered" spin s = ± (1/2) h, ± ( 3/2) h, ....
  These are mainly all building blocks of matter: proton, neutron, electron. On the leptons, they are also muons and all kinds of neutrinos. From other baryons then also hyperons. All the listed fermions have spin 1/2, except for the hyperon W which has spin 3/2.
    In quantum mechanics, it is shown that sets of particles with a half-number spin follow the so-called Fermi-Dirac statistics, which is characterized by the fact that two or more particles cannot be in the same quantum state (Pauli's exclusion principle, they are "intolerant" particles) - in a given quantum state it can be only one fermion. Therefore, the individual electrons in the atomic shell acquire and occupy different quantum states, and the resulting electronic configurations of the atomic shell levels are the cause of all the diversity of chemical compounding of elements and their other properties *). And in a similar way, in the atomic nucleus, nucleons occupy different energy levels in a field of strong interactions. It can be said that we owe the diversity of nature to the fermions, which are able to form diverse structures..!..
  *) If all electrons could occupy the same (lowest) quantum state, the atoms of all elements would have the same properties and our world would be very drab. Fortunately, however, due to their "intolerance", electrons gradually occupy different levels in the atomic shell, and different elements thus have different properties and coupling capabilities, given the number of electrons per outer (valence) layer.
  Fermion gas 
  Pauli's exclusion principle for fermions also has important implications for the behavior of a set of free fermions, the so-called "fermion gas". When a such gas is strongly compressed, the fermions occupy all the lower possible energy states, so that such a gas is very strongly "prevented" from further compression - the higher states are associated with high momentum and thus high pressure. And every other fermion that gets inside such a compressed mass, it cannot change its state in collisions with other fermions, because all the surrounding quantum states are already occupied and no other fermion can get there; such a fermion then moves as free, the environment cannot change its momentum. A substance in such state with all occupied quantum states is called degenerate fermion gas and plays a major role in the final stages of stellar evolution - white dwarf and neutron stars (discussed in more detail in §4.2 "Final Stages of Stellar Evolution. Gravitational Collapse" in monograph "Gravity, Black Holes, and the Space Physics").
    
• Bosons - particles with "integer" spin s = 0, ± 1h, ± 2h, ....
  This mainly includes a quantum of fields, transmitting the forces by which particles act on each other. They are also referred to as intermediate particles mediating individual interactions. Bosons with spin s = 0 are denoted as scalar, with spin s = 1 as vector (the designations "scalar" and "vector" are related to the mathematical formalism of their theoretical description in quantum physics).
  The most important boson is the photon (spin 1), then the p^- mesons (spin 0), bosons W^-, W⁺, Z⁰ (spin 0), gluons (spin 1), hypothetical gravitons (spin 2).
    Bosons do not follow Pauli's exclusionary principle. From a quantum-mechanical point of view, sets of particles with integer spin are governed by the so-called Bose-Einstein statistic, in which (unlike fermions) there can be an unlimited number of particles ("compatible" particles) in each quantum state.
    The number of bosons is not preserved in nature. For example, when we turn on a light bulb, billions of newly formed photons flood the surrounding space. Conversely, many existing photons are absorbed in matter - they disappear upon interactions with atoms and molecules of matter.
    At low system temperatures, each boson tends to occupy the lowest energy state - a so-called boson condensate is formed, which has superfluid and possibly superconducting (in the case of electrically charged particles) properties.

Fermions in the role of bosons; Superconductivity
Under certain circumstances, even a set of fermions, such as electrons, can effectively behave like bosons. If we reduce the temperature of a conductive substance containing free electrons in the form of an "electron gas", at temperatures around 4 °K, electrons combine into pairs - so-called Cooper pairs, in which the half-number spins of electrons in the opposite direction add up to zero spins (singlet pairing), ie integer. The bond between the electrons of a Cooper pair is mediated by their interaction with an oscillating crystal lattice. Such pairs then behave like bosons, which at low temperature tend to occupy the lowest energy state (Pauli's exclusion principle does not forbid them, because it does not apply to bosons). The so-called boson condensate is formedin the basic energy state, in which the paired electrons move through the crystal lattice completely freely without resistance - electrical superconductivity is created.
Superconductivity
Superconductivity is thus a quantum-electric phenomenon in which the material does not put any ohmic resistance to the passage of an electric current and no heat is released in the material. It was discovered in 1911 by the Dutch physicist H.K.Onnes, who liquefied helium on a device of his own design and measured the electrical resistance of metals at low temperatures in further experiments. With decreasing temperature, the resistivity of metals generally decreases (with slower oscillating atoms of the crystal lattice, electrons precipitate less often, they pass more easily). By extrapolating this slight almost linear decrease in resistance with temperature to absolute zero, a certain small residual value of resistance can be expected *).
*) From the classical point of view, the opposite situation could be expected: when stopping their thermal movements, electrons could combine with ions of the crystal lattice, "freeze" and stop moving - the conductor would become an insulator that does not transmit electric current.
  When Onnes measured the temperature dependence of the resistance on a sample of high-purity mercury, he was surprised to find a sudden drop in the mercury resistance to zero (unmeasurably small) at temperatures around 4.2 °K. Superconductivity was then found for lead, tin and many other materials and alloys. Microscopic theory of low-temperature superconductivity developed in 1957 by J.Bardeen, L.Cooper and J.R.Schriffer (BCS theory) - according to it, the bond between electrons and oscillations of the crystal lattice (phonons) can effectively lead to an attractive interaction between pairs of electrons: the electron as it passes through the crystal lattice creates a positive "hole" through which the second electron is attracted. This dynamic bond creates effectively bound Cooper pairs of two electrons, which form a boson condensate with a high degree of correlated electron arrangement. The temperature at which a substance transitions from a normal to a superconducting state is called the critical temperature. Intensive research on superconductivity has revealed a number of materials with this property, which can be divided into two groups :
- Type I superconductors are some metals that achieve superconductivity at low temperatures (critical temperature lower than 30 °K) and lose superconducting properties in stronger magnetic fields (Meissner-Ochsenfeld effect). This superconductivity is explained by BCS theory.
- Type II superconductors are some alloys of metals (especially copper) and non-metallic admixtures (ceramic oxides), which achieve superconductivity even at higher critical temperatures and retain this property even in strong magnetic fields. Particularly interesting materials of this kind are composite compounds of yttrium, barium, copper and oxygen Y₁Ba₂Cu₃O₇, or analogously lanthanum. This is where superconductivity occurs at a critical temperature of 90-100 °K - high - temperature superconductivity, which allows the use of liquid nitrogen for cooling. A complete microscopic theory of high-temperature superconductivity has not yet been developed, but research to date has shown the mechanism of electron binding to Cooper pairs by electron-spin interactions of electrons with excitations of spin (anti) ferromagnetic structures in a crystal lattice that has a "flake" structure.

Left: The superconducting electromagnet consists of a coil wound from a superconducting material, placed in a cryostat with liquid helium (short-circuiting bifilar line is used to turn on and off the current in strong persistent electromagnets - see "Electromagnets in accelerators") . Right: Temperature dependence of the ohmic resistance of the Nb-Ti superconducting material (for 1m of wire Ø 0.3 mm) .

Superconductivity is already finding significant application in many areas of science, technology and medicine. They are mainly superconducting electromagnets: a coil wound into a large number of turns of suitable superconducting material is placed in a Dewar vessel with a cooling medium (so far mostly liquid helium), a strong current (hundreds and thousands of amperes) is excited in it and both ends are connected. The current then flows indefinitely without consuming electricity and excites a strong magnetic field - units up to tens of Tesla - see below "Electromagnets in accelerators", section "Superconducting electromagnets". The condition of the function is, of course, continuous cooling to a temperature lower than critical *). Such superconducting electromagnets are preferably used in a number of areas - nuclear magnetic resonance , circular accelerators , thermonuclear tokamaks.
*) This continuous cooling of the superconducting coil must be carefully monitored ! If, due to evaporation, the coolant level dropped so much that part of the winding warmed above the critical temperature, the superconductivity would suddenly disappear. At this point in the winding, an ohmic resistance would arise, the current through the winding would decrease rapidly, and the magnetic field would disappear. This would result in an electromagnetic induction of a large electromotive force in the winding. The considerable energy stored in the magnetic field would be quickly converted into induced current by the winding, which would be strongly heated by the ohmic resistance, the rest of the cooling medium would be brought to a boiling boil and the winding could be burned!
   The temperature transition from the normal to the superconducting state in the vicinity of the critical temperature Tc is very steep - there is an almost perpendicular transition edge of the superconductivity at this point on the resistance-temperature curve. This phenomenon is used in very sensitive bolometers working on the edge of superconductivityTES (Transition Edge Sensor) - §2.5, section "Microcalorimetric detectors".
   If a really high-temperature superconductivity could be achieved - to develop materials that would be superconducting even at room temperature, it would probably lead to a revolution in low- and high-current electronics. Superconducting wires could conduct electricity without losses, without the need for high voltage transformation. It would be possible to store-accumulate electrical energy in superconducting electromagnets. Superconducting levitation is being used in industrial applications, in which the interaction of induced eddy currents leads to a force which allows the magnet to float above the superconductor or "hang" in the magnetic field. It is mainly considered for magnetic suspension instead of bearings and for use in magnetically levitating high-speed trains.
Superfluidity 
Similarly, atoms composed of fermions can effectively behave like bosons if their total spin is integer (or zero), resp. when there is a singlet or triplet pairing of atoms with a half-digit spin to the resulting integer spin (0 or 1). Here, too, boson condensate can form at low temperatures, the particles of which (or quasi-particles) can move freely in the environment without frictional resistance. On this principle is founded superfluidity some liquefied gases (especially helium) at low temperatures. It is interesting that helium does not have a solid phase, it remains liquid up to practically absolute zero. Below 2.17 °K, it becomes superfluid - flows without internal and surface friction and has a very high thermal conductivity.

In relation to certain "strange" asymmetries in the production and decay of certain particles (see below), a special group is distinguished :

• Strange particles - this includes mesons K and hyperons .
  Within the quark model, the quark "s" (strange) is the bearer of strangeness. The properties of these particles will be discussed in the relevant passages below.

Antiparticles, antimatter, "anti-worlds"
In the world of elementary particles in general for each particle there is its "opposite" or "associated" partner - an antiparticle that has certain physical characteristics identical to a given elementary particle, but some other physical characteristics have the opposite sign or direction. The antiparticle has the same mass, spin number, lifetime and isospin as the particle, but its charge and magnetic moment are opposite (same in size but of opposite sign); the opposite sign is also attributed to the lepton number, the baryon number, and the isospin projection. In the case of neutral particles without electromagnetic properties, they can either be associated either to semselves (photon, p^o, graviton), so actually they do not have antiparticles, or they may have particles and antiparticles different from each other (eg antineutron, antineutrino). In the case of fermions, particles and antiparticles are formed in pairs and also disappear in pairs.
   In our nature (composed of matter), antimatter, resp. antiparticles, occur where there is interactions of the particles with high energies - higher than twice the rest mass of an electron or positron 2 x 511 = 1.022 MeV; then positrons are formed. Positrons are also emitted during beta⁺ -radioactivity (see §1.2, section "Radioactivity b⁺"), where they form during the transmutation of quarks "u"-->"d" inside protons due to weak interactions (Fig.1.2.5 below). Heavier antiparticles (antiprotons, antineutrons, antihyperons) can then be formed only at very high energies, 3 GeV and higher. This is the domain of large accelerators (in very low intensity also cosmic radiation).
Note 1 - Antiworld
In many places in our treatise on nuclear and radiation physics, we use the term "antiworld " - in an allegorical sense. Antiparticles formed during interactions and radioactivity in laboratories are, of course, part of "our" world. "Anti-worlds" are sometimes thought of in astronomy as those (hypothetical) formations or parts of the universe that are composed of antimatter (cf. also the passage "Antiatoms" below). The difficult question is, why do we observe incomparably fewer antiparticles than particles that are "normal and ordinary" to us? It attempts to answer cosmological theories in co-production with particle physics - see the link below in the note to the passage "Antiatoms, Antiworlds".
Note 2 - Antiparticle => Negative energy? Time inversion? - No !
In the early days of the development of quantum physics, antiparticles (such as the positron) were considered to be "negative energy" particles, or particles moving "back in time" (formal coordinate transformations in Dirac's equation allow this). At one time, these concepts played an important heuristic role in the development of particle physics. Now these misguided ideas are abandoned and particles and antiparticles have an "equal" place in the standard model, in applications, as well as in unitarization schemes.
Dirac particles and Majoran particles
According to their antiparticles, elementary particles are sometimes divided into two groups :
¨ Dirac particles have different antiparticles. This includes in particular all electrically charged particles, but also some neutral particles such as neutrons or neutral K-mesons.
¨ Majorana particles have identical particles and antiparticles. In addition to the photon, this includes neutral p- mesons (pion p^o); some hypotheses even consider neutrinos, it has not been decided yet.
  Some significant antiparticles have their own name or designation - antiparticle to electron e^- is called positron e⁺, charge-associated antiparticles are denoted by opposite signs of charges, eg muons m^-, m⁺, analogously pions p^-, p⁺ and other particles. However, a number of antiparticles are simply denoted by the prefix "anti" and the wavy line "~" above the particle symbol *) - eg antiproton p´, antineutron n´.
*) Unfortunately, in the fonts available in the "html" format, characters with a wavy line at the top are not available, so in our texts we denote antiparticles by a comma ( ´ ) at the top right.
Annihilation of antiparticles with particles
When antiparticles interact with their corresponding "counterparts", particles, these pairs can disappear from each other *) - annihilate - to form other (lighter) particles or antiparticles. These are often photons (positrons annihilate with electrons to produce two gamma photons flying out in opposite directions, at an angle of 180°, which is advantageously used in gammagraphic imaging by the positron emission tomography method in nuclear medicine after the application of a positron beta⁺-radionuclide, e.g. ¹⁸F - §4.3, part " Positron Emission Tomography PET"). The laws of conservation of energy and quantum numbers are met (opposite quantum numbers are "reset"). There is a complete conversion of the rest mass (+ kinetic energy) into the rest mass and energies of other particles and fields, while the original particles disappear. Specific annihilation processes will be described below for each particle type.
*) Annihilation of particles does not mean their destruction, nor the transformation of matter into "pure energy" !
There are still some almost mystical ideas about the process of annihilation of antiparticles with particles. They come from a time when these processes were just discovered and seemed so unusual to physicists that they attributed special philosophical significance to them. We now know two interrelated facts :
× During the annihilation of particles, despite the name (Latin nihil = nothing ; annihilation = destruction, disappearance ), they are not destroyed, extinct or disappear from this world "without a trace", but their transformed into other particles of the microworld, when all the usual conservation laws (energy, momentum, charge and other quantum characteristics). Nothing was lost or gained.
× Annihilation is not the conversion of matter into energy, or matter into "pure energy," as is sometimes stated. In annihilation (as in any known natural process) the law of conservation of energy is fulfilled - but the total, relativistically understood energy, including the rest energy of particles .So it's just about the transformation of one form of matter into another.
  After all, the conversion of "mass particles" into a field (with zero rest mass quantities) occurs in conventional particles only by annihilation of an electron with a positron. Antiprotons or antineutrons "annihilate" to form other massive particles (pions - see below), so the "transformation of matter into pure energy" cannot be spoken of at all ..!..
The largest annihilation in the history of our universe
took place at the beginning of its evolution more than 13 billion years, at a time of about 10^-4 s. after the Big Bang, at the transition between the hadron and lepton eras, when baryons and antibaryons anihilated each other, and immediately after, at the end of the lepton era (approx. 10 s.), when positrons with electrons anihilated. The result was radiation (now observed as relict) and remained a small excess of mass (1:10⁹) from baryon asymmetry.
These grandiose events are discussed in more detail in §5.4 "Standard cosmological model. Big Bang" passage "Baryon asymmetry of the Universe" in book "Gravity, black holes and spacetime physics" (see also below passage "Why is our world of matter and not antimatter?").
"Antiatoms", "antiworlds"
Antiparticles have exactly the same properties *) of their interactions as particles, so that a positron can orbit around the antiproton and thus form an "antihydrogen" atom. Similarly, antiprotons and antineutrons can form atomic "antinucleus^- ", around which positrons⁺ in shells of the same energies and according to the same selection rules as we know from our atomic physics can orbit. Such "antiatoms" will then have exactly the same chemical and spectroscopic properties as the atoms of our matter - they will create elements or compounds of antimatter with the same properties as we know from our matter.
*) Is antimatter exactly the same as matter ? 
Matter and antimatter appear to us in practically all experiments to be the same - except for the opposite signs of el. charges and some other quantum numbers have the same properties. Nevertheless, antimatter differs slightly from matter in behavior - asymmetric production and decay of some "exotic" particles and antiparticles (it was found experimentally mainly in K and B mesons). This hidden difference between matter and antimatter, generated in the earliest stages of the separation of basic interactions in the formation of the universe, may have eventually cooperate in the hadron era to give rise to the baryonic asymmetry (§5.4 "Standard Cosmological Model. The Big Bang.", passage "Baryon Asymmetry of the Universe") in book "Gravity, black holes and spacetime physics"). That's why there is matter and we are here too..!..
  Arises naturally question whether somewhere in the universe is the antimatter? In order to exist in the long term, it must find antimatter separated from matter, otherwise there would be a massive annihilation. So the question is: are there "anti-worlds" somewhere? We do not know this remotely using conventional spectrometric methods - light from "anti-stars" or "anti-galaxies" would have exactly the same spectra as we know from our stars and galaxies due to the identical properties of "antiatoms".
  However, there are two compelling indications that there is no free antimatter in the available part of the universe :
1. In primary cosmic rays from outer space there are only protons, not antiprotons (a small proportion of about 10^-4 antiprotons observed in cosmic rays are secondary antiprotons; they form when high-energy protons interact with the interstellar medium - with particles and photons of relic radiation; similarly positrons). No more complex "anti-nuclei" of helium or heavier elements (which would be composed of antiprotons and antineutrons) have been registered in cosmic rays so far *). Such "anti-nucleus" would have to be emitted in large quantities into space with each explosion of a possible "anti-star" as a supernova, in an (anti)stellar wind, as well as in jets from antimatter accretion disks around black holes. If cosmic rays contained more antiprotons or more complex "antinucleus", we could think of them as a kind of "envoy" of anti-stars and antigalaxies. In reality, however, we observe very few of antiprotons, just as many as are created by the interactions of ordinary high-energy protons of cosmic rays with ordinary matter.
*) A possible detection of more complex "antinucleus" would be strong evidence of the existence of a large amount of antimatter - "anti-stars", "antigalaxies" - somewhere in space. Such more complex "anti-cores" cannot be formed secondarily by any high-energy particle interactions, but could only originate in primary formation in a large amount of antimatter - in the thermonuclear synthesis of antiparticles in "anti-stars". Therefore, satellite "antimatter detectors", such as the AMS (Alpha Magnetic Spectrometer), are capable of detecting "antihelium" (anti-alpha particles), are important.
2. If some stars, galaxies or clouds of gas were made of antimatter, intense annihilation would occur at the interface of matter and antimatter, producing hard radiation g of energy 511keV. No measurements have yet recorded such annihilation radiation.
  In the universe, therefore, there is either no appreciable amount of antimatter, or the "antiworlds" are so far away from us --> the radiation is extremely weak that we are unable to register any of its manifestations with our devices.
Why is our world made of matter and not antimatter ? (or why isn't it just from radiation?) 
The interesting question is, why do we observe almost exclusively "ordinary" matter and almost no antimatter in the universe today? Or even why is there any matter at all and not just radiation? To answer these questions, we would have to go back to the very beginnings of the universe. According to current physical ideas, the same amount of matter and antimatter should initially be formed at the beginning of the universe. All experiments in nuclear physics show that in all particle interactions there is always a associeted - equal production of particles and antiparticles, in a ratio of 1:1.
  Due to certain specific phenomena - violation of the symmetry of interactions in the initial moments of the evolution of the universe - the amount of matter slightly prevailed over antimatter (ca. 1:10⁹), there was a slight baryon asymmetry of universe. A more or less random quantum fluctuation caused the victory of matter over antimatter in our very early universe. In hypothetical other universes, the opposite could have been the case, quantum fluctuation occurred at the appropriate moment occured on the opposite direction, and such a universe would be of antimatter ...  
           
  This slight excess of 1:10⁹ caused this matter to remain for the further development of the universe *), while all the other matter and antimatter had already anihiladed each other during the hadron and lepton eras and eventually transformed into radiation (now observed as relic radiation). If there were no baryon asymmetry at the beginning of the universe, all particles would anihilate each other and the universe would consist only of radiation (in such dull univers could not have forme any stars, planets, life...). The questions of antimatter and baryon symmetry or asymmetry of the universe from astrophysical aspects are discussed in §5.4 "Standard cosmological model. Big Bang.", passage "Baryon asymmetry of the universe" and §5.5 "Microphysics and cosmology. Inflationary Universe." of book "Gravity, Black Holes and the physics of spacetime".
*) The terminology of antimatter is relative. What remains and what our surrounding world is, we simply called matter - "ordinary" matter, sometimes called koino-matter (Greek koinos = usual, ordinary ). And a hypothetical substance composed of opposite particles is antimatter to us. In the imaginary universe, where baryon asymmetry would prevail on the opposite side, the inhabitants there would have the opposite terminology, for them ordinary matter would be what we call antimatter.
Combined particle-antiparticle systems
Interactions of antiparticles with particles result in annihilation processes, but this annihilation may not occur immediately. If the particles and antiparticles have opposite signs of electric charge (+ and -), they can form a bound particle-antiparticle system after sufficient deceleration just before annihilation. The best known bound system of this species is the positronium - a bounded system of electron and positron, which according to the model idea revolves around a common center of gravity to balance the centrifugal force of circulation and the electric attractive force (see below "Interactions of the most important elementary particles", passage "Positronium"). Similarly, an antiproton can be trapped in orbit around an atomic nucleus to load an electron - an antiproton atom is formed. The simplest antiproton atom is protonium, which is formed as a bound system of proton and antiproton orbiting a common center of gravity. Both positronium and protonium are unstable, in a short time (depending, among other things, on spin orientations) the antiparticle with the particle eventually annihilates. Thus, positronium and antiprotonium are of no general importance (except in special cases and applications).
  However, bound combinations of positrons and antiprotons (+ possibly also antineutrons), creating antiatoms, are important. Only this it can be real antimatter... From the point of view of nuclear physics, the properties of these antiatoms are important. Primarily spectrometric properties (briefly mentioned in the passage "Artificial production of antimatter. Antihydrogen.") and also gravitational properties :
Antimatter: gravity or antigravity ?
The most difficult is the measurement of the gravitational properties of antimatter. Although we know that particles and antiparticles have the same (rest) mass, it remains to be verified whether the anti-hydrogen "falls" in gravity in exactly the same way as hydrogen? For ordinary matter composed of atoms formed by electrons, protons and neutrons, Newton's law of general gravitation ("Newton's law of gravitation") applies. In the general theory of relativity - the physics of gravity and curved spacetime - the very precisely proven principle of equivalence ("Universality - the basic property and the key to understanding the nature of gravity") applies, with the result that gravity does not depend on the composition and structure of matter. The gravitational interaction between matter and antimatter should be identical. An object made of antimatter will thus fall in the gravitational field of the Earth with the same acceleration as a body made of matter (here on the surface of the Earth its fall will take place with a known value of the gravitational acceleration of 9.81 m/s²) .
  Logically, we conclude that this also applies to individual elementary particles - common (electrons, protons, neutrons), and probably also exotic (neutrinos, mesons, hyperons, ...). However, direct experimental verification of the gravitational properties of individual isolated particles is practically impossible, because these particles move at high speeds and show electromagnetic (and possibly strong) interactions with the environment, much stronger than gravitational - this completely "overpowers" a slight gravitational force. In general, however, it can be said that ordinary (koino) matter gravitates, showing universal attractive forces.
  However, as is the case with antiparticles (positrons, antiprotons, antineutrons), "antiatoms" composed of them, and antimatter in general? We know from experiments on accelerators that particles and antiparticles have the same inertial mass. But will antimatter gravitate or antigravity ? - does attractive or repulsive gravity act between matter and antimatter? However, some unsubstantiated hypotheses, as well as laymen's opinions suggested by the name "anti-", hold the opinion of antigravity of antimatter.
  The analysis of the probabilities of short-term existence of virtual electron-positron, proton-antiproton and other particle pairs ("vacuum polarization") shows that the results of Eötvös, Dicke and Braginski measurements confirm the validity of the principle of equivalence for common antiparticles (such as positron and antiproton) with accuracy ~10^-5 to 10^-6. Therefore, "antigravity" can certenaily not be expected with antimatter - no "falling upward"! Antimatter will normally gravitate (only the strength of this gravitational interaction could theoretically be slightly different - a brief discussion is in §2.2, section "Principle of equivalence" of the book "Gravity, black holes and space-time physics").
  How does an antiproton "fall" in a gravitational field, compared to a normal proton? It is not possible to measure the gravitational effects directly on the basic particles of antimatter - positrons and antiprotons - because they are charged and the electrical action with the environment many times exceeds the investigated force of gravitational (it is the same as discussed above for particles of ordinary matter ). For this purpose, it is necessary to prepare an electrically neutral antimatter composed of antiatoms. It would be optimal to create macroscopic bodies from antimatter-antiatoms. We would then release them downwards in the earth's gravitational field - as G. Galileo did historically (perhaps from the Leaning Tower of Pisa...). These bodies would be initially at rest and their instantaneous velocity would be determined only by the acceleration due to gravity. Alternatively, we would launch them horizontally with a defined initial speed and track their movement along a parabola.
  However, we cannot do anything like that with individual atoms. We are only able to create a gas composed of hydrogen antiatoms, in which the individual atoms move chaotically at different speeds in different directions, with a distribution of speeds according to the "temperature" that we would try to minimize. These atoms are not initially at rest, but have different initial velocities in different directions. In the gravitational field, they then fall along parabolic paths, whose instantaneous velocities in the vertical and longitudinal directions would add up to the initial velocities of the antihydrogen atoms.
  However, experiments are being prepared that would be able to eliminate or correct these effects and precisely measure the gravitational effects directly on the antihydrogen atoms - as discussed in the "Artificial Antimatter Production", section "Experimental Measurement of Antihydrogen Atoms" - AEGIS :
 Artificial production of antimatter. Antihydrogen.
When antimatter does not exist in the available part of the universe (we do not have any "mining mines" for antimatter), would it be possible to "make" it artificially? In accelerators, we produce large amounts of positrons and amounts!), so it would seem that nothing stands in the way of artificially (more difficultly) antiprotons and antineutrons (but these are only submicroscopic "folding" these particles into "antiatoms". In reality, however, the artificial creation of antimatter is difficult !
extremely   The particles produced in accelerators move at high velocities close to the speed of light - they have high kinetic energies, many orders of magnitude exceeding the binding energies of atoms. If we aimed such fast antiprotons and positrons at each other, they would fly past each other "without noticing" - almost without interaction - and no antihydrogen atoms would be formed. In order for the antiproton and positron to electrically combine into an antihydrogen atom, they must be slowed down a million times!
  Therefore, in order for an anti-hydrogen atom to form, positrons and antiprotons from the original energies of the order of MeV must be slowed down to a sufficiently low mutual speed, that the antiproton can capture and hold the positron. This is not easy at all, so only recently (1995) on the LEAR accelerator in the CERN laboratory managed to create only 9 atoms of anti-hydrogen (now it has managed to produce many thousands of antihyxdrogen atoms).
  Antiprotons were allowed to fly through the xenon, which slowed them down and the interaction also created pairs of electrons and positrons. In these several cases, the positron was subsequently captured by a flying antiproton to form an anti-hydrogen atom. During the order of 10^-11 sec. then, during his flight through the environment, he annihilated with normal matter, and a flash of annihilating radiation proved its brief existence. With such a short period of existence, no properties of antiatoms can be measured.
  For more efficient "antimatter production", resp. anti-hydrogen atoms, has now been constructed at CERN electromagnetic antiproton decelerator. In the electromagnetic field (generated by a high-frequency resonator), the antiprotons in the beam from the accelerator decelerate from the original energy of about 100 MeV to MeV units. This is still too high an energy for efficient production of antihydrogen atoms and for further experiments. Antiprotons are further slowed down by passing through thin aluminum degradation foils to approx. 5 keV (the yield here is very low, only approx. 0.1%). However, the last effective deceleration stage ELENA (Extra Low ENergy Antiproton ring), consisting of a 30 m hexagonal ring with radio frequency cavities and electron cooling, is in the preparation stage. Here, the antiprotons received from the antiproton decelerator are further slowed down from 5MeV to 100keV. Only a minor slowing down with degradation foils to ~5 keV is then sufficient, with significantly lower losses than with the use of only degradation foils; double the number of antiprotons is achieved. This leads to significantly more efficient production of a larger number of antihydrogen atoms.
  The slowed particles are then led to a cooled magnetic trap, where a cloud of antiprotons is trapped in a magnetic field and further "cooled" in it (the kinetic energy of their movement decreases). Positrons are simply obtained from beta⁺ -radioactivity, most often the radioisotope ²² Na, or also by reactions using a linear accelerator. After basic deceleration in a thin film, they are led to a magnetic trap where they slow down further ("cool" similar to antiprotons) and then slow antiprotons and positrons are simultaneously injected into a reaction chamber with a magnetic trap, where positrons are trapped by antiprotons to form antihydrogen atoms. When decelerated and trapped in a magnetic trap, both particles have enough time to bind to each other in anti-hydrogen atoms. This method succeeded in detecting 80 antiatomic hydrogen atoms in the first phase, but after further improvement - the ALPHA device (Antihydrogen Laser PHysics Apparatus) - it is possible to produce tens of thousands of anti-hydrogen atoms for experiments, eg to compare electromagnetic spectra of anti-hydrogen and hydrogen atoms.
  For the production of anti-hydrogen atoms, it is advantageous to use positrons in the form of positronium - the electrically bound state of the electron and positron (see "Electrons and positrons"). Positrons from beta⁺-radioactivities are passed through a porous target of siliceous material, in which they capture electrons and form positronium e^--e⁺. Using laser beams, the positronium is then excited to a higher quantum state (up to n = 25) and directed to the antiprotons. Highly excited positronium can relatively easily transmit a positron to an antiproton - there is a "charge exchange" in which the antiproton assumes the position of an electron in the positronium: (e^--e⁺)* + p^- -> H^~* + e^-, to form an excited antihydrogen atom H^~*. This process has a relatively high effective cross section (depends on the 4th power of the quantum number n of positronium). Another advantage is the lower kinetic energy of the formed anti-hydrogen atom. Antihydrogen atoms are created here in a highly excited (Rydberg) state, so they are sensitive to gradients of electric and magnetic fields, which makes it possible to manipulate them in experiments.
  In addition to the production of the antiatoms themselves, another very difficult problem is their isolation from the surrounding mass in order to prevent immediate annihilation with the materials of the reaction vessel. A magnetic field is commonly used to keep charged particles (e.g. in tokamaks - see §1.3, section "Tokamak", or in the above-mentioned magnetic traps). However, the hydrogen atoms are electrically neutral on the outside. However, they have a magnetic moment, so they react to the magnetic field (albeit weakly). With the help of strong superconducting electromagnets, a "magnetic trap" can be created, which is able to keep anti-hydrogen atoms in the magnetic field inside the reaction vessel for some time. The magnetic field is specially shaped so that it is strongest at the edges and decreases towards the center. The atoms are drawn into the "magnetic well" in the middle, where they can remain trapped for some time. If this time is long enough, antiatoms have time to return to a ground state in which their physical properties can be measured, paving the way for accurate testing of the presumed symmetry of matter and antimatter (some minor differences are discussed below in the passage "CPT symmetry of interactions"). Revealing possibly small differences could help to explain why our universe is made up only of matter (cf. "Baryon's asymmetry of the universe").
 Experimental measurement of anti-hydrogen atoms - AEGIS, GBAR
The AEGIS (Antihydrogen Experiment: Gravity, Interferometry, Spectroscopy) project is being developed at CERN for the precise measurement of the physical properties of antihydrogen atoms. It consists of several basic follow-up steps :
1. Production of antiprotons p^- in the proton synchrotron. A beam of protons p⁺ accelerated to an energy of 25 GeV hits an iridium target, where, thanks to the high energy, showers of many secondary particles, including proton-antiproton pairs, are created. The antiprotons p^- are separated using a magnetic field. They have high energies, velocities close to c, wide energy spectrum. They are not directly applicable for the creation of antiatoms, they must be slowed down :
2. The antiproton decelerator, which applies a strong electric radio-frequency field of opposite polarity, on a circular track in a magnetic field (created by electromagnets), it works "oppositely" to a synchrotron. It has an oval shape (diameter 60 m, in the diagram below it is drawn as a circle for simplicity), along its perimeter there are four short straight sections with radiofrequency electrodes, where antiproton braking takes place. In AEGIS, there is a slowdown to 5.3 MeV, which corresponds to about 10% of the speed of light. Antiprotons are further slowed down by passing through thin aluminum degradation foils to approx. 5 keV (the yield here is very low, only approx. 0.1%; not drawn on the diagram).
3. Capture and accumulation of antiprotons in an electromagnetic trap (the so-called Penning-Malmberg trap), a chamber with a magnetic field and a set of circular electrodes. Another slowing down of antiprotons by collisions in the electron cloud is also carried out here.
4. Production of positrons e⁺ using the beta⁺ radionuclide ²²Na. ....
5. Creating positronium Ps by passing positrons through a nanoporous material. Ortho-positronium is used, which has a longer lifetime of 142 ns (compared to para-positronium which has a lifetime 1000 times shorter). Excitation of positronium to the Rydberg state Ps* with n=~25 using UV and IR lasers.
6. Creation of antihydrogen atoms H^~ using the charge exchange reaction of an antiproton with an excited positronium Ps*. The slow antihydrogen atoms created in this way (with a speed of ~ 25-80 m/s, corresponding to a temperature of the order of 100 mK) are then already led to experiments to measure their properties.
7. For AEGIS, the creation of a pulsed horizontal beam of H*^~ antihydrogen atoms with a constant speed of around 400 m/s. The effect of the inhomogeneous electric field on the highly Rydberg excited H*^~ atoms is used here (it makes it possible to manipulate them using the Stark effect). It is important for further analysis of the parabolic motion of H^~ atoms in the gravitational field.

Framework simplified scheme of experimental study of physical properties of anti-hydrogen atoms - AEGIS and GBAR.

In a gravitational experiment  at AEGIS, the horizontal stream of antihydrogen atoms is led from there into a system of two separation slits (grids) *) with a grid period of 80 mm, which create parallel bundles of antihydrogens. Subsequently, at the end of the L- path, these anti-hydrogens are annihilated by a silicon position-sensitive detector with a spatial resolution of 10 mm. The structure of the grating is analyzed, which is displayed on the position-sensitive detector as a series of maxima and minima at different heights when detecting a larger number of antiprotons. Their vertical positions depend on the decrease (deflection) of anti-hydrogen atoms in the Earth's gravitational field (approx. 20mm). It correlates with the arrival times of anti-hydrogen atoms on the detector (which correspond to their horizontal velocities v ). It is evaluated to what extent the height decrease h of antihydrogen at distance L corresponds to the law of horizontal velocity throw in the gravitational field of the Earth with gravitational acceleration g^~ : h = ¹/₂ .g^~. (L/v)². This is a direct laboratory test of the validity of the weak principle of equivalence in the general theory of relativity (see §1.2, passage "Principle of equivalence" in the book "Gravity, black holes ...") which says that the trajectory of motion (here fall) of a material body depends only on its initial position and velocity, not on its structure and other properties - does it also apply exactly to antimatter..?... The accuracy of the determination of g^~ in the AEGIS experiment is expected to be approximately Dg^~/g^~ ~1%.
*) This arrangement of two or three grids equidistantly placed in a row is called a moiré deflectometer in optics (French moiré = fabric, fine structure, grid). The last third grating is replaced by a position-sensitive detector. It is not used here in the interferometric mode as in optics, but serves to precisely define the horizontal parallel trajectories of anti-hydrogen atoms. The annihilating anti-hydrogen atoms will create bands on the detector - patterns of grid slits, by analyzing which it is possible to determine how much H^~ dropped when moving along the parabola from the second grid to the impact on the detector.
  In addition to AEGIS, the gravitational measurement of antihydrogen is dealt with by the alternative experiment GBAR (Gravitational Behavior of Antihydrogen at Rest), operated at the same antiproton decelerator at CERN. To measure the gravitational acceleration of anti-hydrogen atoms, it does not use horizontal movement with evaluation using a moiré-deflectometer, but the vertical free fall of anti-hydrogen atoms in the measuring chamber, with the evaluation of the exact time of annihilation when the anti-atoms hit the bottom of the chamber from above. The trajectory - the height h of freely falling H^~ atoms - is related to time by the relation h = ¹/₂.g^~.(t₂-t₁)², where t₁ is the time of entry of the atom into the upper detector of the chamber and t₂ is the time of impact and annihilation of the antihydrogen atom on the bottom of the chamber. In the GBAR experiment, additional stages of slowing down antiproons (ELENA) and "cooling" of the p^- beam will be used, eventually down to an energy of 1 keV. Antihydrogen atoms are prepared by further reaction with positronium in the form of positive antihydrogen ions H^~+- one antiproton and two positrons (this requires a higher flux of positrons, which are generated here using a 9MeV linear accelerator). These H^~+ are then cooled using Be⁺ ions to a temperature of around 10mK. Using a laser pulse, the outermost positron is then removed just before the measurement and a neutral antihydrogen atom H^~ is created, whose free fall time is measured in a vertical chamber with detectors. Thanks to the measurement of the fall of very slowed down antihydrogen atoms (with almost zero initial velocity, ~0.5m/s), one can expect an improved accuracy of the determination of g^~ about Dg^~/g^~ ~10^-3.
  In anti-hydrogen atomic spectrometry, a slow beam of anti-hydrogen is led to another magnetic trap, where it is excited and the radiation emitted or absorbed during the jumps between the individual energy levels is measured. The energy levels in an atom depend on the inertial mass and the charge of an electron in a hydrogen atom or a positron in an antihydrogen. By comparing the energy of the electron transitions between the excited and ground levels of hydrogen and antihydrogen, we can verify whether the inertial masses and charges of the particles and antiparticles are exactly the same, or there is a slight difference. If the inertia mass of the particles and antiparticles differ, it could possibly be measure a slight difference by this spectrometry.
Production of more and heavier antimatter ?
Despite all the partial successes in the above-consuming experiments is unfortunately necessary to admit, that the creation of large quantities of antimatter, or more complex antiatoms than hydrogen *), yet there is no hope in the near future ...
*) The targeted "production" heavier antinuclei really is not hope for the foreseeable future. However, in small numbers (with negligible probability) they may arise randomly in high-energy interactions. Heavy nuclei collisions produce more antiprotons and antineutrons. If several co-produced antiprotons and antineutrons coincidentally fly in the same direction and at approximately the same speed, they can "bind" to the heavier antinucleus - nucleus anti-deuterium, anti-helium - by nuclear forces. Because this process is very unlikely, many billions of trillions of nuclear collisions to make any such heavier anti-nuclear accidental to formation. In 2011, at the RHIC heavy ion accelerator in Brookhaven, 18 nuclei of anti-helium-4 were identified in this way (during several months of collisions), other successful experiments of this kind are taking place at CERN. The formation of even heavier antinuclides in this way, due to the almost zero probability, will probably not be proven....
Antimatter - a possible source of energy ?
In the popular science and sci-fi literature, it is often stated that annihilation of matter with antimatter results in a 100% conversion of matter into energy, in accordance with Einstein's relation E = m.c². Thus, in the distant future, antimatter could be an inexhaustible source of energy, or to power interstellar ships (photon rockets - see below) at speeds close to the speed of light? Unfortunately, this is not true, the problem is much more complicated, there are obstacles not only of a technical, but also of a fundamental physical nature.
  When annihilation an electron with a positron, in fact all the rest mass of both particles changes into electromagnetic radiation: e⁺ + e^- ® 2 g. However, it is not light, but hard gamma radiation, which would not be reflected by the mirror of the photon rocket, but absorbed. However, the annihilation of protons and neutrons with antiprotons and antineutrons does not produce electromagnetic radiation (at least not directly), but p- mesons, eg p^~+ p ® 2 p⁺ +2 p^- + p^o ; they then decay into muons and neutrinos, eg: p^- ® m^- + n'_m , p⁺ ® m⁺ + n_m . This is followed by the decay of muons, eg m^- ® e^- + n'_e + n_m , m⁺ ® e⁺ + n_e + n'_m , and only then could annihilation of electrons with positrons e⁺ + e^- ® 2 g ( all these interactions are discussed in more detail below). Thus, in the hypothetical "annihilation reactor" of the future, would therefore need to achieve not only the efficient energy utilization of hard radiation g, but also the closure of proton, pion, muon and electron (+antiparticles) high-energy "plasma" so that secondary particles can effectively annihilate together. So far there is no known physical mechanism that would alow this. And it is absolutely impossible to use the energy carried away by neutrinos...
  The energy utilization of annihilation of matter with antimatter is also hindered by technical difficulties. If, for example, we want to combine two macroscopic bodies, one of matter and the other of antimatter, with the aim of complete annihilation, it would not be very successful in practice due to the emergence of the so - called Leidenfrost insulating barrier*). When the surfaces of both bodies touch, a powerful flow of energy (radiation and particles) is created, which repels, delays and insulates the next mass of the bodies from each other so that effective volume annihilation does not occur; the reaction is planar rather than massive volumetric. One possibility would perhaps be to collide the two bodies at high speed so that the kinetic energy overcomes the pressure of the generated radiation. Or even better, perform the annihilation sequentially in a stream of particles of matter and antimatter (the aforementioned "annihilation reactor"). None of this is feasible in the foreseeable future ...
*) A similar phenomenon can be observed in everyday life when we drip water on a hot stove. Water droplets usually do not evaporate immediately (explosively), but "jump" for a while on a hot plate: when the droplet comes into contact with the plate, steam is created, which for a while creates a gaseous "cushion" isolating the droplet from the plate.
Photon rocket ?
The collimated source of electromagnetic radiation shows the effect of a "rocket thrust" (it is the inverse effect to the light pressure, which Lebedev first observed with light). This is a consequence of the law of conservation of momentum, or the law of action and reaction: electromagnetic radiation has a flow of momentum, which in clasical electrodynamics is describes by the Poynting vector and from a quantum point of view is given by the momentum of photons (each photon of the wave frequency f has energy E = h.f and momentum p = h.f /c). During radiation, this momentum is transmitted to the source in the opposite direction, the transmitted momentum per unit time indicating the applied "pull" force. In order for this "rocket effect" to be noticeable, an extremely high flux of radiation is required, which is not achievable by existing technical means. The photon rocket project envisages an annihilation reaction, or with a thermonuclear reaction that would take place in the focus of a large hemispherical or parabolic mirror that would reflect the resulting photons and collimate them "backwards". As already outlined above, the radiation generated by an annihilation or thermonuclear reaction is not light, but high-energy gamma and corpuscular radiation for which the law of reflection does not apply; a mirror of any known material would not reflect this radiation, but would mostly absorb it, leading to its thermal destruction.
Note: Instead of a "photon rocket", the name "quantum rocket" can be used , as the desired effect is created not only by the emission of photons, but also by other quantum particles carrying momentum. However, for photons, the most favorable ratio is [transmitted momentum ® thrust] / [required emitted mass and energy].
 Antimatter and antiworlds in sci-fi
The mysterious impresion of the term "antimatter" led in the science fiction literature to the idea of "antiworlds", in which everything is "opposite" and in which possibly our "doubles" - "anti-people" may live. This sci-fi idea has no astronomical justification (as discussed above in the section "Antiatoms, Anti-Worlds") , it is rather a game for our imagination :
  Consider, therefore, the hypothetical situation that somewhere in the distant universe there is indeed a large region of antimatter, where (anti)galaxies and (anti)stars formed, including the (anti)Sun with the planetary system orbiting and the (anti)Earth, on which it evolved exactly the same life as here, including anti-people :

Imagine, for example, in a sci-fi experiment, that would "girl made of matter" here on Earth via communications by electromagnetic signal, colluded with "antimatter boy" somewhere from a distant galaxy, a meeting - "dating" - at a certain point in space about halfway of path, without they would know they are composed mutually from antimatter. They would park in rockets near each other, get out into the open, and go to greet each other - "Hello!"; nothing special would happen yet. However, the moment they shook hands, there would be a massive annihilation of matter and antimatter *) and both partners would be destroyed in a massive atomic-particle explosion.   *) Due to the formation of the above-mentioned Leidenfrost insulating barrier, there will be no total annihilation of both bodies, but only the surface parts of the palms of the hands. Even that would be enough to doom and destruction for both partners!   If they were far-sighted, they could remotely test whether they were of the same nature. The easiest way is to send a weak beam of electrons against each other and measure whether annihilation gamma radiation of 511 keV is produced after their impact. If so, they should not approach each other (not a step!) - they would have to run away from each other quickly so that they do not perish ..!..

We do not deal here with the ideas of antimatter and antiworlds based on errors and misunderstandings, where the prefix "anti" is mistakenly attributed to other meanings, such as philosophical, reverse flow of time, etc. ..!..

Interaction of elementary particles - general properties
Mutual actions - interaction - the various objects are the basis of all events in nature. Interactions transfer energy, momentum, angular momentum, and charges between bodies. Physics has come to knowledge, that the essence of all interactions and forces in nature is the interactions between elementary particles of matter. In principle, we describe the interaction of particles in three ways :
-> Mechanical force action
Bodies and particles when approaching and contacting each other simply "act with a force" (the origin and microscopic nature of which we are not interested here), and we investigate the "mechanical" consequences of this force action (basically according to Newton's 3 laws of mechanics). With this immediate mechanical force action we have the greatest experience of everyday life. This is how physics proceeds in classical mechanics.
-> Physical field - acting at a distance
One particle in the space around it creates a field that exerts a force on another particle located in it. This very successful description is the basis of classical electrodynamics and gravitation.
  We assign a corresponding field to each type of interaction - a space in which certain forces act on particles. The magnitude of the field action at each point in space is expressed by the field intensity (force acting on the "unit test particle") or by its potential (work associated with the transfer of particles to a given place). In classical physics, it is an electric, magnetic, gravitational field. The changes - "commotion" - in this field propagate at a finite speed from place to place, which is accompanied by the transfer of energy, momentum, and other physical quantities.
  From the point of view of classical physics, quantities such as energy and momentum are transmitted continuously during field changes. In quantum physics, it turns out that during changes (disturbances) in the field, physical quantities are transmitted discontinuously over certain "portions" - by quantum. Quantum field theory assigns certain particles to these quantums as carriers of the interaction, which leads to the following process :
-> Exchange of particles in quantum physics
Particles transmit and receive certain quantum of fields, which causes their interaction. We imagine this exchange quantum as a particle - a carrier of interactions. This description is characteristic of quantum field theory (basic principles are outlined in §1.1, passage "Quantum field theory").
  In the standard particle model, interactions are mediated by the exchange of intermediate bosons, which are in a virtual state during this exchange - they exist so short that we cannot directly observe them due to the quantum principle of uncertainty. However, if the virtual particle gains sufficient energy during the interaction, it can be released and become a real particle; this is commonly observed for photons, in accelerator experiments it is also possible to indirectly observe heavy bosons W^{+, -} and Z⁰.

Spatial reach of interactions
In everyday life and in the surrounding nature, we encounter two types of interactions: electromagnetic and gravitational. They have an infinite reach - the field intensity E(r) at a distance r is given by the inverse square law E(r) ~ k/r² and the potential f(r) ~ k/r. The inverse square law has a geometric origin: a spherical surface of radius r has a surface S=4pr². Coulomb's law of electrostatics and Newton's law of classical gravity have this dependence.
  In the microworld, we encounter two other types of forces, which, however, have a short reach: the so-called strong nuclear interactions (§1.1, passage "Strong nuclear interaction") and weak interactions (§1.2, passage "Mechanism beta. Weak interaction."). If the field-interaction has a short range, the dependence of its potential f(r) on the distance r is modeled by an additional exponential factor e^-m.m.r: f(r) ~ k.e^-m.m.r/r, where m is the mass of the intermediate particle, m is the scaling constant. Such dependence is called the Yukawa potential (H.Yukawa introduced it in 1935 for strong nuclear interactions; however, here it later turned out differently...). The value r ~ 1/(m.m) is the effective reach of the interaction (the distance at which the interaction drops to a value of 1/e).
  The spatial reach of interactions in the concept of particle exchange is closely related to the rest mass m_o (or rest energy E_o=m_o.c²) of exchange intermediate particles. It can be shown most simply using the quantum uncertainty relation DE.Dt » h, from which it follows that for an mediated virtual particle that perturbs the energy by the value DE (equal to its rest energy E_o=m_o.c²), the maximum time of this perturbation can be Dt » h/DE = h/E_o. During that time, this particle can travel the path áhu Ds= c.Dt » c.h/E_o at the speed of light, which represents the maximum or effective range of the interaction mediated by this mediated particle.
  Electromagnetic interaction has an infinite range, the mediating particle is a photon with zero rest mass (photons can therefore transmit almost zero energy in the limit, so according to the uncertainty relations they can exist virtually for an almost infinite time and reach an infinite distance also). Gravitational interaction also has an infinite range, it is mediated by gravitons with zero rest mass (so far hypothetical or model particles that we cannot observe in any way).
  On the other hand, weak interactions are mediated by heavy intermediate bosons W^+,- and Z⁰ with rest energies of 80 and 91 GeV/c², so their reach is very small, on the order of 10^-15cm (see the passage "Bosons W^+,-, Z⁰" below). Therefore, even on subnuclear scales, this interaction is very weak (on even smaller scales, however, it is not weaker than the electromagnetic one).
  The situation is more complicated for strong interaction. In atomic nuclei (and in general between hadrons) we observe a very short range of the strong nuclear interaction of about 1,2×10^-13 cm. This fact was previously (provisionally, incorrectly...) explained using the exchange of intermediate p-mesons with a rest mass of approx. 135 and 140 MeV/c². However, after the clarification of the quark structure of hadrons, this concept was abandoned. The strong interaction is known to act primarily between quarks inside hadrons and is mediated by gluons of zero rest mass, so its range should be infinite. Now, the nuclear forces between nucleons are understood as a residual manifestation of the strong interaction between quarks (discussed in more detail below in the section "Quark structure of hadrons" and "Four types of interactions in nature", also in §1.1, section "Strong nuclear interaction").

Scatering experiments
The basis of studying the structure of the microworld are the so-called scattering experiments *). They consist in firing the studied object with suitable particles - electrons, protons, a -particles, etc., and we study the products of collision (or close convergence) of the arriving particle with the target object (resp. with the second particle). These are either the original particles dispersed (that is, at lower energies) or other secondary particles, emitted during interaction (this occurs at higher energies). By analyzing the energies, momentum, charges, angles of flying away and other parameters of secondary particles, we can obtain important information about the structure of the investigated micro-objects and the mechanisms of interactions of the respective particles. Particle interactions are important in the study of the structure of matter, and they play a key role in the formation of matter in universe. All the matter that is here (and of which we are composed ourselves) was formed during the interactions of particles in the initial stages of the universe, or inside the stars.
*) We simply do not have another option to study microstructures so small that they are not directly observable (after all, even ordinary visual observation is to some extent a kind of "scattering experiment" with visible light photons...). The first important scattering experiment was carried out as early as 1911 by E.Rutheford together with H.Geiger and E.Marsden - it led to the discovery of the atomic nucleus (see §1.1, section "Structure of atoms", Fig.1.1.4) .
  By interactions of elementary particles we understand the processes of mutual collisions of two particles, or collisions of a particle with an atomic nucleus (here the problem is partly intertwined with the nuclear reactions discussed in §1.3 "Nuclear reactions and nuclear energy"). The simplest two - particle interaction of primary particles a and b can be symbolically written as: a + b ® c + d - Fig.1.5.1.A. The resulting secondary particles c and d after the interaction can be either the same as a and b, or different particles. However, the interaction often results in different particles than the original and also a different number of particles - especially at high energies, a higher number of secondary particles is usually formed (see below). Primary particles a and b, entering the reaction, are already known "in advance" (they were purposefully created in the "ion source" and accelerated in the accelerator, or one of them prepared in the target - see "Accelerators" below). Flying-out particles c , d , or other new secondary particles, we detect and measure their properties using detectors. The processes of itself interaction (collisions) take place in a spatial area with micro-dimensions of the order of 10^-8 -10^-15 cm, so they are not available for direct observation. Based on reconstructions of the interaction, we create certain model ideas and theories about their mechanisms, which explain the transition from the initial state (a + b) to the final state (c + d + /or other particles).
  During the interactions of particles between them, there are three basic types of forces (physical fields) *) :

• Strong interactions between hadrons (mesons, baryons) can cause both scattering and nuclear reactions, and at high energies the processes of formation of new particles and antiparticles, such as p- mesons, nucleons, hyperons and their combinations.
• Weak interactions , manifested in leptons, mesons and baryons, are only relatively marginally applied in collisions of most types of particles. They are significantly manifest in neutrons (due to their beta decay), neutrinos (interactions of neutrinos with nucleons - see the description of neutrino experiments in §1.2, section "Neutrinos") and at high-energy processes, where p and K mesons , hyperons and other decaying particles are formed due to weak interaction.
• Electromagnetic interactions in charged particles cause Coulomb scattering, radiation processes such as braking radiation, formation of electron-positron pairs and their annihilation, photonuclear reactions. It is characteristic of all these types of processes that the interaction of electric charges with the electromagnetic field in which the charges are located produces a quantum of radiation - photons, mostly gamma-ray photons. Electromagnetic interactions are the most common processes occurring in the collisions of most particles.

*) The gravitational interaction of elementary particles is completely negligible and has never been observed se far. It could perhaps only manifest itself at extremely high energies (»10¹⁹ GeV), many orders of magnitude higher than we can now achieve. However, this would not be a commonly known gravitational attraction, but gravity would be part of the unitary field (see §B.6 "Unification of fundamental interactions. Supergravity. Superstrings" in the book "Gravity, Black Holes and the Physics of Spacetime").

  In the interactions of particles, the principle is generally applied: "what is allowed is also realized" - all kinds of processes *) occur, which are compatible with the laws of conservation of energy, momentum, angular momentum, electric charge, lepton number. If enough energy is available, a number of processes take place during particle collisions, but with different probabilities. This probability is given by the internal mechanisms of interaction of the respective fields and the relationship between the respective initial and final state configurations. The probabilities of individual processes ("channels" of interaction) are determined by quantum field theory using so-called matrix elements (elements of the scattering matrix S, see also below "Feynman diagrams").
*) As if all quantum of all fields were potentially, covertly and implicitly - virtually - present everywhere in space, in a "vacuum". From this "unitary" field, by supply of energy - excitation of the field - then releases the relevant particles, whether virtual or real.
  The course and result of the interaction of particles depends mainly on two circumstances :
¨ On the type of interacting particles.
¨ On the kinetic energy with which the particles collide (determined here by the energy in the center of gravity of both particles).
Note: Even with collisions of the same particles and with the same energy, however, the interaction usually takes place in a slightly different way each time - through different "channels" of the reaction. We can explain this by the fact that on the one hand the collision can take place "frontally" or "peripherally" (ie with different impact factor and mutual angular momentum of both particles), and on the other hand due to stochastic laws of quantum physics the individual possible configuration states are realized with different probabilities.

Feynman diagrams
The so-called Feynman diagrams are often used for a clear graphical representation of the mechanisms of particle interactions (R.Feynman first introduced them in 1948). They come out from an exchange description of particle interactions. The trajectories of "matter" particles, fermions (electron, proton, ...) are marked by straight solid lines with arrows - particles have an arrow pointing to the right, antiparticles to the left. Exchangeable intermediate particles (photons, W-bosons, gluons ...) are marked with dashed lines or wavy lines. In the horizontal direction there is a time orientation (other conventions are also used) - however, only symbolic, these diagrams do not serve to concretely express the time course of interactions, but only to "topologically" represent their mechanisms; are a kind of analogy of spacetime diagrams used in relativistic physics. The basic Feynman diagram of the general unspecified interaction of two particles a + b ® c + d is shown in Fig.1.5.1.A. The primary particles a and b arrive into close proximity to each other - the interaction area, the actual processes of interaction take place inside, after which the resulting particles c and d fly out of this area. The upper part of Figure 1.5.1.A shows the usual spatial drawing of the collision of both particles, the lower part of the figure shows Feynman's presentation of this interaction.
  Feynman's own diagrams then specify and illustrate possible processes within the interaction region for specific types of incoming and outgoing particles. Again, they consist of outer lines with "free ends", showing the particles entering and leaving the interaction. The actual interaction processes are drawn by the so-called interaction vertices - points at which wave or dashed lines connect to the initial outer line of the particle, corresponding to exchangeable intermediate particles mediating the interaction *). The laws of conservation of energy, momentum, electric charge, lepton number are fulfilled in the interaction vertices . The inner lines between the interaction vertices of the outer lines correspond to the virtual particles which do not leave the interaction area and are not present between the incoming or the resulting "physical" particles in the initial or final state; however, in their own interaction, they act and contribute to the result. Lines with a second free end can also emerge from some interaction peaks: these correspond to real particles (photons, W-bosons, fermions) emitted during the process.
*) In quantum field theory, these lines correspond to the so-called propagations - functions indicating the amplitude of probability (amplitude of "wave propagation") when moving a particle with a certain energy and momentum. These are fermion (eg electron) and boson(eg photon) propagator. Propagators can be expressed using the so-called Green's functions , which are solutions of the wave equations of the respective particles (either inhomogeneous Dirac equations with d -function of coordinates and time, or d´Alembert's equation for electromagnetic field potentials). The actual interaction peaks correspond to the operators of creation and annihilation of the respective particles.
  We will give examples of Feynman diagrams for some specific typical interactions of particles - Fig.1.5.1. From the point of view of nuclear, radiation and particle physics, these interactions are discussed in more detail in other relevant places (§1.2, 1.3, 1.5, 1.6) of our treatise. Let's start with low energy interactions. The simplest process with particles is the interaction of two electrons under the influence of electromagnetic force. According to the concept of quantum electrodynamics, the basic mechanism operating in the interaction region is the exchange of photons between the two electrons - in the Feynman diagram, the electron lines in their interaction vertices are connected by a photon line (Fig.1.5.1.B) - one electron emits a virtual photon g*, the other absorbs it, whereby both electrons scatter in their orbits (elastic scattering). The resulting state is again two electrons. However, this is only one of the possible processes and, moreover, only in the first approximation. It is already known from classical electrodynamics, that with each accelerated movement of electric charges, electromagnetic waves are emitted. Photon emission of braking radiation occurs even when electrons are scattered. At higher energies, interaction peaks with energetic particles can also be realized, which can generate real particles - lines with free ends corresponding to secondary leptons; at the highest energies also the production of heavy particles (see below).
  Another simple process of electromagnetic interaction is the scattering of a photon on an electron - Compton scattering (is described in §1.6 "Ionizing radiation", part "Interaction of gamma and X-rays", Fig.1.6.3). In the Feynman diagram in the upper part of Fig.1.5.1.C we see a solid electron line and a wavy photon in the input region. In the interaction vertice, a virtual electron e* (which seems to "absorb" the energy of the photon) is formed, which in the second vertice changes again into a flying away electron and a photon. The interaction of the positron with the electron can take place again at low energies either as a Coulomb elastic scattering (Feynman diagram is completely analogous to Fig.1.5.1.B), or as a process of annihilation with the formation of gamma photons - lower part fig.1.5.1.C. At higher energies, there are again more possibilities in both of these processes with the formation of additional secondary particles.
  At the highest energies, there are many possibilities for the production of heavy particles, including Higgs bosons. Two such possibilities of "electro-weak production" of the Higgs boson are shown in Fig.1.5.1.D: direct interaction of e⁺ + e^- ® Z* ® Z + H ( H-emission ) and combined production of W or Z and their subsequent fusion to H. Higgs bosons are highly unstable particles and immediately decay into either two high-energy photons or four leptons (via intermediate W or Z bosons), or other ways (the properties of Higgs bosons are described below in the section "Hypothetical and model particles").

Fig.1.5.1. Examples of Feynman diagrams of some significant particle interactions.
Note: Symbolic images of protons, neutrons and p- mesons are not part of standard Feynman diagrams; they are drawn here for illustration only.

  Weak interactions are mediated by exchangeable intermediate bosons W (or Z). In Fig.1.5.1.F is a diagram of an important process of transmutation of the d to u quark in the b^--radioactive conversion of a neutron to a proton, an electron and an (anti)neutrino: n^o ® p⁺ + e^- + n'_e . This process, as well as the analogous b⁺ process, corresponds to Figure 1.2.5 in §1.2 "Radioactivity", section "Radioactivity beta". Other important processes, taking place due to weak (or electroweak) interaction, are decays of pions into muons and neutrinos, eg p^- ® m^- + n'_m (the decay of p⁺ takes place analogously) and muons into electrons and neutrinos, eg m^- ® e^- + n'_e + n_m (analogously for m⁺) - this is shown by the Feynman diagrams in Fig.1.5.1.G.
  Strong interactions are mediated by "exchange" gluons between quarks contained inside hadrons - mesons (especially p and K) and baryons (protons, neutrons, hyperons). The nonlinearity of quantum chromodynamics of strong interaction together with the idea of asymptotic freedom (see below "Inprisoned Quarks", or "Unification of Fundamental Interactions. Supergravity. Superstrings.") allows Feynman diagrams (and the perturbation approach) to be used only in processes where high momentum is passed to quarks. The "quiescent" interactions of quarks in hadrons, the strong interaction of nucleons in nuclei, and the "hadronization" of quark-gluon plasma cannot be analyzed in this way. However, high-energy interactions between hadrons can be well described. Fig.1.5.1.E shows a Feynman diagram of pion production in the collison of twoo protons p+p®p+p+p^o; it is one of the possible processes, alternatively a proton, a neutron and a p⁺ can be formed , or two neutrons and a p^-.
  In high-energy interactions (see below), when enough energy is available, a wide range of different internal processes can be realized. In particular, intermediate W-bosons or gluons attached at interaction vertices can acquire such high energy that they can generate very heavy particles - Higgs bosons H and heavy t- quarks - in the associated production of particle-antiparticle. These then disintegrate under the action of intermediate bosons W to electrons, muons, tauons, neutrinos and their antiparticles. Higgs bosons can also decay into a pair of high-energy photons g. Furthermore, repeated processes with intermediate particles can create multiple particles in a single collision - including quarks, which then hadronized. Fig.1.5.1.H shows an example of high-energy collision of two protons at the energy of a hundred GeV, where interactions with exchangeable gluons can also form heavy t- quarks, b- quarks, then W-bosons and finally leptons (electrons e^±, muons m^±, tauons t, neutrinos n) that fly out of the interaction area and can be detected. With an even higher energy of tens of TeV (not yet achieved ...) one of the more possibilities is the formation of the Higgs boson ("strong production" of H by the exchange interaction of energy quarks with gluons or W-bosons) and a series of subsequent decays into W-bosons and finally again leptons or quarks - fig.1.5.1.I. And, of course, this is accompanied by the hadronization of energy quarks. Fig. 1.5.1.I shows the formation of the Higgs boson by the so-called gluon fusion; other possibilities are W or Z fusion (analogous to Fig. D below, only instead of electrons there are quarks), or combined production with W or with t-t'-pair.
  In these high-energy collisions, other quarks of colliding protons also enter the interaction area - the interaction with gluons can then create a so-called quark-gluon plasma (see below the passage "Quark-gluon plasma -"5th state of matter"," and in §1.3 passage "High-energy collisions of heavier nuclei. Quark-gluon plasma."), the hadronization of which creates other secondary hadrons (especially pions, nucleons), flying out of the interaction region. In Fig.1.5.1.H,I two interaction areas are marked. The first - "asymptotically free"- corresponds to high-energy interactions in which even quarks behave as free and their interaction can be described by Feynman diagrams; it is analogous to the interaction areas in other diagrams. The second interaction region corresponds to the hadronization of quarks, which cannot fly out alone, but in the gluon field generate further pairs quark-antiquark which combine in pairs and triples - fly out as hardon - mesons p and K, protons, neutrons, hyperons. These particles fly out often narrowly directed sprays, called jets, at a small angle around the direction of flight of the original energetic quarks.
  In quantum field theory (in the so-called perturbation access), Feynman diagrams are used as a guide for counting contributions from different kinds of possible processes with intermediate quantums into so-called matrix elements ( S-elements of scattering), indicating the probabilities of quantum transitions between states of a given system - here between the state before interaction and after particle interaction.
  First, the corresponding Feynman diagrams are constructed, the outer lines of which correspond to the incoming particles of the initial state and the outgoing particles of the final state. The 1st approximation (diagram with 2 interaction vertices), 2nd approximation (4 vertices), ..., N-approximation (number of 2N vertices) are investigated. For each of these approximations, all different ones are drawn ( topologically non - equivalent) diagrams with the same outer lines and numbers of vertices. In each such diagram, specific terms (coefficients) containing (4-) momentum and the binding constant g of the respective interaction are determined for its individual parts - outer lines, inner lines, vertices. Then integration is performed across all momentums. The contributions of all the diagrams are finally added up.
.............. comes to add ?.................

Formation of new particles during interactions
A specific phenomenon in high-energy interactions of particles is the formation of new particles - the emission of additional particles that were not previously present. They can be either particles of the same species as entered into the interaction, or particles of a different species. We explain this phenomenon using Dirac's quantum concept of vacuum *), which is not "empty space", but is filled with virtual particles, resp. pairs of particles and antiparticles. If a sufficiently large gradient of a certain field is created during the interaction at a certain place - a sufficiently large energy is transferred - these virtual particles are transformed into real particles; we observe it as the emission of new particles. Occur at the same time a associated production of particle-antiparticle pairs. A necessary condition for the formation of new particles is the achievement of a sufficiently high energy of interaction - threshold energy, higher than Sm_o.c², where Sm_o is the total rest mass of the resulting particles.
*) Quantum field theory and unitary theory deal in detail with the mechanisms of particle formation. The above-mentioned Feynman diagrams are also used to represent them graphically.
Multiple interactions - cascades of interactions and sprays of particles
When the interaction of high-energy particles in a sufficiently voluminous medium environment, the effect of multiple interaction occurs. The secondary particles, released during the first interaction of the incident primary particle, cause further interactions, producing additional (tertiary) particles, which do the same. From one incident particle, a whole spray of secondary particles is formed in a cascade of interactions. As the evolving spray penetrates to the depth of the material, the number of secondary particles increases and their average energy decreases. Once this energy falls below a certain threshold, the multiplication process will stop and the energy of the particles will be dissipated by ionization and excitation; the number of particles in the spray will decrease until the spray finally disappears. In practice, we distinguish two types of cascade interactions :
¨ Electromagnetic sprays
arising from the interaction of high-energy photons or electrons with atoms of matter. Secondary electrons and photons emitted during the primary interaction, due to paired e^- e⁺ production, Compton scattering, photoeffect and braking radiation, produce additional electrons (+ positrons) and photons; etc.
¨ Hadron sprays
resulting from inelastic interactions of high-energy hadrons with atomic nuclei of the material. Nuclear fragments are formed and new secondary particles are produced - p, n, p, K. The number of these secondary particles is approximately proportional to the logarithm of the energy n ~ ln E.
  In many cases in practice, this spray is not purely hadron or electromagnetic, but mixed. The hadron spray includes pions, which then decay: p^{+, -} ®m^{+, -} + n_m , p^o ®g + g; this leads to the formation of an electromagnetic electron-photon-muon spray that accompanies the hadron cascade. Thus, each hadron spray also has an electromagnetic component. And with the interaction of high-energy photons or electrons, photonuclear reactions emit protons and neutrons, which can enrich the electromagnetic spray with a hadron component. Cascades of interactions and sprays of secondary particles are observed in cosmic rays (see Figure 1.6.7 in §1.6, section "Cosmic rays") and in particle interactions on accelerators (in bubble chambers, trackers and calorimeters).

Effective cross section of particle interactions. Impact parameter .
Similar to chemical and nuclear reactions, interactions of elementary particles take place differently "willingly" - with different efficiencies or probabilities, depending on the type of interaction and energy of the particles. The probability of particle interactions can be illustratively expressed in a geometric way using the so-called effective cross section of the interaction. The effective cross section expresses the probability that the bombardment particle will interact with the target particle in a given specific way.
  The concept of the effective cross-section is based on the illustrative idea that the target particle (black disk in the picture) behaves as an "absorbing body" with a radius r with respect to the incident particle, which this particle either hits and the desired interaction occurs, or it does not hit (misses, flies around) and no interaction occurs. The larger the radius of this body, resp. its effective area s = p .r² - effective cross section, the greater the probability of interaction (probability that the particle "hits").

Expressing the probability of the interaction of a firing particle with a target particle using an effective cross section

The cross section may, but need not be directly related to the "geometric diameter" target particle r_geom or its "geometric cross section" s_geom = p.r²_geom . For "attracting" particles, is s > s_geom , for repellent particles, is s < s_geom . In addition, the same firing particle can cause different interactions on the same target particle, the different probabilities of which are described by different partial effective cross sections. These effective cross sections no longer have anything to do with the geometric dimensions of the particles - they are the result of the internal mechanisms of specific types of interactions (the geometric dimensions of the particles were discussed above in the section "Size of elementary particles ...").
  The unit of effective cross section in the SI system would be m², which is, however, inadequately large and therefore the unit barn (bn) is used in nuclear physics: 1 bn = 10^-28 m², which has the order of magnitude of the proton geometric cross section due to strong interaction (resp. heavy nuclei - so this unit and its bizare name originated in the study of uranium nuclear reactions...).
  The effective cross section of the interaction is very closely related to the absorption coefficient, the so-called linear attenuation coefficient m, in the exponential law of absorption of ionizing radiation in substances. This connection will be clarified in the following §1.6 "Ionizing radiation", passage "Absorption of radiation in matter".
  For specific course of the interaction is important the impact parameter b: it is the geometric distance of centers effective "disks" interacting particles in which around fly throughs or intersect. In the case of small impact parameter b << r_geom with it is a central collision, at larger values of b it is a peripheral collision. If the impact parameter is greater than r_geom , resp. greater than the sum of the effective radii of the two particles (target and flying), there is no longer a direct interaction by the basic mechanism (strong short-range interaction), but particles can interact through their electric fields if they are charged (such a collision is sometimes called ultraperipheral).
Dependence of the effective cross section on energy
  For a given type of particles and interactions, the effective cross section is a relatively complex function of the energy of the incoming particle. The energy dependence of the effective cross-section often has a resonant character: if we change the energy of the interacting particle continuously, significant maxima appear on the curve of the effective cross-section around certain specific energy values. By their shape, these dependences resemble the dependence of current, voltage or impedance in RLC electrical circuits (containing ohmic resistance R, inductance L and capacitance C), on the frequency f of the AC electrical signal around the frequency f_res = 1 / [2pÖ(LC)]. For effective cross section of this kind of interaction was already in 1936, derived important Breit-Wigner relationship *)
                s = (l/2p)².g.G². 1 / [(E-E_r)² + (G/2)²] ,
where E_r is the resonant energy, G represents the width of the excited level of the intermediate state during the interaction, l is the wavelength of the particle, the factor g is a function of the spin ratio of the initial and final states.
*) Breit and Wigner derived this relationship for a special case of elastic scattering of an incident particle in the potential field of a target particle. However, with some modifications, this formula applies to all types of interactions exhibiting resonant maxima of the effective cross section.
  The presence of resonant maxima in the energy dependence of the effective cross section indicates the existence of certain dynamic processes in the interaction - the formation of bound systems, discrete excited states or intermediate particles.

Interactions of high-energy particles
In §1.3 and 1.6, interactions are discussed mainly at lower and medium energies, which lead to characteristic phenomena of excitation and ionization of atoms, or to nuclear reactions associated with the transmutation of atomic nuclei and the emission of nuclear particles. At low energies (less than about 1MeV), the total number of elementary particles before and after the interaction does not change, arise event. only photons that carry away energy during the deexcitation of excited states. If the energies of interacting particles (including gamma photons) exceed the threshold value 2.m_e.c² = 1.022 MeV, new (secondary) particles can be formed during the reaction - a pair of electron e^- and positron e⁺.
  Under the interaction of high energy particles means the reaction induced by particles with an energy which lies above the threshold for the production of mesons p, which is above the energy »140 MeV in the center of gravity system. With increasing energy, such interactions can produce gradually more new secondary particles (mostly p- mesons) and also particles with higher rest mass - mesons K, nucleons and antinucleons, hyperons, bosons W and Z (at the highest energies of many TeV and more are also expected the production of Higgs bosons, supersymmetric particles, leptoquarks and other "exotic" as yet unproven particles).
  When atomic nuclei are bombarded by high-energy particles (eg protons), several nucleons and "splinters" are ejected - the "shatter" or fragmentation of nuclei is occur.
  At the highest energies (of the order of 100 GeV and higher), the interactions are already quite complex and diverse, a large number of secondary particles are produced. In a laboratory (target) system, a narrow beam of secondary particles is formed, especially pions p, collimated forward in the direction of movement of the primary particle - a kind of nozzle or spray of particles. Furthermore, a wider cone of heavier particles and also gamma quanta is formed. In these reactions, the kinematic and dynamic effects of the special theory of relativity are fully manifested - sometimes referred to as ulrarelativistic. During high-energy collisions of heavy particles (protons and especially heavier atomic nuclei), a special mixture of locally free quarks and gluons may form for a short time - the so-called quark-gluon plasma (discussed in more detail below in the section "Quark structure of hadrons", passage "Quark-gluon plasma - 5th state of matter").
   The study of particle interactions at high energies is of great importance for understanding the structure of elementary particles and the nature of forces that operate between them. During a high-energy collision, particles penetrate each other "deep inside" and the result of the interaction can tell something about their structure. Due to quantum processes in the fields of strong, weak and electromagnetic interactions, high-energy collisions create new secondary particles, which are both interesting in themselves and carry important information about the nature of fundamental natural forces, including the possibility of their uniform understanding within unitary field theory. Particle collisions at high energies are a kind of "probe" into the deepest interior of matter *) - and at the same time into the processes of the formation of the universe (see §5.5 "Microphysics and cosmology. Inflationary universe." book "Gravity, black holes and space-time physics"). Specific ways of particle interactions will be described below for individual types of elementary particles.
*) Let's also compare with the left part of Fig.1.0.1 in §1.0. "Physics - fundamental natural science".

Analysis of the dynamics of particle interactions
  High-energy interactions of elementary particles are studied using large accelerators (see section "Charged particle accelerators" below). The accelerator itself is followed by very complicated and precise detection apparatus and systems *) that analyze secondary particles and radiation generated by the interaction of high-energy primary particles with the target material or in mutually oppossite collided beams. They contain a large number of individual detectors of various types (scintillation, semiconductor, ionization), located in strong and specially configured magnetic fields (for the analysis of the momentum of charged particles). By analyzing the type, charge and mass of these flying-out particles, their energies, momentum and emission angles from the site of interaction, a number of parameters of the interactions that occur can be reconstructed. From this it is possible to deduce the structure of elementary particles, the properties of acting fields and interactions, the existence of new hitherto unknown quanta and particles.
*) Large bubble chambers were previously used for this purpose (see §2.2, part "Detectors trace particle"). Now they are replaced by large and complex electronic detection systems (§2.1, section" The arrangement and configuration of the radiation detectors") containing, inter alia, so-called trackers - electronic particle paths detectors. They mainly use multidetector semiconductor systems (§2.5 "Semiconductor detectors"), or systems of special ionization chambers and scintillation detectors.
  Even when a particular intermediate particle decays immediately at the site of interaction (and therefore cannot be detected directly), the products of its decay carry some information about its properties. From the measured energies and momentum these secondry products, the mass of the original particle can be determined. If we plot on the horizontal axis the measured energy of the detected set of particles corresponding to the respective "channel" of decay - secondary particles on which the sought intermediate particle should decay - and plot on the vertical axis the registered number of cases (or normalized per unit energy of primary collided particles, e.g. protons), a small "bump" may appear on the otherwise smooth curve, indicating the existence of a short - lived particle of appropriate rest mass corresponding to the energy on the horizontal axis. Based on the quantum uncertainty relation between the lifetime t of a particle and the uncertainty of determining its rest energy E = m.c² (t.DE » h), the lifetime t of the intermediate particle can be estimate from the stastistic "blur" of the rest mass values.
Dalitz diagram
At the output of detection systems surrounding the site of interaction, a large number of pulses of various sizes, shapes, temporal and angular correlations appear, carrying information about energies, momentums and other parameters of secondary particles. It is by no means easy to find your way around such a large amount of data. For clear display and kinematic analysis products of particle interactions the so-called Dalitz diagrams are sometimes used (diagrams of this type were first compiled by R.H.Dalitz in 1953 during the research of K-mesons and their decays). It follows from the laws of conservation of energy and momentum, that the kinematics of the interaction can be suitably parameterized by the square of the energy of the particles. On the axes of the diagram, the squares of the effective masses»energies of the pairs of daughter particles (products of interaction *), mostly p- mesons, are plotted (in GeV² energy units).
*) If, for example, during the interaction of two primary particles P1 and P2 : P1 + P2 ® A + B + C, three secondary particles A, B, C are formed, we plot m²_AB on the X axis and on the Y axis the values of m²_BC . These squares of masses are equal to the squares of the sums of the 4-momentums of the particles: m²_AB = (p_A + p_B)², analogously to m_BC .
  If the studied type of interaction takes place directly, without being affected by dynamic processes of intermediate particles or resonant states (which is the same from a certain point of view...), the resulting particles are randomly distributed and the distribution of relevant measurement points on the Dalitz diagram is approximately homogeneous, filling the triangular area below the diagonal given the energy used. However, if a short-lived intermediate particle (or resonance process) is formed during the interaction, whose decay products are detected secondary particles, the distribution of measured points on the Dalitz diagram is inhomogeneous - local densities appear (peaks in the profile - slice of diagram) in the areas around the mass of the intermediate particle.
  Analyzes of this kind were previously performed manually with dots drawn on paper. They are now performed using powerful computer technology, diagrams are digitized and displayed using computer graphics, sometimes with color image modulation. Fourier transforms are also introduced to analyze the relationship between the time and energy spectra of the short-lived state of an intermediate particle or resonance. All these methodological approaches are useful not only in the analysis of particle interactions, but wherever we need to distinguish kinematic effects from dynamic ones, to prove the existence of some short-lived bound state that is not directly observable.
Energy dependence of the effective cross-section
This procedure is suitably combined with the analysis of the energy dependence of the effective cross-sections an interaction, whose possible resonant character is expressed by the above-mentioned Breit-Wigner relation. If there are resonant peaks in the energy dependence of the effective cross-section of the interaction and at the same time local densities and peaks are visible on the Dalitz diagram of the energy distribution of secondary particles, it is almost certain that dynamic processes of excited states or intermediate particles occur during the interaction.
Missing energy
If the studied interaction is accompanied by the formation of neutral weakly interacting particles, these cannot be detected in the normal way. Here is a certain possibility an analysis of the energy balance we determine the energies and momentums of other particles and, based on the law of conservation of energy and momentum, we determine the values of energy and momentum that an unknown particle carries away. From them we can then determine the rest mass of an unknown particle.
...? add-other types of diagrams + pictures ..? ...

Properties and interactions of the most important elementary particles
In this section we will briefly approach the individual most significant particles of the microworld, their origin and formation in the interactions of particles, their properties and the main ways in which they interact with each other and with other particles. In this brief description of the properties of elementary particles, we will not stick to the systematics outlined above, but will move from known, widespread and practically used particles to "exotic", less known and more hidden particles, whose significance for the structure and properties of matter is sometimes unknown.

Photons
are a quantum of electromagnetic radiation. They have zero rest mass, they move at the speed of light *), they carry energy E = h.n, where h is the Planck's constant and n is the frequency of the electromagnetic wave of wavelength l = c/n. They are bosons with spin number 1. According to the laws of electrodynamics, photons are generally formed during all accelerated movements of electrically charged particles (eg braking radiation). They are emitted during deeexcitation in atomic shells (visible and UV radiation, characteristic X-rays - §1.1., passage "Radiation of atoms") and atomic nuclei (gamma radiation - §1.2, part "Gamma radiation") , where they carry away the corresponding energy difference of the excited states. Photons of gamma radiation also arise during annihilation of positrons with electrons e⁺ + e^- ® 2g (§1.6, part "Interaction of charged particles - directly ionizing radiation", Fig.1.6.1 below, passage "Interaction of positron (beta ⁺ ) radiation"), as well as in a number of other elementary particle interactions. Here we will consider mostly photons of higher energies - radiation g.
*) However, see the theoretical note on the possible influence of quantum fluctuations of spacetime on the speed of hard radiation g in §1.6: "Is high-energy g- radiation moving slower than light?".
  Interactions of medium energy photons with matter are described in §1.6, part "Interaction of gamma and X - rays", it is mainly a photo effect, Compton scattering, formation of e^-e^{+ -} pairs. High-energy photons (> 10MeV) can, through their interactions, cause so-called photonuclear reactions, in which neutrons, protons, or multiple nucleons, deuterons, a-particle, are ejected from the nuclei. Above the threshold energy of gamma radiation of about 140 MeV, other particles are formed during the interaction, eg p -mesons: g + p ® n + p⁺ , g + p ® p + p^o, etc. At very high energies of gamma photons (> 300MeV) , a number of other particles can be generated, including heavy ones (cf. above "Interactions of high energy particles").
  Photons, as a quantum of electromagnetic waves, were actually introduced by A.Einstein in 1905 during the study of the photo effect (§1.1 "Atoms and atomic nuclei", Fig.1.1.1); the proper name "photon" was later proposed by the American chemist G.N.Lewis.

Electrons and positrons
Electrons e ^-
are basic, truly elementary, stable particles of matter that form the electron shell of atoms. The electron carries a negative elementary charge e = 1.60219.10^-19 C, its rest mass is m_e = 9.1095.10^-31 kg (= 511keV/c²), it belongs to the leptons, it is a fermion with spin (1/2) h. The magnetic moment of an electron is e.h/4p m_e - the so-called Bohr magneton. According to the ideas of modern cosmology, electrons were formed in the earliest stages of the evolution of the universe after the Big Bang, during the separation of electromagnetic and weak interactions. In addition, electrons are formed in a number of processes and interactions of other elementary particles, such as in b^- -radioactivity n^o ® p⁺ + e^- + n_e´ and in many other processes, as can be seen from the interactions of other particles described below. In addition to atomic and nuclear physics, electrons play a key role in electromagnetic phenomena, the vast majority of which are based on the motion of electrons that generate electric current.

1895: J.J.Thomson - discovery of electrons => first model of atom
The electron was discovered, as the first elementary particle of the structure of matter, in 1895 by J.J.Thomson during the study of electric discharges in gases in a cathode ray tube.

Positron e ⁺
is an antiparticle to the electron, so it has the same mass and spin, the electric charge is the same size, but of the opposite (positive) sign. In a vacuum, a positron is a stable particle, just like an electron. However, as soon as it is in a material environment filled with atoms and therefore also electrons, it disappears in annihilation interaction with electrons: e⁺ + e^- ® 2 g (§1.6, section "Interaction of charged particles - directly ionizing radiation", Fig.1.6.1 below passage "Positron (beta ⁺ ) radiation interactions"), producing two quantums of gamma radiation of 511 keV energies, flying out in opposite directions (at an angle of 180°). This perfect angular correlation is advantageously used in gamma imaging by positron emission tomography imaging in nuclear medicine after the application of a positron beta⁺-radionuclide, e.g. ¹⁸F (§4.3, section "Positron emission tomography PET").
Note : These patterns apply exactly only in the center of mass frame of reference of the positron and an electron. The energy of photons 2x511 keV is a consequence of the law of conservation of energy (resting energy of the electron and the positron is m_0e .c² = 511keV), the opposite direction of 180° is a consequence of the law of conservation of momentum. In the case of collisions of positrons and electrons of higher energies, the angle of inclination of annihilation photons would differ from 180°. In the material environment, however, the positron and the electron have relatively low velocities at the moment of annihilation, so that the emitted quantums actually fly in almost opposite directions.
Positronium
Just before the actual annihilation, the electron e^- and the positron e⁺ can orbit around itself for a moment (they orbit the common center of gravity) - they form a special bound system (similar to a hydrogen atom) called positronium (Ps). The dimension of the "atom" of the positronium is twice the hydrogen atom, the binding energy of the positron is 6.8 eV. Depending on the mutual orientation of the electron and positron spins, the positronium can be either in the singlet state ¹S₀ with oppositely oriented spins - so-called parapozitronium p-Ps (1/4 cases), or in the triplet state ³S₁ with consistently oriented spins - so-called orthopositonium o-Ps (3/4 cases).
  However, this system of positronium is unstable, the two particles approaching each other in a spiral under the emission of electromagnetic waves; in p-Ps in about 120ps they "fall" on each other and there is a self-annihilation on two photons g, each with an energy of 511 keV. In the case of o-Ps, annihilation to two photons is prohibited by quantum selection rules (related to the law of conservation of the spin momentum - each of the photons has spin 1), so o-Ps would decay in a vacuum with a relatively long lifetime of about 140ns emission of 3 photons with a continuous energy spectrum (the total energy of 1022 keV is divided by photons in a stochastic manner). In the substance, however, the positron bound in o-Ps much earlier is enough to annihilate with some "foreign" electron from the environment, which has the opposite spin orientation - again, two photons g with energies of 511 kV are formed.
  The annihilation of a positron with an electron produces 2 gamma photons in the vast majority of cases, as mentioned above. Sometimes, however, there may arise more, but with a very small probability (the probability that 2 + n photons will be formed during e^-e⁺ annihilation is proportional to a^-n, where a = 1/137 is the fine structure constant). If a positron interacts with an electron bound in an atomic shell, the extinction of such a pair may be accompanied by the emission of only a single photon, and some of the energy and momentum may be transferred to either the atomic nucleus or one of the other electrons; however, the probability of this process is very small and does not apply in practice.
  The lifetime of positrons in substances is in the order of hundreds of picoseconds. However, the exact value depends on local electron densities and configurations, which is used in the spectroscopic method PLS (Positron Lifetime Spectroscopy ....). Material tested locally irradiated b⁺- g emitter (usually ²²Na), the lifetime of positrons is determined by measuring the delayed coincidence between the detection of photon radiation g of irradiating radionuclides (from ²²Na, it is g 1274 keV) and the detection of the annihilation photons g 511 keV.
  In terrestrial nature, therefore, positrons do not normally occur permanently, they occur only for a short time during certain interactions of elementary particles and then (for about 10^-10 -10^-7 s) again annihilate with electrons. The most common process in which positrons are formed is b⁺-radioactivity caused by the conversion of the proton p⁺ in the nucleus into neutrons n^o, positron e⁺ and neutrino: p⁺ ® n^o + e⁺ + n_e (§1.2, part "Radioactivity b⁺"). Positrons are also relatively common products in the interaction of particles at high energies (will be shown several times below) and in the decay of muons and pions (see below "Muons m and tauons t"); thus they occur in secondary cosmic rays (see the passage "Cosmic rays" in §1.6). Positrons can also be formed with the aid of gamma radiation: if the higher energy gamma rays than 1022 keV, one way of its interaction with matter is the formation of an electron-positron pairs (§1.6, section "Interaction of gamma rays and X" passage "Formation of electron- positron pairs").
  For completeness, we will mention one "exotic", not yet realized in practice, method of positron formation :
Breit-Wheeler process of e⁺ e^- pairs production
According to quantum electrodynamics the electron-positron pair could theoretically be formed even when two photons collide g₁ + g₂ ® e⁺ + e^- ; it is an inverse process to the above annihilation of a positron with an electron: e⁺ + e^- ® 2g (G.Breit and J.A.Wheeler designed it in 1934). However, this two-photon process has a very low probability (slight effective cross-section), which would require extremely intense collimated beams of gamma photons with an energy higher than 511keV; upon detection, the desired effect would be covered many times by much stronger secondary radiation - so far it has not been possible... Another possibility of photoproduction could be the so-called multiphoton Breit-Wheeler process (...), in which high-energy photons, when passing through a very strong electromagnetic field, could decay into electron-positron pairs. Here is a possibility of realization in the near future using high-power laser systems ...
  History: In 1932, the positron first observed C.D.Anderson in cosmic rays detected by a Wilson nebula camera placed in a magnetic field, where a trace of particles with the same ionization properties as an electron appeared, but with in the opposite direction of rotation in a magnetic field, ie a "positive" electron.

Protons and neutrons
Protons and neutrons, collectively called nucleons, are the building blocks of atomic nuclei. These are heavy particles from the group of baryons, they show a strong interaction which ranks them among the hadrons - they are composed of 3 quarks. They are of natural origin - they originated in the "fiery furnace" of the Big Bang at the beginning of the so-called hadron era, in the first millionth of a second of the universe's existence. In addition, they arise in a number of processes and interactions of other elementary particles; during radioactive transformations of b^{- , +} there are mutual transformations of neutrons and protons (§1.2, passage "Mechanism of decay b. Weak interactions.").
  Protons, as nuclei of hydrogen, were discovered in the study of electric discharges in gases at about the same time as electrons (late 19th century). Neutrons were discovered only in 1932 by J.Chadwick during the bombardment of beryllium nuclei with alpha particles (§1.1 "Atoms and atomic nuclei", part "Construction of the atomic nucleus").
Proton p ⁺
carries a positive elementary electric charge of the same absolute magnitude e as the electron, its rest mass is m_p = 1.6726.10^-27 kg = 1836.151 m_e = 938.256 MeV/c². The magnetic moment of a proton is e.h/4p m_p - the so-called nuclear magneton, which is 1836 times smaller than Bohr's magneton (simply put, we can imagine that at the same spin and charge, a heavy proton "rotates more slowly" than a light electron). A proton is a stable particle (omitting here some speculation about the possible decay of a proton *). The number of protons in the nucleus (proton number Z) also determines the number of electrons and their energy levels in the shell - and therefore the "size" of the atom and its chemical properties when combined with other atoms. The proton itself forms the core of the simplest element - hydrogen ¹H₁. Free protons are encountered in ionized hydrogen plasma and in nuclear reactions in which accelerated protons enter or are their products. Protons are the most common particles that are accelerated in accelerators for the purposes of nuclear physics (see the chapter "Charged particle accelerators" below). The number of protons in the atomic nucleus indicates the proton (atomic) number Z , which also determines the number of electrons in the atomic shell and thus the chemical properties of the atom - the position of the element in Mendeleev's periodic table.
*) Instability of proton ?
The so-called grandunification theories admit the instability of a proton, which should decay into muons or positrons and into one neutral or two charged pions [p⁺ ® (m⁺ or e⁺) + (p^o or p⁺ + p^-)] with a lifetime of the order of t_p » 10³⁰ -10³³ years. This decay would be caused by the conversion of a quark to a lepton via the X boson, and due to the enormous mass of the X boson, its probability is extremely small. Experiments so far give estimates of t_p > 10³⁰ years. These attempts to observe proton decay are made deep underground (due to cosmic ray shielding), where large water tanks are located, equipped with many photomultipliers that could detect faint flashes caused by the passage of fast particles formed as proton decay products. The most perfect device of this kind is the Superkamioka-NDE in Japan, which did not detect any proton decay, but was very successful in the detection and spectrometry of neutrinos (see the "Neutrinos" passage in §1.2 "Radioactivity").
Note: Another hypothetical and very curious mechanism could be the decay of a proton through a virtual black hole (§4.8 "Astrophysical significance of black holes" in a monograph "Gravity, black holes and spacetime physics"). Black mini-holes emitting by quantum Hawking mechanism the particles that are generally different from those that the black hole swallowed, violates the law of conservation of baryon number (§4.7 "Quantum radiation and the thermodynamics of black holes" in the same book). Therefore, if two quarks in a proton fall into a virtual black mikro-hole, it is possible to back emission of e.g. antiquark and leptons, thereby proton converted into muon or electron and pion.
Neutron n ⁰
is electrically neutral and its rest mass m_n = 1.6748 .10^-27 kg = 1838.65 m_e = 939.55 MeV/c² is slightly higher than the proton. In stable atomic nuclei, neutrons are stable, the free neutron (in vacuum) decays with a half-life of about 13 minutes by b^--radioactivity of n^o ® p⁺ + e^- + n'_e into proton, electron and antineutrino. Free neutrons are not commonly encountered in terrestrial nature, in the upper layers of the atmosphere a smaller number of them are formed during interactions of cosmic radiation (§1.6, section "Cosmic radiation"). However, they are common products of nuclear reactions and are also willing to enter into nuclear reactions (§1.3, passage "Reactions induced by neutrons"). Intensive sources of neutrons are nuclear reactors, whether fission or so far experimental fusion thermonuclear (§1.3, part "Fission of atomic nuclei" and "Fusion of atomic nuclei"). As laboratory neutron source are constructed as small specific accelerators of charged particles (mostly deuterons with tritium target) called neutron generators (see below "accelerators of charged particles," passage "neutron generators"), or radioisotope source consisting of a mixture a -radionuclide with light element (such as a mixture of americium and beryllium, the reaction a, n), or a heavy transuranic radionuclide (most often californium 252), during the spontaneous fission of which neutrons are released (§1.3, "Transurans").
Origin of the masses of protons and neutrons
Protons and neutrons are much heavier than the sum of the masses of their quarks. E.g. the proton has a mass of 938MeV, while the mass of the "u" quark is 2MeV and the "d" quark is 5MeV. Therefore, most of the mass of a proton comes from the kinetic energy of the internal motion of its quark components. This is explained on the basis of quantum uncertainty relations, according to which the product of uncertainty in the position and momentum of a particle is greater than the Planck constant. Quarks are enclosed in a proton or neutron ("imprisoned") in a spatial area with a diameter of aprox. 10^-13 cm; this forced very small uncertainty in position quantum, implies considerable momentum and thus the kinetic energy of each of the quarks, at least about 200MeV. The kinetic energy balance of such three intensely oscillating quarks is approximately equivalent to the mass of the proton.
  If all quarks had the same mass, one would expect the proton to be slightly more massive than the neutron, because the electric charge of the proton (which the neutron does not have) contributes to its internal energy. However, the difference in the mass of the "u" and "d" quarks (which is explained in unitary field and particle theories by interaction with the Higgs field - see below) causes the neutron (u, u, d) to be somewhat "heavier" than the proton (u, d, d). This difference in mass causes the instability of the free neutron, its b^--decay into proton, electron and neutrino by weak interaction.
Antiparticles to protons and neutrons
Antiproton p' ^- differs from a proton only in its negative charge and the opposite direction of the magnetic moment, in a vacuum it is also a stable particle. The antineutron n' ⁰ is a neutral particle like a neutron, from which it differs only in the opposite orientation of the magnetic moment, its half-life in vacuum is the same as that of a neutron, it decays according to the scheme n'^o ® p'^- + e⁺ + n_e to an antiproton, positron and neutrino.
  Antiprotons and antineutrons are not commonly found in terrestrial nature, they are formed by the interaction of high-energy particles and then disappear by interactions with nucleons. Due to the law of conservation of the baryon number, antinucleons can only be produced in pairs together with nucleons. The most common way of producing antiprotons p' is in reactions p + p ® 2p + p + p' , resp. p + n ® 2p + n + p' ,
while the threshold kinetic energy of the firing proton (in the laboratory target system) is about 5.6 GeV, resp. 3.6GeV; however, if this interaction occurs during nuclear bombardment, the threshold energy of antiproton production may be lower (around 3GeV). Antineutrons are formed in similar reactions p + p ® 2p + n + n' , resp. p + n ®p + 2n + n', furthemore in reactions antiprotons p' + p ® n + n' , p' + n ® n + n' + p^-.
  In antinucleon interactions, the most important are the interactions (p', p) of antiprotons with protons. At high energies, other heavy particles such as hyperons can be formed here, which will be mentioned below. At low energies of antiprotons or when they are stopped (see below), leads to nucleon pairs annihilation with the production of mesons, quantum gamma, or there is a reaction p' + p ® n + n' occurs ("charge exchange"). The extinction of pairs (p', p) is a strong interaction, in which mesons p *) are most often formed (only in a small percentage of mesons K); the smallest number of formed mesons with respect to the law of conservation of momentum are 2 mesons p, but most of them enter more, most often 5 mesons - a typical interaction of this kind is: p' + p ® 2p⁺ + 2p^- + p^o.
*) The formation of mesons p during the annihilation of an antiproton with a proton is due to the quark structure: antiquarks in the antiproton and quarks in the proton combine into quark-antiquark pairs, which are mesons.
  When an antiproton enters a substance, atoms are ionized by electromagnetic interaction, just like any other charged particle, thereby the antiproton braking and slowing down. During this deceleration may antiproton disappear when interacting with the nucleus, but can be slow (or almost stopped) so much, that it can be trapped by a proton (hydrogen nucleus) - a new "exotic atom" is formed, called protonium, consisting of a proton and antiproton orbiting a common center of gravity. Similarly, it can be captured by another heavier nucleus on some higher orbit (where eject the electron) and during its orbit it then passes to lower orbits, which is accompanied by the emission of either X-ray photons or Auger electrons. Finally, it is absorbed by the nucleus and disappears by interaction with a proton or neutron to produce pions.
Antimatter 
Antiproton around which revolves positron constitute atom of "antihydrogen", which has similar properties as normal hydrogen. Antiprotons and antineutrons can form "anti-atomic nuclei" around which positrons can orbit in exactly the same configurations as the respective ordinary atoms - they are "antiatoms", that would have exactly the same chemical and spectroscopic properties like our atoms, within the "anti-world" - they would form antimatter - (discussed above, the passage "Antiparticles, antimatter, antisworlds").
  History: The antiproton was discovered in 1955 at an accelerator in Berkeley while bombarding a copper target with protons accelerated to 6.2 GeV. In 1956, an antineutron was discovered on the same accelerator: a beryllium target was bombarded with protons with the same energy and the resulting antiprotons were led to a system of scintillators and a Cherenkov detector connected in anticoincidence, where antineutrons were formed by the reaction of p'+ p ® n + n' with hydrogen nuclei produced antineutrons, which when interacting with nucleons in the Cherenkov detector were registered as intense flashes.

Neutrinos and antineutrinos (for more details, see the link "Neutrinos - "ghosts" among particles")
These are ubiquitous but almost elusive particles. Neutrinos n and antineutrinos n' are the lightest and weakest interacting of all known types of elementary particles - they belong to the leptons. They are fermions with spin number 1/2, they do not carry an electric charge, they do not show a strong interaction, but only a weak interaction (and a universal gravitational interaction, which we are not interested in here from the point of view of elementary particle physics, can have certain Cosmological consequences). We recognize three types of neutrinos: electron neutrino n_e , muon n_m and tauon n_t neutrinos, which, however, can spontaneously transform each other during the so-called neutrino oscillation. Neutrino as such is a mixing of the proper states of electron, muon and tauon neutrino and therefore there is a periodic transformation of one neutrino to another.
  Electron neutrinos are typically formed during the mutual transformations of neutrons and protons by b^-,+ -decay: n^o ® p⁺ + e^- + n'_e , p⁺ ® n^o + e⁺ + n_e , muon and tauon neutrinos then during the decay of muons and tauons: m^- ® e^- + n'_e+ n_m , t^- ® n_t + e^- + n'_e , t^- ® n_t + m^- + n'_e , ......
In addition, neutrinos arise in a number of interactions of elementary particles in which weak interactions take place. Large amounts of neutrinos are formed during thermonuclear reactions inside the Sun and stars, from where, thanks to their very weak interaction, they easily penetrate outside and are radiated into the surrounding space. A extremely strong "flash" of neutrino radiation occurs during a supernova explosion - see §4.2 "The Final Phases of Stellar Evolution. The Gravitational Collapse" of the book "Gravity, Black Holes and the Physics of Spacetime". There is also a huge amount of so-called relict neutrinos in the universe, originating from the lepton era of the universe just after the Big Bang. Neutrinos, along with photons, are among the most abundant particles in universe. Properties of neutrinos, their origin, detection methods and possibly the cosmological significance of neutrinos are described in more detail in §1.2 "Radioactivity", part "Neutrinos - "ghosts" between particles".
  Neutrinos were introduced as hypothetical particles by W.Pauli in 1930 in the study of the energy balance of b- decay (see §1.2, part "Radioactivity beta", Fig.1.2.3), their name and specification of properties come from E.Fermi. Neutrino was experimentally demonstrated only in 1956 by experiments outlined in the mentioned reference "Neutrinos...".

Muons m and tauons t
Muons m ^- and m ⁺
(they are antiparticles each other), also referred to as "heavy electrons", are medium-heavy particles with mass m_m = 206 m _e, carry a negative or positive electric charge of the same size as the elementary electron charge; there are no neutral muons without electric charge. Muons are unstable particles that decay with a half-life of » 2.10^-6 s. to an electron , resp. positron, and two neutrinos: m^- ® e^- + n'_e + n_m , m⁺ ® e⁺ + n_e + n'_m . This decay has the character of a weak interaction and is similar to the radioactive decay of beta; also the energy spectrum of electrons or positrons here is continuous, the maximum energy is »53 MeV.
  Muons occur in terrestrial nature in secondary cosmic rays (see the passage "Cosmic rays" in §1.6). They are formed in the upper layers of the atmosphere (above 10 km) during the collisions of protons and other particles of primary cosmic radiation with protons and neutrons in nitrogen and oxygen nuclei in the atmosphere. In these primary collisions, p-mezons are formed first, which decay into muons during about 2.510^-8 s, which move with a kinetic energy of about 4 MeV at a relativistic speed. Due to its lifetime of »2.10^-6 seconds, according to classical mechanics, the muon would fly only about 500 meters and then disintegrate - so virtually no muons should hit the Earth's surface. However, due to the relativistic dilation of time , the muon "lives longer" from the point of view of the observer on Earth and has enough time to hit the Earth's surface. This experimental fact that the muon flies a path 20 times longer than would correspond to its lifetime in classical mechanics, is convincing evidence of the effect of slowing the flow of time according to a special theory of relativity.
  The most common way of forming muons is during decay p -mesons: p^- ® m^- + n'_m , p⁺ ® m⁺ + n_m (see the following passage "Mesons p and K"). The interactions of muons with nucleons proceed according to the scheme: m^- + p ® n + n_m , m⁺ + n ® p + n_m , .....   
  If a negative muon m^- enters into matter, it can (after its slowing down by ionization) be captured by the Coulomb field of the nucleus and form a peculiar bound system similar to an atom - the so-called muon atom or mesoatom. A positive m⁺ mion passing through the medium can in turn capture the electron and form an unstable bound system of the m⁺ mion and the orbiting electron e^-, called the mionium; it is a system analogous to positronium and has a structure similar to a hydrogen atom.
  The muon m was discovered in 1936 by C.D.Anderson and S.H.Neddermeyer while studying cosmic rays in the Wilson nebula chamber (similar to a positron).
Tauons t^- and t⁺
(they are antiparticles each other), also referred to as "superheavy electrons", are very heavy particles with mass m_t » 3484 m_e » 1177 MeV/c², carrying a negative or positive electric charge of the same magnitude as the elementary charge of an electron. Tauons are highly unstable particles that decay to an electron or muon and two neutrinos with a half-life of »3.10^-13 s: t^- ® e^- + n'_e + n_t , t^- ® m^- + n'_m + n_m . However, due to their high rest mass, tauons are able to decay even into hadrons, especially pions p^-, p⁺, p^o and tauon neutrinos, eg. t^- ® p^- + n_t , t^- ® p^- + p^o + n_t , t^- ® p^- + p⁺ + p^- +n_t , etc.
  Tauon t was discovered in 1974-77 by a team led by M.Perl during experiments with high-energy collisions of positrons and electrons in the beams of the accelerator at Stanford. During the collisions of electrons with positrons, t⁺ and t^- pairs were formed, which flew only a short distance (about 1 mm) and then decayed into electrons, muons and neutrinos. The formation of tauons was proved on the basis of the detection of charged particles, analysis of their energies and angular distribution (by the methodology mentioned above "Analysis of the dynamics of particle interactions").

Mesons p and K
p -mesons (also called pions)
are the most common type of new secondary particles, formed by particle interactions at high energies exceeding about 300MeV; at even higher energies (above »1 GeV) K-mesons and hyperons are also formed.
  The mesons p and K have the following common properties: they are medium-heavy particles with spin 0 (thus belonging to the bosons), show strong interactions (they are hadrons) and are very unstable. According to the standard model of particles, they consist of a bound quark and an antiquark.
  Charged mesons p ^- and p ⁺, which are antiparticles to each other, carry a negative or positive elementary charge of the same size as an electron, have a rest mass » 2.4898.10^-25 g »273 m_e » 140 MeV/c² and with a half-life » 2.55.10^-8 s disintegrate (by weak interaction) to muons and neutrinos: p^- ® m^- + n'_m , p⁺ ® m⁺ + n_m (muons then decompose further into electrons and neutrinos). During this decay, kinetic energy is released (m_p -m_m).c² » 34 MeV, of which the muon m carries out a smaller part of about 4.2 MeV and the rest of the kinetic energy of less than 30 MeV is obtained by the muon neutrino n_m .
  In addition to particle interactions in accelerators, pions are formed for a brief moment in the upper atmosphere during the interactions of high-energy protons from primary cosmic radiation with nucleons in the nuclei of nitrogen, oxygen and carbon; they immediately decay into muons (see the "Cosmic Radiation" passage in §1.6).
  The neutral meson p ^o has a rest mass of »264 m_e » 135 MeV/c² and with a very short half-life »0.9.10^-16 s decays (by electromagnetic interaction) into two quantum gamma: p^o ® g + g.
  Note : In terms of internal structure, mesons are a bound quark-antiquark system. However, this system is unstable and its disintegration can be simply understood as a process of "annihilation" of a quark-antiquark pair; either by a weak interaction via the intermediate boson W^± , or electromagnetically directly on the quantum g (cf. the corresponding Feynman diagram in Fig.1.5.1). It is a bit analogous to the positronium mentioned above, which is also an unstable bound state of a particle-antiparticle pair (e^- - e⁺), which annihilate to quantum g .
  p- mesons have played a varied and interesting role in the history of nuclear physics. For a long time (40s-70s), they were considered to be exchangeable particles, mediating strong short-range nuclear interactions of protons and neutrons in the nuclei of atoms (comes from H.Yukawa). The fact that pions are often formed during high-energy collisions of protons and neutrons also seemed to indicate this. Idea p -mezons as carriers of strong interactions, however, did not work in the end. It turned out that the essence of a strong interaction lies deeper - it lies in the internal quark structure of protons and neutrons. During the interactions of protons and neutrons, pions are formed not as exchangeable particles, but because p -mesons are lighter and simpler particles also composed of quarks (and their antiparticles), just like nucleons. Nevertheless, p- mesons are the most important of all unstable "exotic" particles; they may have perhaps a practical use, see eg §3.6, section "Hadron radiotherapy".
K mesons ,
also called kaons, are more than 3 times heavier than p- mesons.
  Charged mesons K ⁺ and K ^- , which are mutually antiparticles, carry a positive or negative electric charge of the same size as an electron, have a rest mass » 966.6 m_e » 494 MeV/c² and with a half-life » 1.24.10^-8 s decay into p -mesons, muons and neutrinos: K⁺®p⁺+p^o, K⁺®m⁺+n, K⁺®p⁺+p⁺+p^-, K⁺®p⁺+p^o+p^o, K⁺®p^o+m⁺+n, K⁺®p^o+e⁺+n; by analogy (associated) also K^-.
  The neutral meson K ⁰ has a mass of » 974.2 m_e » 498 MeV/c² and decays very rapidly into p -mesons and also into muons, electrons and neutrinos by two types of decays :
two- particle decays : K^o ® p⁺ + p^- , K^o ® p^o + p^o, - (half-time » 0.9.10^-10 s) ;
three-particle decays: K^o® p^o+p^o+p^o, K^o® p⁺+p^-+p^o, K^o® p^+,-+m^-,++n, K^o® p^-,++e^+,-+n, - (half-time » 5.7.10^-8 s).
  The fact that the meson K^o decays with two different half-lives and different processes, can be explained by the assumption that the meson K^o is a quantum "mixture" of two neutral particles K^o _L ("Long") and K^o _S ("Short"), which have different lifetimes and different decay patterns. These facts are interpreted as the observed meson K^o being internally a "mixture" or superposition of K^o and its antiparticle K'^o. Between these two states, the neutral kaon spontaneously "oscillates".
Interactions of mesons p and K 
Mesons p^- and p⁺ interact with nucleons at low energies mainly by reactions: p^- + p ® n + g , p⁺ + n ® p + g , at high energies pions there is also a combined production of kaons, hyperons and antihyperons, eg p^- + p ® K⁺ + K^- + n , p^- + p ® L + K^o, etc. - for further reactions, see the section on hyperons below.
  When interacting with the substance, p^- mesons may be (after appropriate braking by ionization energy losses) captured in orbit around the nucleus (similar to electrons in an atom), so for a very short time a mesoatom is formed with a pion p^-, which is then absorbed by the nucleus and there it combines with a proton (p^- + p ® n + g).
Formation of mesons p and K 
p -mesons are formed mainly as new secondary particles during interactions of protons with nucleons, if the kinetic energy in the laboratory (target) system is higher than 2.m_p.c² » 300 MeV. There can be several reactions of this type :
p+p ® p+n+p⁺, p+p ® p+p+p^o, p+n ® n+n+p⁺, p+n ® p+p+p^-,
p+n ® p+n+p^o, n+n ® n+p+p^-, n+n ® n+n+p^o , ....,
while these reactions can take place both on free nucleons and on nucleons bound in the nucleus. Pions can also be produced by photonuclear reactions of hard gamma radiation: g + p ® n + p⁺ , g + p ®p + p^o, whose gamma radiation threshold energy is about m_p.c² » 140 MeV.
  Mesons K are formed by the so-called associated production in pairs either together or in pairs with hyperons, either by mutual interactions of nucleons or p- mesons with nucleons. Examples of such interactions are: p + p ® L + K⁺ + p , p^- + p ® K⁺ + K^- + n , p^- + p ® L + K^o, etc.; other combinations with hyperons are given in the following section.
The strangeness of particles
These K-mesons, as well as the hyperons mentioned below, have some special - "strange" - properties that we do not encounter in other particles. These are asymmetries in the production and decay of these particles. These particles are formed in high-energy hadron collisions with a high probability - pair production by strong interaction. However, their decay is usually relatively slower (on the order of 10^-10 s) through weak interaction. To explain this situation, a new quantity or (additive) quantum number called strangeness S was introduced (for ordinary particles is S = 0, strange particles have S = ±1, ± 2, hyperon W even S = -3), which is preserved in strong interactions, but not in weak interactions. This explains that with strong interactions of ordinary particles, strange particles are formed in pairs, the sum of the strangeness of which is zero, but by a weak interaction, the strange particles can decay into particles without strangeness.
  To explain the new quark model of hadrons, a new quark "s" (strange) has been introduced, which carries strangeness; quark s has strangeness S = -1, antiquark s' has S = 1, other quarks S = 0. The presence of the quark "s" in a two-quark combination is characteristic of strange mesons K, if "s" occurs in a three-quark combination, there are hyperons - Fig.1.5.3.

Hyperons
The heaviest particles known to date (except tauons), resulting from high-energy particle interactions, are hyperons. All hyperons are fermions, mostly with spin 1/2, except W^- which has spin 3/2. Furthermore, all hyperons are hadrons showing a strong interaction and are highly unstable particles with a very short lifetime. We know 7 types of hyperons (+ their antiparticles), which we briefly list here :
Hyperon L ^o is electrically uncharged, has a mass of »2183 m_e » 1116 MeV/c², lifetime » 2.5.10^-5 s. and disintegrates according to the schemes: L ® p + p^- (66%), L ® n + p^o (34%).
Hyperon S ⁺ with a positive elementary charge has a mass of »2327 m_e » 1189 MeV and with half » 0.8.10^-10 s. decays per nucleon and pions: S⁺ ® p + p⁰ , S⁺ ® n + p⁺.
Hyperon S ^- with negative elementary charge has weight »2340 m_e » 1197 MeV and with half-life » 1.65.10^-10 s. decays into neutron and pion: S^- ® n + p^-.
Hyperon S ⁰ without electric charge has a mass of »2332 m_e » 1193 MeV and with a very short half-life close to 10^-20 s it decays into a hyperon lambda and a photon gamma: S^o ® L + g.
Hyperon X ^- with negative charge, weighs »2585 m_e » 1321 MeV and with half-life » 1.7.10^-10 s decays into hyperon lambda and pion: X^- ® L + p^-.
Hyperon X ⁰ - uncharged has weighs »2566 m_e » 1315 MeV and half » 3.10^-10 s decaying into lambda hyperon and pion: X⁰ ® L + p⁰.
Hyperon W ^- with negative charge has a weight of »3405 m_e » 1675 MeV/c² and with a half - life » 1.5.10^-10 s decays into hyperons and mesons: W^- ® X^{o, -} + p^{-, o} , W^- ® L + K^- .
Note: In a very small percentage of cases, other possibilities of hyperon decay were observed, eg L® p + e^- + n , S⁺ ® p + g , X^o ® p + p^-, and many others.
Hypernuclei
  Hyperons show strong interactions, so they can enter the nucleus and be bound there by nuclear forces - a so-called hypernucleus or hyperfragment is created. In a typical hypernucleus, one of the neutrons is replaced by the hyperon L^o; such hypernuclei then represents ^NA_L. E.g. in nuclear emulsions irradiated with mesons K^- from the accelerator, hypernuclei ⁹Be_L were observed. Hypernuclei are unstable formations that decay in two ways: by meson decay or by nucleon decay. In the meson method, the hyperon L inside the nucleus decays according to the scheme L® p + p^- , or L® n + p^o, so for example the hypernucleus ⁹Be_L decays into the meson p^-, the proton p⁺ and the nucleus ⁸Be₄ (which in this case then decays into two alpha-particles ⁴He₂). During nucleon decay, L + p ® p + n, or L + n ® n + n reactions occur, so that, for example, the mentioned ⁹Be_L hypernucleus would decay in the following way: ⁹Be_L ® ⁴He + ³He + n.
Antihyperons
Similar to nucleons, there are antinucleons, so for each of these hyperons there is a corresponding antihyperons (all these hyperons are separate, they are not antiparticles, as is the case with mesons p^- and p⁺ or m^- and m⁺). According to the principle of charge symmetry, antihyperons have the same mass, spin and lifetime as hyperons, but the opposite signs of el. charge, baryon number and magnetic moment. The decay patterns of antihyperons are also charge-associated with the decay patterns of hyperons, as well as the reactions of particles in which antihyperons are formed are analogous to hyperons (there is often "associated" production of hyperons and antihyperons or mesons - see below). It should be borne in mind that antihyperons to charged hyperons have opposite signs of el. charges, eg antihyperon S'^- has a positive unit charge, so we could more accurately label it as ( S'^-)⁺.
  Hyperons formed by the interaction of protons, antiprotons, p and K mesons with nucleons at high energies (> » 5 GeV), wherein the strong interactions of the type (nucleon-nucleon) or (p + nucleon) two particles from the group of mesons and hyperons (meson + meson, hyperon + meson, hyperon +antihyperon) are formed simultaneously - there is a combined or associated production of hyperons, antihyperons and mesons, eg.:
p + p ® 2p + L + L' , p + p ® p + L + K⁺ ,
. ...........
.............
.............
K^- + p ® W^- + K^-+ K^o .
  Hyperon paths, resp. of their decay products are observed in Wilson nebulae chamber, nuclear photoemulsions and bubble chambers. Already in 1947 C.C.Butler and G.D.Rochester observed in the study of cosmic rays in a cloud chamber tracks of two particles rising from one point - further research showed that it was a K^o meson decaying into mesons p^- and p⁺ and the hyperon L crumbling on proton p⁺ and meson p^-. When accelerators with sufficiently high energy made it possible to form beams of protons and mesons p, all other hyperons and regularities of their associated production with mesons K were discovered during the study of their interaction in bubble chambers and photoemulsions.

Resonances
Form during some interactions of high-energy particles (such as p^{+, -} + p⁺ ® p^{+, -} + p⁺, or interactions of a proton with an antiproton to form several p- mesons) and immediately decay, their lifetime is about 10^-23 to 10^-20 seconds. They are manifested only by a significant resonant maximum in the energy dependence of the effective cross section of the given interaction, or by densities and peaks on the Dalitz diagram of energies of secondary particles, which indicate the formation of some temporarily bound state. We recognize baryon resonances and meson resonances (such as meson r or some types of mesons *K). Resonances are often not even considered special particles, they are called quasiparticles. Rather, they are only temporarily excited states created by the interaction of two or more baryons or mesons, which decay as soon as they fly beyond the region of the strong nuclear interaction in which they originated. Due to the extremely short lifespan, they probably have no significance for the structure and properties of matter. However, their study is important for better penetration into the subnuclear structure of hadrons, their quark structure and understanding the properties of strong interactions within quantum chromodynamics (QCD). Some meson and baryon resonances are marked below on the quark diagram in Fig.1.5.3.

Bosons W ^- , W ⁺, Z ⁰
These bosons are intermediate particles mediating weak interaction (Weak int.) within the Weinberg-Salam model of unification of electromagnetic and weak interaction.
  W^- and W⁺ carry a negative and a positive elementary charge of the same size as an electron, they have a mass of »82 GeV/c², they are their antiparticles to each other. W-bosons mediate mutual b -conversion of neutrons and protons (according to the scheme in Fig.1.2.5 in §1.2 "Radioactivity", passage "Mechanism of decay b. Weak interaction."). In this radioactivity b the W-bosons causes conversion of "u" and "d" quark inside nucleons, which themselves W remain virtual - it immediately decays into the resulting quark, electron or positron and neutrino.
  The neutral Z⁰ boson has a mass of » 93 GeV and is its own antiparticle. Z⁰ is less important than W, it does not show much in Earth nature or in the present universe. However, it was apparently more significantly used in high-energy processes in the extreme conditions of the very early universe (possibly also during a supernova explosion..?...) - it can mediate mutual interactions between neutrinos (§1.2, passage "Interaction of neutrinos with particles and matter").
  When W or Z is formed by the high-energy interaction of particles, they are highly unstable (with a lifetime of approx. 3x10^-25 sec.*) and then break down into leptons and neutrinos; typically: W^-® e^- + n', W⁺® e⁺ + n, Z^o® m⁺ + m^- (or e⁺ + e^-). Or for quarks and antiquarks. At very high energies, there are many other possibilities for their interactions, including the production of heavy particles such as Higgs bosons. Feynman diagrams of some important interactions bosons W^±, Z⁰ are illustrated in Figures 1.5.1.D, F, G, H, I . Particle interactions caused by the exchange of charged intermediate bosons W^± are sometimes referred to as "weak charged currents", reactions caused by an uncharged Z⁰ boson as "weak neutral currents".
*) Particles with such a short lifetime cannot be directly detected experimentally (they disintegrate before they have time to fly out of the place of interaction, they will not reach any detector...). Only their decay products can be detected. Our detectors at accelerators are unable to detect neutrinos at all (they have no electric charge and hardly interact with anything), they can only be proven indirectly by measuring a certain value of the missing energy or momentum in the overall balance of energy and momentum.
  Intermediate bosons W^-, W⁺, Z⁰ were indirectly experimentally demonstrated in 1983 in interactions in opposite proton-antiproton beams of the 270GeV « 270GeV Super Proton Synchrotron at CERN.

Hypothetical and model particles
For the sake of completeness, we will briefly mention some "exotic" particles, which should exist according to certain more or less verified theories and models, but most have not yet been directly experimentally proven - they remain hypothetical or model particles.
Quarks
are model "building" particles of hadrons (as outlined below - "Quark structure of hadrons"). Quarks are fermions with spin 1/2 and carry a one-third electric charge -(1/3) e, +(2/3) e. A total of 6 types of quarks have been introduced, each with its own antiparticle - an antiquark. The individual quarks and quark model of hadrons are briefly described below. Quarks are the primary carriers of strong interaction, mediated by gluons. At the same time, however, they may be subject to mutual internal transmutations under the influence of a weak interaction mediated by intermediate bosons W^-, W⁺, Z⁰ (the main manifestation of this quark transmutation is radioactivity b , see Fig.1.2.5). Free quarks have never been observed - see the following section "Gluons" and below the section "Quark-gluon plasma".
Gluons (glue - holding quarks "glued together" in hadrons)
are particles that mediate strong interactions between quarks (and with their "residual manifestations" also nuclear interactions between nucleons). They are bosons with spin 1, have zero rest mass, have no electric charge, but carry the so-called "color charge" *), which characterizes different types of quarks. Like a photon, a gluon does not have an antiparticle (it is its own antiparticle). The gluon interaction of quarks has special properties. If the quarks have high energy and are close to each other, the gluon interaction is negligible and the quarks behave as free particles - so-called asymptotic freedom. However, when the quarks move away from each other by about 10^-13 cm, the gluon interactions begin to act intensively and strongly bind the quarks to each other - the quarks are "trapped" in hadrons. Further discussion is below in the section "Quark-gluon plasma".
*) A photon that mediates an electromagnetic interaction does not itself carry the charge of that interaction (electric charge); photons do not interact with each other. However, gluons carry a "color" - the charge of a strong interaction, so they can interact with each other. They could theoretically create bound systems - so-called gluonium.
Preons 
- are hypothetical sub-quark particles that could make up quarks (see the "Preon Hypothesis" passage below).
Gravitons 
are the quantum of gravitational waves. Gravitational waves are predicted by the general theory of relativity as a physics of gravity and spacetime; they are solutions of Einstein's equations of the gravitational field, similarly to Maxwell's equations of electrodynamics implies the existence of electromagnetic waves. Gravitational waves differ from electromagnetic waves in their very slight effect on matter, and in their so-called quadrupole character. The hypothetical graviton has zero rest mass, moves at the speed of light, its spin number is 2.
  Gravitational waves have alredy been directly detected, although this is at the limits of current experimental techniques. However there is no hope for experimental demonstration of gravitons in the foreseeable future. Gravitational waves are discussed in detail in §2.7 "Gravitational waves" in the book "Gravity, black holes and space-time physics". A skeptical note on the reality of the existence of gravitons is there in the passage "Gravitons - a quantum of gravitational waves? ".
Higgs bosons
- they are quantum of the so-called Higgs-Kible *) scalar field, that in the unitary calibration field theories is introduced into the Lagrangian for purpose of so-called spontaneous disruption of symmetry of the electroweak interaction (see, e.g. §B.6 "Unification of fundamental interactions" in the book "Gravity, Black Holes and the Physics of Spacetime"). This field also leads to some intermediate bosons gaining mass (rest mass) and the corresponding interactions becoming short-range forces - they are mainly W and Z bosons of (electro)weak interactions. In this Higgs mechanism the rest mass of the particles is created by interaction with the ubiquitous Higgs field, which permeates the entire universe; the stronger the interaction of a given particle with this field, the greater its mass. Some quantum, such as photons, do not affect this field and therefore have no rest mass, other particles attract the Higgs field and add mass to them. This could explain why some intermediate bosons are so heavy, while other particles, such as electrons, are very light. Simply put, the Higgs bosons should be part of an invisible quantum field that fills a vacuum in space and causes material particles in the universe to form material structures; without them, there would be no world as we know it. If some basic building blocks did not gain mass, the universe would look completely different: Particles without a rest mass would fly freely through space at the speed of light and would never form atoms, from which stars, planets and life would then form ...
*) This hypothesis was first introduced in 1964 by the authors P.Higgs, F.Englert and R.Brout, G.Guralnik, C.Hagen and T.Kibble. The Higgs field in 1967 was used by S.Weiberg, A.Salam and S.Glasshow to build the theory of electroweak interaction with heavy intermediate bosons W^±, Z°.
  The Higgs boson H itself has a high rest mass, in the order of hundreds of GeV *). Higgs bosons could be formed by a strong interaction in high-energy proton collisions by the exchange interaction of energy quarks with gluons or W-bosons (so-called gluon fusion, Fig.1.5.1.I, W or Z fusion, or associated production with W or with t-t ' pair), or an electro-weak interaction at electron collisions eg by interactions e⁺ + e^- ® Z* ® Z + H (H-emission), or again by W or Z fusions - see Fig.1.5.1.D. Higgs bosons are highly unstable particles with a lifetime of only about 10^-22 seconds. Therefore, they cannot be detected directly, but only on the basis of the analysis of secondary particles formed during their decay - their decay products. If the Higgs boson is formed during a high-energy interaction of particles, it is assumed that it will decay very quickly into other energetic particles. The simplest decay H® g + g per two gamma photons could occur even at lower masses around 100GeV. If the Higgs boson has a mass greater than 160 GeV, it can decay into two W-bosons: H ® W + W, which then decay into two leptons and two neutrinos (as mentioned above in the passage "Bosons W^-, W⁺, Z^o"). At a mass H higher than about 180 GeV, the decay can lead to two Z-bosons: H ® Z + Z, which decay into 4 leptons - by pairs of muons m⁺ + m^- or electrons e⁺ + e^-. In case the Higgs boson is heavier than about 500 GeV, other ways of its decay may occur, eg H ® b + b', or H ® t⁺ + t^-, others may or may not go through intermediate Z-bosons; finally, they can result in the production of quarks, whose hadronization would create sprays (jets) of particles. Feynman diagrams of some possibilities of formation of Higgs bosons and their decay are given above in the section "Feynman diagrams" (in Figure 1.5.1.D, I).
*) Collision experiments (on Tevatron and LEP accelerators - see "Large accelerators" below) previously provided only the lower limit for the mass of the Higgs boson about 170 GeV/c². After all, according to supersymmetric models, there could be several species of Higgs bosons: light scalar h^o , heavy scalar H^o, positively and negatively charged H^±.
Discovery of the Higgs boson 
At the ICHEP2012 conference in Melbourne, Australia, on July 4, 2012, the discovery of a new boson whose properties are consistent with the Higgs boson was announced, based on data from ATLAS and CMS experiments at CERN. Careful analysis of about 60,000 cases of photon pair detection (derived from high-energy proton collisions) found a small (but significant, about 160 photon pairs) peak on the photon number -to-energy curve, in the energy range around 126 GeV. This peak should probably come from the 2-photon decay of the Higgs bosons. The level of reliability of detecting a new particle by detecting its decay products is 5s. Further experiments are needed to make sure it is a Higgs boson and not another unknown particle. For this discovery, the Nobel Prize was awarded to P.Higgs and F.Englert in 2013.

^{Source: CERN-LHC
Discovery of the Higgs boson at the LHC great accelerator by detecting its decay products - here two opposite photons of gamma specific energies on the ATLAS detection system.}

Higgs boson - a "divine" particle ?
In the popularization literature, it is often stated in the journalistic bonmot that the Higgs boson is a kind of "divine particle" that gives the universe mass. That's not quite true. More than 99% of the ordinary ("radiation") matter that makes up the universe, ordinary matter, and our bodies is made up of protons and neutrons. These consists of quarks whose mass, associated with the Higgs mechanism, represents only about 5% of the mass of protons and neutrons. With the Higgs field substantialy related only the mass of the W and Z bosons and the mass of leptons, but these represent only a small part of the mass of the Universe. The importance of the Higgs boson lies in the fact, that it was the last undiscovered particle of the standard model, the discovery of which confirms the (otherwise undetectable) Higgs field, without which the standard model could not explain experimentally measured masses of leptons, quarks and intermediate bosons - force carriers. Without the Higgs mechanism, quarks would be massless and would not create protons and neutrons, atomic matter would not exist...
Supersymmetric particles  
In supersymmetric unitary theories of elementary particles, each basic particle is assigned its so-called superpartner - each boson has its fermion superpartner and fermion, on the other hand, has its boson counterpart. These "partner" particles have not yet been observed. This is explained by the fact that boson-fermion supersymmetry is disturbed; this means that the mass of the superpartners is not the same, but the supersymmetric partners to the known particles have a much higher mass, so we cannot observe them at the energies available to us. The names of these particles are formed by the suffix "ino" (for interaction bosons) or by the prefix "s-" (for fermions) to the name of the starting particle. The most frequently discussed supersymmetric particles are gravitins, photins, or neutralins :
Gravitins
are quantum of the calibration field in supergravity unitary field theory (graviton superpartner), they have a 3/2 or 5/2 spin.
Photins
are weakly interacting particles with spin 1/2, introduced as a supersymmetric partner of photon.
s - particles
Supersymmetric particles to other fermions are sometimes discussed: s-leptons as superpatters to leptons, eg s-electron, s-muon, s-neutrino (also called neutralino - should have a high mass of tens or hundreds of GeV); or to the quarks - s-quarks.
Higgsino - a supersymmetric fermion to the Higgs boson.
Other hypothetical particles:
Axions
are very light (rest mass approx. 10^-5 -1 eV/c²) hypothetical particles with spin 0, which should interact with the surroundings by weak and gravitational interaction. They are considered possible particle candidates for dark matter in the universe.
Within quantum chromodynamics, disturbances of the combination of charge symmetry and parity in quark theory are introduced in solving the CP-problem. CP symmetry, which is disturbed by weak interactions, should theoretically be disturbed even by strong interaction. Since this is not observed experimentally, additional symmetry has been introduced into quantum chromodynamics (which is spontaneously disturbed), the quantum of the respective field being a new type of particles called axions (their supersymmetric partners are called axina). Relic axions could perhaps have formed in the very early universe in the lepton era. It is assumed that even in a small percentage they could be formed during the scattering of photons on electrons, so their intensive source could also be the interior of the Sun.
  Recently, some possibilities have been discussed as to how it would be possible to detect such particles. The interaction of an axion with electrons or a very strong magnetic field could lead to the production of a quantum of electromagnetic radiation - a microwave photon - which could be detected. Experiments are even being attempted with laboratory production of axions by means of interactions of intense photon beams from powerful lasers with electrons in a strong magnetic field, with subsequent detection during the reverse conversion of axions to photons, again in a strong magnetic field. All unsuccessful so far...
WIMPs
The above (so far hypothetical) particles - gravitin, photin, axions - are sometimes collectively referred to as "weakly interacting material particles" - the abbreviation WIMP (Weak Interacting Massive Particles). They interact weakly and gravitationally with the environment. They are predicted by the supersymmetric extension of the standard model. They could form an essential component of the so-called dark matter in space (see eg §5.6 "The future of the universe. Time arrow. Hidden matter." in the book "Gravity, black holes, and physics of space-time"). They haven't been detected yet...
Magnetic monopoles
- a hypothetical particle dual respect to electrical charge. The magnetic monopole arises when exchanging the electric and magnetic quantities in Maxwell's equations and subsequent application of quantum field theory.
Classical electromagnetic theory does nor allow magnetic monopoles: one of Maxwell's equations div B = 0 says that the magnetic field is non-source with closed lines of force, ie magnetic monopoles do not exist (see eg §1.5 "Electromagnetic field. Maxwell's equations" in the book "Gravity, black holes and the physics of space-time"). Magnetic monopoles were introduced as an attempt (at least hypothetical) formal equalization, or establish symmetry, with electricity and magnetism. They have never been detected, they do not exist in our nature, their hypothetical presence just after the big bang was nullified by the inflationary expansion of the early universe (§5.5 "Microphysics and cosmology. The inflationary universe.").
Leptoquarks X , Y
- hypothetical vector bosons X and Y (called leptoquarks, they cause transitions between quarks and leptons) introducing in the so-called grandunification GUT theories (already mentioned §B.6 "Unification of fundamental inetractions" in "Gravity, black holes and spacetime physics"). They should have a very high weight on the order of m_{X ,Y} ~ 10¹⁵ GeV/c², so far beyond the possibilities of experimental proof in large accelerators...
Superstrings 
are hypothetical (model) one-dimensional elementary structures of the order of 10^-33 cm (Planck's length), whose variously excited vibrational states and interconnections should be the basis of all particles and fields according to the so-called superstring theory - the basis of unitary field theory unifying all 4 interactions in nature. The strings can be open or closed. Depending on the way the strings vibrate, different weights, charges, spins, etc. are created. Such strings could then form the basic particles (fermions - quarks, electrons, ... and bosons - photons, gluons, ...) of a standard model.
  The generalizations of superstrings are the so-called p-branes, which can have more (p) spatial dimensions and evolve in multidimensional (mostly 11-dimensional) spacetime.  The theory of superstrings is briefly discussed in the final part of §B.6 "Unification of Fundamental Infections" of the book "Gravity, Black Holes and the Physics of Spacetime".
Tachyons (Greek: tachyos = fast)
are purely speculative particles that can move only at superluminal speeds and have (in connection with the known relationship of mass versus velocity m = m_o/Ö(1-v²/c²) in a special theory relativity) imaginary mass. The motivation for the introduction of tachyons is only speculation about a kind of symmetry with respect to the speed of light, there is no physical arguments for them; rather, they would raise serious problems with the principle of causality. From the point of view of the theory of relativity, tachyons are briefly discussed in the passage "Tachyons" §1.6 "Four- dimensional space-time and special theory of relativity" of the mentioned book "Gravity, black holes and space-time physics".
"Shadow" or mirror matter - Catoptrons ?
At the end of our brief overview of the "zoology" of hypothetical particles, we mention a somewhat vague idea of the so-called mirror matter, which could perhaps hiden coexisting with "our ordinary" matter. The hypothesis is based on experimentaly measured non-preservation of parity in weak particle interactions (discussed below - "CPT symmetry of interactions"). The idea arose that mirror symmetry could be restored if for every "our" observed fundamental particle there was a hidden, "shadow" partner ("twin") - a mirror particle whose interaction involves the opposite violation of parity. Our common particles are "counterclockwise", mirror particles are "clockwise", overall parity symmetry is maintained. Parity can then be spontaneously disrupted by the Higs mechanism; in the case of undisturbed parity symmetry, the masses of the particles and their mirror partners are the same; in the case of parity disturbance, the masses of the mirror partners are different. Miror particles are somentimes collectivery refered to as catoprons (Greek katoptro = mirror ).
  Mirror matter, if it exists, interacts only very weakly with ordinary matter. This is because the forces between the mirror particles are mediated by mirror bosons, which are generally different from the intermediate bosons of "our" matter. The mirror mass is therefore practically unobservable *), at least not by direct methods, optically. The exception is gravitation, so mirror matter should have gravitational effects - it could therefore be a candidate for the still mysterious dark matter in the Universe (discussed in more detail in §5.6 "The Future of the Universe. Arrow of Time. Hidden Matter.)" monograph "Gravity, black holes and space - time physics").
*) In superstring theories, mirror particles are sometimes even placed not in "our" 3- dimensional space, but in three other "extradimensions".

Unitary symmetries and multiplets of particles
The large number of elementary particles discovered in high-energy interactions naturally led nuclear physicists to try to systematize them and introduce unitarization schemes - to create a kind of periodic table of particles, analogous to Mendeleev's periodic table of elements (§1.1, part "Bohr's model of the atom" and "Interaction of atoms", passage "Periodic chemical properties of atoms"). In particular, each baryon and lepton is assigned a baryon number B and a lepton number L (particle +1, antiparticle -1), which are preserved in all interactions. Significant similarities and symmetries between some elementary particles, especially hadrons, were found.
  If we look away from the electric charge, protons and neutrons, for example, can be considered as two states (doublets) of one particle - a nucleon. Similarly, the pions p⁺, p^o, p^- form a triplet of similar particles. When studying the strong interactions themselves, which are charge-independent, we can disregard the charge. To describe these similarities and symmetries, a new quantity isotopic spin or isospin T was introduced *). Nucleons have an isospin T = 1/2, with the projection of the isospin T = +1/2 corresponding to a proton and a T = -1/2 neutron. The pions were assigned isospin T = 1, with projections -1, 0, +1 for p^-, p^o, p⁺. In the system of interacting nucleons and pions, the law of conservation of isospin applies.
*) It was based on a formal analogy with ordinary spin, where a particle with spin 1/2 occurs in two states with spin projection -1/2, +1/2 and a particle with spin 1 in three states with spin projections -1, 0 , +1. Isospin T is a vector in the imaginary (auxiliary) "isotopic space". In general, a particle with isospin T can occur in (2.T + 1) states with isospin projections on the reference axis: -T, (-T + 1), (-T + 2), ..., -1, 0, 1, ..., (T-2), (T-1), T.
  Another important step was the discovery of some "strange" (unexpected) properties of the interactions of mesons K and hyperons in their combined pair production, which led to the introduction of the concept of strangeness described by the quantum number S ("Strange"). Later we were introduced general quantum number called hypercharge Y = B + S, the sum of baryon number B and strangeness S. It turned out that both isospin T and hypercharging Y are preserved during strong interactions. This extended symmetry led to the construction of a baryon-decuplet multiplet (3/2⁺), which, however, lacked one place at the time; was thus the prediction of the hyperon W, which was soon actually discovered.
  The individual hadrons were drawn in special diagrams, where the horizontal axis showed the projection of isospin Tz , the vertical axis the hypercharge Y and the oblique axis the electric charge Q. The connectors of the thus marked multiplets of particles formed regular geometric shapes - triangles, hexagons and their combinations, see below Fig.1.5.3. Such an analysis of unitary symmetry (found in 1964 by M.Gell-Mann and Y.Ne'eman) showed that the system of hadrons can be very well explained by the hypothesis that hadrons are composed of subparticles called quarks - baryons from a triplet of quarks, mesons from a pair of quarks, as will be outlined in the following passage.

Are elementary particles really elementary ?
Let us now try to look at the "elementality" and the internal structure of the basic building blocks of matter. An important guide for assessing the "elementality" ("fundamentality") of particles can be whether the particle spontaneously disintegrates (transforms) or does not disintegrate into other types of particles. According to current knowledge, a photon and an electron can be considered as truly internally "uniform", compact elementary particles without an internal structure, which always arise or disappear as a whole and are not transformed into other types of particles. The neutron and proton can transform with each other with the participation of electrons, positrons and neutrinos; they cannot, therefore, be "elementary" in the true sense of the word. The same applies to p- mesons and hyperons. So generally hadrons ...
Note: Since many particles are compound, the designation "elementary" is misleading here. However, it is a common name, similar to the name "atom", which no longer means "indivisible". In recent years, however, the word "elementary" has often been omits and speaks only of "particles".
Bootstrap model of hadron interactions
The "predecessor" of the quark model was the so-called bootstrap hypothesis of hadron interactions developed by G.F.Chew in the 1960s. No more fundamental particles were found to be behind the properties of the interactions, but it was assumed that they were essentially the "same" hadrons (including hadron resonances) acting in a kind of feedback (bootstrap, self-booting). In particle physics, this concept is now only marginal and is not generally accepted ...
Quark structure of hadrons
The above described systematics of hadrons shows that significant so-called unitary symmetries can be found in their properties. Based on these symmetries, the so-called quark model of hadrons was compiled in 1964 (authors M.Gell-Mann and Y.Ne'eman), according to which all hadrons are composed of even more "elementary particles" - quarks.
  The word "quark", which has no linguistic meaning, was taken over by the authors of the quark model with a significant dose of recession from the play by the writer James Joyse.
  Quarks are fermions with spin 1/2 and with a third electric charge: -(1/3) e, +(2/3) e, each quark has its antiparticle - antiquark´. To explain the system of hadrons using an additive quark model, a total of 6 types of quarks were gradually introduced, the most important of which are two: "u" (up), "d" (down) - nucleons are composed of them. The third quark "s" (strange) is the bearer of "strangeness". The quark "b" (bottom) participates in the violation of the CP symmetry. The characteristics of all quarks are given below in a clear table in the section "Standard model - unified understanding of elementary particles".
  Mesons are composed of two quarks - a quark-antiquark combination (q q´). In the case of opposite orientation of the spins of both quarks, we get the so-called scalar mesons with spin s = 0, eg p⁺ = (u d´), p^- = (d u´), p^o = (u u´) + (d d´). If one of the quarks is "s", these are strange mesons K^{+, -, 0}.... In the parallel orientation of the spins in the quark-antiquark pair, so-called vector mesons with spin s = 1 creates, which we observe only as meson resonances with a very short lifetime (approx. 10^-23 s) - meson r^{+, - , 0} or ^*K^{+, - , 0}.
  Baryons are composed of three quarks, wherein the spins of these quarks can be oriented so that the resulting spin baryon is s = 1/2, or s = 3/2. E.g. proton p = (u u d) and neutron n = (d d u) with spin 1/2, or hyperon L⁰ with spin 3/2.
  Baryons containing the "s" quark are called hyperons (the properties of hyperons have been described above).
  The system of mesons and baryons in terms of quark structure is schematically grawn by the diagrams in the following Fig.1.5.3 :