The model of quark
quasiparticles is a theoretical model, which is alternative to the
ideas of the origin of quarks as a result of the Big bang and to the quark
model in Quantum Chromodynamics and the theory of elementary particles. To
substantiate the model of quark quasiparticles the theory of Infinite Hierarchical Nesting of Matter,
theory of similarity of matter levels, SPФ symmetry, strong gravitation, substantial neutron model and substantial proton model are used. The
model of quark quasiparticles shows that quarks are not independent particles
but quasiparticles, that is a manifestation of symmetry of the hadrons’ states
of matter in the transformation of this matter under the influence of
fundamental interactions, as well as in reactions with elementary particles. It
follows that the quark model is not final, but rather an intermediate theory of
hadrons’ structure.
Originally the theory of quarks
was developed as an artificial theoretical scheme to describe the symmetry of
hadrons’ interactions. In chromodynamics the quarks are treated as point
objects with not precisely determined mass that make up hadrons – baryons and
mesons. There are six types (flavors) of quarks: u, d, s, c, b, t, which are
generally denoted by the symbol q. Antiquarks are denoted by tilde or a bar
over the quark symbol. It is supposed that baryons consist of three quarks and
mesons consist of a quark and an antiquark.
Quarks are considered to have a
special charge characteristic – color, as well as quantum numbers that
distinguish each quark from other particles. It is assumed that the essence of
strong interaction between hadrons is strong interaction between quarks by
exchanging gluons that transfer color. Quark decays result from weak
interaction with emission of massive vector Wbosons. Quarks transfer
fractional charge and halfinteger spin and can be located only inside hadrons
(the confinement effect, i.e. color confinement). In this case hadrons do not
have color due to color compensation in the quarks that constitute them.
Due to introduction of a number
of specific properties and additional characteristics in the structure of
particles and the action of new fields the idea of quarks allowed us to put in
an ordered system the set of hadrons and to describe the dynamics of their
interaction, including particle decays, the estimates of crosssection of their
interaction with each other, lifetime, spins and magnetic moments, energy
levels and particle masses. Despite these successes the theory has a
significant number of important problems,
which have not yet been solved.
The principal difficulty of the
theory is that in quantum chromodynamics the interaction of elementary
particles (quarks, leptons, vector bosons) is considered practically as a point
event with particles that do not have the size. Describing such an interaction
based on the symmetry of the gauge field theory leads to mathematical divergences,
which cannot be fully eliminated, and to deliberate inaccuracies of theoretical
predictions.
Unobservability of quarks in a
free state, locality of their interaction, approximation of the quark matter
behavior by ideal fluid in collisions with high energy ^{[1]}
lead to the idea that quarks are a special kind of quasiparticles, which are
closely related to the hadrons’ matter. Elementary particles have spin
(characteristic angular momentum due to selfrotation), electric charge,
magnetic moment, and can have a complex inner structure. Both quarks and
hadrons are involved in all the four fundamental interactions. It is assumed
that during strong interactions quarks are redistributed between hadrons and
new quarkantiquark pairs and gluons are produced from vacuum due to its
polarization by gluons.
On the other hand, the strong
interaction can be explained by the strong
gravitation, gravitational torsion field
and electromagnetic forces based on the gravitational
model of strong interaction. ^{[2]} The
density of the matter inside the nucleon is only a few times greater than the
mass density of the neutron star, ^{[3]} where
the matter is in the state of neutron liquid with a small admixture of protons
and electrons. Decrease in the neutron star mass below the limit of 0.1 – 0.2
solar masses inevitably leads to transformation of the stellar matter into a
less dense phase, similar to the matter of a white dwarf or even an ordinary
star, with energy release. ^{[4]} If we consider the
hadrons’ matter in a similar way, then in reactions of particle scattering at
sufficiently high energy matter masses can break away from hadrons, with
subsequent change in their state and transformation into new elementary
particles. In many cases pions are produced (mesons with minimum mass), which
from the standpoint of the similarity of
matter levels are similar to a neutron star with the mass equal to 0.2
solar masses, which is close to the stability limit of such stars in respect of
the state of matter.
Besides, we can also assume that
over time the matter of many elementary particles undergoes transformation due
to interactions similar to the weak interaction, which leads to decay of these
particles. Hence, due to quantization of various properties of elementary
particles, complexity of their structure and possibility of different types of
interactions, the observed symmetry of hadron properties and their resonant
states can be not the consequence of the existence of quarks but the
consequence of the intrinsic properties’ symmetry of the hadrons’ matter and of
the surrounding fields.
The αphase of hadrons’ matter
means the same matter as in a magnetized neutron nucleus and the βphase
corresponds to the matter in the neutron shell, which is oppositely magnetized.
These phases of matter arise from the substantial
neutron model. In this model the magnetic moment of the neutron is composed
of the magnetic moments of the nucleus and shell, while the neutron nucleus and
αphase of matter are positively charged, and the neutron shell and βphase of
matter are negatively charged. The total charge of the neutron is zero, and the
magnetic moment is determined by the negative magnetic moment of the βphase of
matter, which exceeds in the absolute value the magnetic moment of the αphase
of matter due to the large volume of the shell and the increased magnetic flux
in comparison with the nucleus.
Neutron betadecay occurs as a
result of the weak interaction reactions in the neutron matter, the magnetic
field structure transformation and the emission of negative electric charge
from the shell in the form of electron, with transformation of neutron into
proton. In the first approximation we can assume that the magnetic moment P_{β}
of the shell changes its sign and becomes directed the same way as the magnetic
moment P_{α} of the nucleus. Since the sum of magnetic moments of the
shell and nucleus should equal the magnetic moment of the proton and their
difference should equal the neutron magnetic moment, then we can estimate that
P_{α} = 0.44 μ, P_{β} = 2.35 μ, where μ is the nuclear
magneton. These magnetic moments reflect the fact that the change of sign of
the internal volume electric charge density occurs in the middle of the neutron
radius. Thus the αphase and βphase in the neutron matter are oppositely
charged and magnetized.
In Fedosin’s model it is assumed
that not only nucleons, but all hadrons and hence quarks can be composed of
certain combinations of the two abovementioned matter phases. The composition
of quarks is presented in the Table. ^{[2]}
Quarks’ composition 

Quark 
The share of α–phase 
The share of β–phase 
u 
1/3 
1/3 
d 
1/3 
–2/3 
s 
–2/3 
1/3 
c 
4/3 
–2/3 
b 
4/3 
–5/3 
t 
4/3 
–2/3 
According to the table, the ratio of the matter phases for quark u is: u = α/3 +
β/3, and similarly for quark b: b = 4α/3 – 5β/3. If we assume that the values α
and β correspond to the unit elementary electric charge, then upper quarks u,
c, t will have charges +2/3 and lower quarks d, s, b – respectively –1/3 in the
units of elementary electric charge.
The composition of α and β for
hadrons is obtained by summing α and β composition of the quarks, which are
part of these particles. The following Tables show the α and β composition of
some hadrons.
Baryons’ composition 

Particle 
Massenergy, MeV 
Quark composition 
α , β composition 
p^{+} 
938.272029 
uud 
α 
n^{0} 
939.565360 
udd 
α – β 
Λ^{0} 
1115.683 
[ud]s 
0 

1321.31 
dss 
– α 

3519 
dcc 
3α – 2β 

5774 
dsb 
α – 2β 
Mesons’ composition 

Particle 
Massenergy, MeV 
Quark composition 
α , β composition 
π^{+} 
139.57018 

β 
π^{0} 
134.9766 

0 
K^{+} 
493.677 

α 
K^{0}_{S} 
497.648 

2α – 2β 
K^{0}_{L} 
497.648 

0 
D^{0} 
1864.5 

α – β 

5367.5 

–2α + 2β 

6286 

β 
Υ^{0} 
9460.3 

0 
In tables the hadrons of the type have zero or
indefinite matter phase. It means the absence of uncompensated electric charge
in these particles and indicates the matter state that is not the full α or
βphase. It can be assumed that the matter of these particles is in a mixed
state, with α–β or –α + β phases. Typically, such particles have a much shorter
lifetime as compared to particles with a different matter composition. An
example is the decay in
which the indefinite matter phase of particle is transformed into αphase of proton and (–
β)phase of negative pion. Some neutral hadrons clearly consist of both matter
phases, with the composition of the form α – β, –α + β, 2α – 2β. In charged
hadrons the α or βphase of respective sign prevails. The analysis of known magnetic
moments of hadrons shows that almost in all positively charged particles the
magnetic moment is directed along the spin, while in neutral and negatively
charged particles it is directed against the spin. This is due to the fact that
prevailing of one matter phase over the other leads to prevailing of the charge
and magnetic moment of this phase over the other phase.
According to the theory of Infinite Hierarchical Nesting of Matter
and SPФ symmetry, the same scenario of
new objects formation is repeated at each level of matter: they result from
accumulation of matter of lower matter levels under the influence of
gravitational and electromagnetic forces, as well as in the decay processes of
the matter of higher matter levels, which occur due to different interactions.
From this point of view, for production of elementary particles as well as
quarks there is no need in the “Big Bang” hypothesis. Thus the wellknown
problem of the observed absence of antimatter in the Universe is removed,
because without the Big Bang there should not be much antimatter. In the model
of quark quasiparticles, quarks are the consequence of the symmetry of various
phases of hadrons’ matter and of the quantum behavior of particles in their
interactions. In particular, in such processes the amount of matter, energy and
momentum, characteristic spin, electric charge, magnetic flux and other similar
quantities are conserved and redistributed. The results of interactions of
elementary particles also depend on the interaction configuration and the
corresponding summation (subtraction) of the vector physical quantities of
particles. In order to move from the formal quark scheme to real interaction
models and to replace quarks as certain particles with quarks as quasiparticles
in the form of combinations of hadrons’ matter phases, it is necessary to show
that for each reaction with hadrons there is a certain and clear physical mechanism
that does not require introduction of a number of new entities (gluons, massive
vector bosons, color charges, mixing angles of states, etc.) used to describe
the observed symmetry of hadrons.
In some cases particles interact
with each other so closely, that they significantly change their state. For
example, in the chargeexchange reaction of the negative pion , the proton is transformed into the
neutron. At the same time the sum of matter phases remains the same before and
after the reaction, which is equal to α – β. In connection of pion and proton
the total spin does not change, the proton spin is equal to the neutron spin,
the spin of pions are approximately equal to zero. It can be assumed that
transformation of the proton into the neutron occurs due to annihilation of the
positive charge in the proton shell by the negative charge of the pion,
followed by magnetization reversal and charge exchange of the proton shell. The
electric charge of the pion flows into the proton shell under the influence of
the Coulomb force from the positive charge in the center of the proton, which
leads to the charge distribution, typical for the neutron (the center is
positively charged, the shell is negatively charged). This charge configuration
is stable, since the negative charge in the shell repels from itself and therefore
does not recombine with the positive charge in the center of the neutron.
During interaction with the massive proton the pion loses its primary βphase
of matter, is transformed into a neutral pion with zerophase of matter and
then decays into two gammaquanta.
Indefinite or zero matter phase
can be understood as the state of hadrons’ matter, when it has no full ordering
of the magnetic moment and the total charge is equal to zero. The lifetime of a
neutral pion is 0.084 fs, converted to the lifetime of a corresponding star by
multiplying by the coefficient of similarity in time П = 6.1•10^{19},
according to the theory of similarity of
matter levels, gives 1.4 hours. Among all hadrons, pions have the smallest
mass, which is 6.8 times less than the mass of nucleons. The mass of a neutron
star, corresponding to a negatively charged pion, is about 0.2 solar masses. If
such a star would collide with a magnetar, which is the proton’s analogue at
the stellar level, then in not more than 1.4 hours defragmentation would occur
with explosive ejection of excess matter and strong emission. This occurs due
to both the initial kinetic energy of stars’ motion and release of
gravitational and electromagnetic energy during their combination. In this case
charge exchange and magnetization reversal of the magnetar shell take place, so
that the star as a whole becomes electrically neutral and its magnetic moment
changes its sign. The ejected matter and emission can be directed by the
magnetic field of the star, creating oppositely directed fluxes (jets),
starting at the magnetic poles. This explains the neutral pion’s decay into two
gammaquanta and the short lifetime of this pion.
The energy of the reaction can
easily be estimated quantitatively for the case, when the proton is at rest and
the pion’s kinetic energy is low. When pion and proton are combined, the energy
of strong gravitation is released, which can be estimated by the formula:
where is the strong
gravitational constant, and are the masses of proton and pion, respectively,
m is the
average distance from the proton’s center to the pion, which is approximately
equal to the proton radius. For the absolute value of the energy it equals MeV
in energy units. Part of this energy is emitted in the form of two gammaquanta
with the total energy not less than the value 134.963 MeV, which is considered
the massenergy of a neutral pion at rest. Hence it follows that in this case
the neutral pion is not an independent particle and it exists as a transitional
state of matter on the surface of a massive hadron.
Another reaction of charge
exchange is the reaction: . In this case, the positive pion produces
magnetic reversal and charge exchange of the neutron shell, turning it into a
proton. At the same time the pion becomes neutral, as described above, and
decays with emission of gammaquanta.
In the interaction of the
gammaquantum with the proton, the pion and the neutron can be produced in the
reaction: . The matter composition in the reaction
is conserved, since the proton consists of αphase matter, the pion consists of
βphase matter, the neutron matter composition is α – β, and the gammaquantum
is considered neutral, with zerophase of matter. The speed of the
gammaquantum equals the speed of light and corresponds to the characteristic
speed of the matter inside the proton. Therefore, if we select a wavelength of
the gammaquantum close to the proton size, then the quantum energy would be
resonantly absorbed by the proton, and the reaction becomes possible. It
follows from the experiment that the reaction crosssection is m^{2},
and the required energy of the gammaquantum is about 0.3 GeV in
the laboratory reference frame. If we assume that , then for the proton
radius we obtain the value of 0.8 fm. The estimated
wavelength of the quantum is: m. The simplest resonance condition is placing
half of the wavelength on the proton diameter: as for
oscillations between two fixed ends. Hence the determined quantity exceeds not more than 1.15 times the current radius
of the proton.
One of the problems in the
photoproduction of particles is the origin of mass of the newly formed
particles. If we use the formalism of the special relativity, then the particle
mass or the experimentally determined state of the system of particles is a
secondary parameter and is determined with the help of the total energy and
total momentum. In such determination, contributions to the mass are made by
both the energy and momentum, while the question of retaining the matter amount
as a measure of the matter mass is not considered. This follows naturally from
the approach, when we consider only the energy and momenta of the initial and
final states of the particles, without analyzing the transformation of matter
and energy of the particles in the course of their interactions (see the
mass–energy equivalence). Taking into account the strong gravitation allows us
to add into the energy balance equations the terms associated with the total
energy of the particles in the strong gravitational field, and thus to take
into account the law of matter conservation of the particles involved in the
interactions. ^{[5]}
The analysis of reactions with
elementary particles shows that due to the presence of precise models of
particles and their interactions the quark hypothesis becomes unnecessary. This
is most clearly manifested in the formation of baryons N and Δ, with the spin
ħ/2 and 3ħ/2, respectively (ħ is the Dirac constant). These baryons usually
arise from irradiation of nucleons by gammaquanta, from scattering of
electrons and pions in the matter, and are considered nucleon resonances, i.e.
the excited states of nucleons with a short lifetime. Composition of nucleons
coincides with the α, βcomposition of Nbaryons, as well as of neutral and
singly positively charged Δbaryons. It is noticed that collision of negative
pions with the corresponding energy with nucleons leads mainly to emergence of
different resonances of Ntype, and collisions of nucleons with positive pions
mostly produce resonances of Δtype.
For the formation of resonance Δ_{1}
(1232 MeV), it is necessary that the orbital angular momentum of the pion of
ħsize and the nucleon spin of ħ/2size sum up at the time of the pion’s flying
near the nucleon. Although the pion partially spins up the nucleon and
transfers its energy of motion to it, the main part of the spin of resonance Δ_{1}
arises from the orbital angular momentum of the pion, the velocity of which is
almost equal to the speed of light. The lifetime of the state Δ_{1} is
determined by the formula τ = ħ/Γ_{k}, where Γ_{k} = 118 MeV is
the width of the resonance level. Hence we obtain τ = 5.6•10^{–24} s.
Based on the given time and orbital angular momentum we determine the minimum
distance between the centers of the pion and nucleon (0.86•10^{–15} m),
which is close to the nucleon radius. ^{[2]} In
order to estimate the angle θ of the pion’s rotation near the nucleon, which
occurs in time τ under the influence of strong
gravitation and electromagnetic forces, we can write: θ ∙ R_{p} ≈ c
∙ τ, where θ <111º. In experiments on scattering of pions on nucleons the
maxima in differential crosssections are found at scattering angles of the
order 40º .^{[6]} The binding energy of the resonance
is close to zero, due to which it decays quickly into nucleon and pion.
The described pattern is repeated
for the resonance N_{1} (1440 MeV), with the difference that in this
case the orbital angular momentum of the pion and the nucleon spin are directed
oppositely and are subtracted from each other, and the lifetime of the state is
much less and equals 1.5•10^{–24} s. The analysis of other resonances N
and Δ indicates that the peculiarities of their emergence in the processes of
pions’ scattering on nucleons can be explained by the action of different
forces: a) between the magnetic moments of the particles; b) between the spins
of the particles; c) the Coulomb force; d) the magnetic Lorentz force; d) the
spinorbit force (the gravitational torsion
field from the spins of particles in the strong gravitational field acts on
the moving masses of particles). The forces differ in different sets of initial
particles with different configurations of interaction. ^{[2]} If we do not consider a particular interaction
model in each case and use the idea of quarks, then the quarks at the
resonances in addition to spins must have orbital angular momenta, and the
resulting particles should be considered the formal consequence of the symmetry
of spatial wave function of the compound system of quarks. In this case, the
spin, orbital and spinorbital interaction of quarks is considered. Apparently,
these interactions of quarks reflect the reality in such a way, that they
correspond to the forces from magnetic moments and spins of particles, the
Coulomb forces, the magnetic and gravitational Lorentz forces, that occur
between hadrons in their interaction.
The analysis of the reactions of
interactions, decays and models of strange hadrons shows that they can
represent a combination of simpler hadrons. ^{[5]}
For example, it is assumed such that Λhyperon consists of fastrotating near
each other and along one axis proton and pion, which are held by strong
gravitation and spin torsion fields. To calculate the equilibrium condition the
equations for the forces and energies are used. Over time, nucleon and pion
slowly approximate, collide with each other and Λdecay takes place. Similarly,
it is shown that Σhyperon is a compound of neutron and pion. Strange Ξbaryons
are more complex structures, containing a proton and two pions. The composition
of Ωbaryons in addition to proton includes three or four pions, giving the
baryon strangeness, which is equal to 3.
Kmesons are likely the compounds
of three pions and have the following compositions:
The difference in the pion
configurations of and leads to the fact that the lifetime of the
first kaons exceeds significantly the lifetime of the second, and to the
difference between the results of the reactions of interaction with other
particles. This allows us to give up the idea of representation of neutral
kaons in the form of quantum superposition of two basic states, accepted in the
standard theory in order to explain the differences between the two types of
neutral kaons, with introduction of the socalled mixing angles of basic
states.
Vector Φmeson with the energy
1019.455 MeV during the lifetime of the order of 1.5•10^{–22} s decays
into two kaons. If we assume that the velocity of kaons is of the order of the
speed of light, during the lifetime of the Φmeson the kaons will cover the way
not more than the length of kaons, composed of three pions. Then it follows
that the shortlived state of Φmeson emerges in close interaction of two
mesons, consisting in total of 6 pions.
There are quite longlived
hadrons, which in addition to a strange quark contain charmed quarks and
beautiful quarks. The examples are the baryon with the energy 2471 MeV and the lifetime of
0.112 ps, and the baryon with the energy of 5792.9 MeV and the
lifetime of 1.42 ps. The analysis of the products of their decay shows that the
sums of energies of secondary particles can be insufficient for them to be in
equilibrium state and to produce a hadron, as it happens in less massive strange
hadrons. It could be concluded that charmed and strange hadrons have additional
characteristics – their states can emerge in collisions of less massive
components, when additional energy is released due to the energy of strong
gravitation and transformation of hadrons’ matter.
Meson resonances emerge in
different processes, for example in photoproduction, in collision of
electronpositron beams, in scattering of pions on nucleons, in annihilation of
nucleons, etc. Some resonances like f and ρ almost always decay into two pions.
The lifetime of these resonances does not exceed 1.6•10^{–23} seconds. ^{[7]} During this time two fastmoving matter masses,
when they collide, can make not more than one revolution around the common
center of mass, and then decay, turning into two relativistic pions (or into
other mesons).
Resonance has the lower limit of the massenergy of
about 400 MeV and zero spin. It can be considered as the result of almost
central collision of two pions, each of which has the kinetic energy of more
than 61 MeV at the velocity more than 0.72 с,
where с is the speed of light.
The lifetime of this resonance is little, so that the pions immediately fly
apart with semiflexible scattering.
The spin of ρmeson (775) is
equal to ħ, and it can be understood in the situation, when two colliding pions
during 4.5•10^{–24} seconds closely interact with each other at the
minimum distance 2R, and then scatter in different directions. The total energy
per one pion equals half of the massenergy of ρmeson, i.e. 388 MeV. Hence,
using the relativistic formula, that relates the mass and energy, it is easy to
find the momentum of each pion. At least one of the pions is charged, and the
second is either neutral or oppositely charged, depending on the availability
and the sign of the charge of the ρmeson. The moving pion creates around
itself the field of strong gravitation,
which has the gravitational field strength
and the gravitational torsion field In case of counter motion of pions, at their
velocity of the order of the speed of light, the force from the torsion field
is summed up with the force of gravitational attraction, doubling the latter
one. ^{[3]} In the first approximation, we can
equate the gravitational acceleration and the centripetal acceleration of
particles relative to the center of mass, as they move close to each other:
where and are the rest mass and momentum of the
pion, is the speed of
light as the approximate velocity of the pion.
From this equality we obtain R =
2•10^{–16} m. On the other hand, for the meson spin we can assume that
ħ = 2 p R, from which R = 2.7•10^{–16 }m. Consequently, the radii of
pions should be greater than R, so that in collision of pions the ρmeson (775)
will be manifested.
Among the mesons there are
particles with large values of spin, for example, If we assume that the spin of this particle
with the size 6 ħ arises from the interaction of two pions, then the half of
the smallest distance R between the centers of pions will equal 4.7•10^{–16}
m. The pion radius will apparently be even more, as it follows from the
calculations, ^{[5] }and from the experimental
crosssections of interactions of pions on each other at high energies.
Dipion state with the lowest
possible energy, equal to the sum of the rest energies of two pions, is
observed in a number of reactions, such as in kaon decay into three pions or
two pions and leptons. ^{[8]} The coupling between the
positive and negative pions has its special name – pionium. Since the standard
theory has difficulty in explaining the dipion states, various explanations are
suggested, for example, by introducing the anisotropic component into the
strong interaction, due to deformation of the Minkowski space metric near the
particles. ^{[9]} If we proceed from the idea of strong
gravitation, then compound of two pions is as possible as in the strange
particles and atomic nuclei, due to the balance of the gravitational force and
spinspin interaction, arising from the gravitational torsion fields. ^{[5]}
By definition, baryonium
production requires combination of two quarkantiquark pairs. In annihilation
of proton and antiproton we can often observe meson with quantum numbers (J – spin, P – parity, C – the eigenvalue
of charge conjugation operator). This meson decays into pions or meson pairs of
the type and often
it is considered not from the point of view of quarks, but as weakly bound and
decaying state of two baryons. There are other examples of baryon states, ^{[7]} such as that decays into and in which decays into pairs are observed. It
is known that some massive mesons can decay not only into mesons, leptons and
photons, but also into baryons and antibaryons, where the latter is the state
of baryonium.
In some researches, attempts are
made, instead of using the quark model, to describe the hadron states at the
level of simpler hadron constituents. For example, the hyperon Λ(1405) is
considered as a dynamically bound state of nucleon and kaon, ^{[10]} and the scalar mesons f(980) and a(980) are
considered to be molecule of kaon and antikaon. ^{[11]}
Hadron molecules of kaon, antikaon and nucleon are considered in ^{[12]} by solving the Schrödinger equation for the wave
function of the three particles and by using two interaction potentials assumed
in the model. In ^{[13]} it is proved that many
resonant states N, Δ, Λ, Σ, Ξ, Ω are
dynamically bound states of vector mesons (such as ρ and ω) with baryons, which
are part of baryon octet with nucleons and of decuplet with Δ.
In the quark theory, weak
interaction, including the decays of quarks, is usually limited to production
of intermediate bosons as carriers of interaction. In contrast to massless
photons, in electroweak theory W and Z bosons have large mass, which
corresponds to the expected small radius of their interaction and the Fermi
constant value for weak decays. Boson masses , according to the
experiments, are equal to 80.398 GeV and the mass equals 91.19 GeV. Intermediate bosons were
discovered in collisions of colliding beams of protons and antiprotons in 1983.
They were determined from decay, in which Wboson decayed into an electron
(positron) and an electron neutrino (antineutrino), and Zboson decayed into an
electron and a positron, while leptons had higher energy and flew in opposite
directions. It is believed that at low energies, the weak interaction is
performed by virtual W and Zbosons allowing to describe the interaction
formally, but at sufficiently high energies virtual bosons become real and give
symmetrical decays of leptons.
In the model of quark
quasiparticles there is another explanation for the fact that at high energies
of nucleon and antinucleon collisions such particle states occur, which are
explained as W and Zbosons. Let us move on from elementary particles to the
level of stars and consider collision of two neutron stars, which are the
analogues of nucleons. In a typical neutron star, the average density kg/m^{3},
the characteristic speed of nucleons m/s, the
characteristic pressure of the star Pa are related by
the formula:
To produce intermediate bosons it
is necessary that the energy of a proton and an antiproton in their collisions
were 270 GeV, which is 287 times greater than the rest energy of proton. In
collision of two neutron stars, the kinetic energy of which is 287 times
greater than the binding energy of the star, the dynamic matter pressure
occurs, which is approximately equal to As the
pressure increases, the average matter density increases as well. In the
approximation of uniform nucleon gas, the following relation exists (in SI
units) between the pressure and density of the neutron star: ^{[5]}
From relation (2) it follows that
the dynamic matter pressure corresponds to the density .
If we now substitute and in formula (1), we will find that the
velocity of nucleons in the stars becomes equal to the quantity . This is a
consequence of rapid conversion of the collision kinetic energy into the
internal energy of the stellar matter.
Then, at the level of elementary
particles, production of W and Zbosons in collisions of protons and
antiprotons at corresponding energy is accompanied by the fact that the matter
of these nucleons acquires the velocity equal to . At the same time, the energies and
momenta of the matter and emission become sufficiently close in magnitude,
explaining the symmetrical production of lepton pairs in the form of an
electron and a neutrino, an electron and a positron. For comparison, we can
also calculate the velocity, which the test body should have on the nucleon
surface in order to overcome the attraction of strong gravitation:
This velocity is lower than the
matter velocity , expected in processes
with W and Zbosons. The fact that the velocity of the test body must exceed
2.5 times the speed of light, in order to be an analogue of the nucleon escape
velocity, is neither contradictory nor paradoxical. Since in the special theory
of relativity everything is measured by the speed of light, there is a problem
with measuring the velocities of objects, which exceed the speed of light. This
problem is avoided by considering the velocities and masses the secondary
physical quantities and finding them by calculating with the help of known
momenta and energies. In this case, the energy and momentum are calculated
using the Lorentz factor , where the
velocity of objects’ motion is always assumed to be
less than the speed of light.
The most massive tquark was
discovered in 1995 in experiments at the Tevatron collider. In collisions of
protons and antiprotons with an energy of 980 GeV per nucleon, the tquark
emerged as a state with the energy 173.1 GeV, in its decay to bquark and
Wboson. The energy 980 GeV exceeds 1045 times the rest energy of the proton.
If using the stellar model we make calculations of the dynamic pressure in the
matter of a neutron star and estimate as well the maximum mass density using
relation (2), from (1) we can find the effective velocity of the particles of
this matter:
Consequently, in collisions of
protons and antiprotons with the energy about 980 GeV per nucleon, the matter
can acquire the velocity of the order of
. The ratio of the
characteristic speed of particles in a neutron star to the speed of light (as
the limiting velocity of nucleons in the stellar matter) is the coefficient of
similarity in speed (see the similarity of matter levels). The same
holds for the matter within the nucleons. If the characteristic speed of the
nucleon matter is equal to the speed of light, then the limiting speed of the
particles of this matter is equal to . The obtained above velocity is sufficiently close to the speed , so that the
occurrence of events with tquarks can indicate the presence of some boundary
state of the interaction between the particles of this matter. ^{[5]} It is interesting that the energy of the
tquark is almost exactly equal to the sum of energies of W  boson and Z 
boson.
With the help of relations, such
as (3), we can estimate the energies required for nucleons in the
centerofmass system, whereby in the nucleon matter the velocity of about would be achieved. We obtain the value 1.4
TeV, so that in the experiments at the Large Hadron Collider, in which the
collision energies are currently up to 2.36 TeV and increase up to 7 TeV in
2015 is planned, after collection of statistic data the events could be found,
in which the nucleon matter starts interacting at the maximum possible speed.
Since 2010 by the detectors ATLAS
and CMS, working at the Large Hadron Collider, recorded events with the
possible appearance of the Higgs boson. This is a neutral scalar boson particle
which has zero spin and positive parity. In 2012, it was announced that the
Higgs boson is found with energies of the order of 125 GeV. ^{[14]}
Among all leptons the tau lepton
is the most massive, its energy is 1.777 GeV, and the lifetime is 2.9•10^{–13}
s. It was discovered in collisions of electrons and positrons with energies in
the centerofmass system more than 3.54 GeV, when pairs of τ^{+} and τ^{–}
leptons were produced. Tau leptons decay either into a tau leptonneutrino plus
hadrons of pion and rho mesons type, or into a tau leptonneutrino plus muon
(electron) and the muon (electron) antineutrino. ^{[15]}
In order to explain how in
collisions of electrons and positrons, muons and even pions are produced, the
maximum dynamic pressure reached in the collision zone is considered.
Calculation shows that close to the energy in the centerofmass system of the
order of 3.54 GeV, the dynamic pressure of the electron matter becomes equal to
the pressure existing inside muons, so that from the matter of colliding
electrons and positrons the muon matter phase is formed. ^{[5]} Then, under the influence of strong
gravitation, the muon phase is combined into sufficiently massive objects such
as muons and pions, observed in the processes, where the states appear that are
treated as tau leptons. Thus, there is no need to use the idea of quarks
required for production of mesons in decays of tau lepton states.
Within the model of quark
quasiparticles the problematic issues of the theory of quarks and quantum
chromodynamics are discussed as follows:
1) Why are there exactly three
generations of quarks, which coincides with the number of generations of
leptons? Apparently, this is a coincidence, since there are no other
considerations besides possible, but not proven symmetry between quarks and
leptons. On the other hand, electrons, neutrons and protons are genetically
related by the processes of their production (see the substantial electron model). Muons have
their analogues at the level of stars – the white dwarfs, containing the
degenerate matter of electrons and ions. The analogues of nucleons are neutron stars
with degeneration of neutron matter. Among leptons there is a tau lepton, which
can be represented as a state in which, in collisions of electrons and
positrons, muons are produced. It turns out, that leptons are correlated rather
with nucleons and special matter states inside leptons, than with quarks as
some parts of hadrons. Then the connection between generations of leptons and
quarks becomes accidental.
2) Why are elementary fermions
divided into two types – leptons and quarks? The standard model is extremely
simplified from the point of view of spin distribution of elementary particles
– they are attributed only quantum spin, either halfintegral or multiple of
the Dirac constant ħ, any intermediate spin values are not considered.
According to the substantial electron model, the electron spin must be
understood as a dynamic spin, associated with the change in the orbital angular
momentum of an electron in an atom due to the shift of electron cloud center
from the nucleus. From the calculations in ^{[5]}
the quantum spin of muon is derived from the characteristic
speed of muon matter and is also close to the value ħ/2. This leads to the
fact that due to their spin leptons are fermions.
Quarks are correlated with
fermions and with the minimum spin ħ/2 due to the necessity of building the
spins, observed in hadrons, with the help of the quark spins. However, unlike
leptons as real particles, quarks are quasiparticles due to their properties,
including their unobservability outside hadrons. All particles can be divided
into three classes – leptons, hadrons and field quanta, while hadrons in the
standard theory are considered to consist of quarks. Besides, it is believed
that leptons do not participate in strong interaction, which differentiates
them from quarks. However, from the point of view of strong gravitation, the
matter of both leptons and hadrons participates similarly in strong
interaction, the difference of field strengths is only quantitative and depends
only on the difference in the mass density, but not on the mass. Therefore,
division of the leptons and quarks can be considered as a formal consequence of
introduction of the idea of quarks.
3) Is the coincidence of the
number of colors and the number of generations accidental? Most likely, this is
an accidental coincidence. The number of colors is determined by the maximum
number of quarks in baryons, which gives new degree of freedom to quarks and at
the same time associates it with the color charge as the source of strong
interaction of quarks. Though the number of generations of leptons and quarks
is the same, but it occurs for different reasons. If the color depends on the
internal symmetry of hadrons, the generations of quarks depend on the level of
interaction energy, so that there is no direct relationship between the number
of colors and the number of generations.
4) Why cannot quark masses be
determined precisely? The quark masses are not determined precisely because
quarks are quasiparticles, not real particles. The properties of quasiparticle
depend strongly on the conditions, in which they are observed, as well as on
the theory used for their introduction and description. For example, the block
mass of quark is considered in the static case, based on the composition of
quarks and gluons inside hadrons. The current mass reflects conversions of
quarks in the dynamic case with change in the number of gluons surrounding
quarks, therefore it differs much from the block mass.
5) What is the reason of such a
large spread in the masses of quarks? In the standard theory inequality of
quark masses leads to breaking interactions’ symmetry and to different masses
of hadrons in multiplets. In this case, the cause of quark masses is assumed to
be their interaction with the Higgs bosons. In this approach, variability of
quark masses is unclear. In the theory of quark quasiparticles, quarks are
considered as combinations of the phases of hadrons’ matter, which are present
in each hadron in the necessary amount, and the question of quark masses is
replaced with the question of the difference between hadron masses. In turn,
the difference of hadron masses is explained by the different number of simple
hadrons (usually nucleons and pions) involved in the construction of their
states and by the difference of their energy inside a massive hadron, including
the energy of strong gravitation, the gravitational torsion field and the
kinetic energy of motion.
6) What leads to the difference of
quarks’ influence on the properties of hadrons, beside quark masses? In the
standard theory the quarks are divided into up and down, and each type there
has different mass. In addition, quarks have their own internal quantum numbers
that distinguish them from each other (e.g., strangeness, charm, beauty,
truth). It turns out that the difference in the properties of hadrons is
reduced to the mass and properties of their constituent quarks. In this
picture, after transition from the hadron level to the level of quarks, the
question remains – what is the reason for the difference of quarks?
7) What do quarks consist of? The
question of quark matter remains the subject of speculation and discussion so
far. It is assumed that collisions of hadrons at very high energies turn their
matter into the quarkgluon plasma, in which quarks become quasifree. In the
standard model, quarks and gluons belong to the fundamental elementary
particles. Besides, two types of vacuum are introduced, which are specific to
quarks and gluons, the electromagnetic vacuum, as well as the Higgs field that
gives mass to all particles except gluons and photons. These vacuums should
contain virtual pairs, such as quarkantiquark, gluonantigluon,
electronpositron, vector W and Z bosons, and the Higgs field should contain
the Higgs bosons. Quarks and gluons outside hadrons, as well as W and Z bosons
can exist only in transitional state, immediately turning into hadrons or other
particles. Quarks inside hadrons wear “coats” of gluons and float among the
clouds of virtual particles. It is obvious that in the standard model it is
impossible to solve the problem of quarks’ composition. One of the obstacles is
the fact that an unlimited number of particles with the spin ħ for gluons and
ħ/3 for quarks, including the spins of virtual particles, is admitted in this
model. This obvioulsy contradicts the theory of Infinite Hierarchical Nesting
of Matter, in which each object is infinitely divisible, and the characteristic
spin of the matter particles, that make up the object, is significantly less
than the characteristic spin of the object. Meanwhile, in the standard model it
is still considered possible that the strong interaction of pions with each
other is performed by pions, but the virtual ones. It implies introduction of
the idea of selfclosure of interactions of a number of known elementary
particles, without the need to involve deeper levels of matter, and inevitably
leads to inability to explain the essence of phenomena.
8) What are the sizes of quarks?
In attempts to find quarks in hadrons and to separate them from each other
highenergy particle collisions are used. With increasing of energy, the
particles can penetrate each other more and more, breaking into pieces and then
flying apart. The analysis of secondary particles shows that quarks, if they
exist, behave as point particles. Recent experiments at relativistic ion
collider in Brookhaven have shown that nucleon matter can be heated in
collisions up to 4•10^{12} degrees. In this case, it behaves similarly
to a liquid with very low viscosity, ^{[16]} and not
like free gas of quarks and gluons, predicted by chromodynamics. In contrast to
gas, in liquid there are forces of attraction, and this attraction property of
hadrons’ matter is predicted by strong gravitation. In the substantial neutron model, the hadrons’
matter, like the matter of neutron stars, consists not of three quarks, but of
a set of smallest particles (praons),
which allows them to behave like a liquid with low viscosity. From experiments
it also follows that the bunches of oppositely charged particles move opposite
to one another from the collision zone and rotate in opposite directions
according to the sign of their charge, as it happens in a magnetic field. ^{[17]} This can be explained by the fact that the forces,
arising from the torsion field of strong gravitation, in case of rapid rotation
of particles exceed significantly the electromagnetic forces and can
effectively influence the hadrons’ matter. ^{[2]}
9) If quarks were formed at the
beginning of the Big Bang, why is there practically no antimatter from
antiquarks? The problem of the asymmetry of matter and antimatter production in
the Big Bang does not have any reliable solution yet, as well as the cause of
the Big Bang. The fact of the Big Bang itself is reasonably questioned, because
its consequences could perfectly be explained by other reasons. ^{[18] [2]} Therefore, there is no answer to the raised
question in the standard theory. But if there were no Big Bang, then the
predominance of matter over antimatter can be explained by the natural course
of evolution of matter in space. And according to the theory of Infinite
Hierarchical Nesting of Matter, the evolution of matter at any level is
prepared by the evolution of matter at the lower and higher scale levels of
matter. As a result, the matter can accumulate under the influence of
fundamental forces and can break up in the processes with large release of
energy, eventually forming a ladder of space matter levels.
10) During formation of hadrons,
the energy of strong interaction of quarks should be emitted due to combination
of quarks. In what form is this energy emitted and can we discover it? In order
to explain the quarks’ confinement in hadrons in the standard theory the
interaction potential is usually introduced, containing two terms. The first
term has the Coulomb form and can be made positive to ensure the forces of
quarks’ repulsion at very small distances (otherwise quarks would simply
merge). This term should be proportional to the color charges and inversely
proportional to the distance between the quarks. The second term is also
positive and is directly proportional to the distance between the quarks,
raised to some degree, and is responsible for the increase of the force between
the quarks, when they move away from each other. The first term has an ordinary
potential form, and the second term is similar to the energy of spring tension.
It is assumed that the role of a spring is performed by gluon strings between
the quarks. If the quarks in hadron collisions get much energy they fly apart,
and the collision energy is converted into the energy of the gluon strings.
Upon exceeding certain distance and energy density limit these strings get torn
and the gluon energy is converted into quarkantiquark pairs, from which new
hadrons are produced. At the moment of formation of new hadrons the quarks
inevitably get closer and gluon bonds occur between them. If we use the analogy
with springs, in the new hadron we should expect damped oscillations of quarks
with the distance between them changing from minimum to maximum. Then the
question is, where does the energy of these oscillations eventually go? We can
assume that the gluon strings have the property of viscosity and they take all
the excess energy of quarks’ motion. Thus the system of quarks and gluons with
their color charges gets closed on itself and becomes responsible for all the
forces and phenomena. However, a new question arises about the origin of the
color charges themselves, as well as other similar questions that remain
unanswered. The theory of Infinite Hierarchical Nesting of Matter considers the
similarity of matter levels and the similarity of forces, acting between the
objects, regardless of their sizes. This approach does not require to introduce
quarks and to explain their extraordinary properties. Instead, only fundamental
gravitational and electromagnetic forces are considered and the weak
interaction is reduced not to forces but to the matter transformation. During
formation of any objects, in fundamental fields the binding energy is released
in the form of quanta of these fields. It is assumed that the quanta of the
gravitational field (gravitons) are the neutrinos emitted by particles at
different levels of matter, while neutrinos themselves are treated as some form
of photons. ^{[5]}
11) Is there any evolutionary
mechanism for generation of quarks and hadrons consisting of them, which is
associated neither with the Big Bang concept, nor with the emergence from other
highenergy elementary particles at their collisions? In the standard theory
the elementary particles such as nucleons and electrons are formed in the Big
Bang, where first quarkgluon plasma appeared, which decayed into hadrons and
leptons. The drawback of this approach is the analogy with the religious idea
of the world’s creation, besides it remains unclear what had existed before the
Big Bang. According to the theory of Infinite Hierarchical Nesting of Matter,
in order to explain the origin of elementary particles there is no need in the
Big Bang, since there is a single evolutionary mechanism for the formation of
any space objects, regardless of their size. In the Universe the fundamental
forces act by the same laws, due to which formation of new objects of disparate
matter can take place. It is assumed that more and more massive bodies are
formed under the action of graviton fluxes within Le Sage's theory of gravitation.
An example is formation of stars from gas clouds. Just like a star of
sufficient mass in the supernova explosion can produce a neutron star, so the
matter bound by the action of strong gravitation can be eventually transformed
into nucleons. Individual objects can also be formed due division of the system
made of a set of associated objects.
12) What is the reason of
nonobservability of free quarks? The exact reason is unknown, but this is one
of the proofs of the fact that quarks are not real particles but
quasiparticles.
13) What makes massive quarks
decay to less massive and stable quarks? What determines the characteristic
time of this decay? Since the properties of quarks due to their
nonobservability are derived from the properties of hadrons, then from decay
of almost all hadrons (except proton) the need of quarks’ decay should follow.
In the standard theory the quarks are assumed to be real particles, the basic
properties of which, including the instability of quarks with respect to decay,
remain unclear. If we treat quarks as quasiparticles, then the cause of
hadrons’ decays should be looked for not in the quarks, but in the interactions
of simple hadrons, like nucleons and pions, which are part of many massive
hadron states, with each other and in the transformation of the matter of these
simple hadrons, with regard to their electric charges and the strong
gravitational field.
14) What is the relationship
between the gluon field, ensuring strong interaction between quarks, and the
electromagnetic and gravitational fields of quarks? At the level of elementary
particles in the standard theory three types of interaction are usually
considered – strong, weak and electromagnetic. Due to the small mass of quark
their gravitational interaction is neglected. If for the strong interaction of
quarks, including change of their color charge or confinement in a hadron,
gluons are required, then charged Wbosons are required for the change of quark
flavor in the weak decay. Quarks have charge, decay into other quarks and
Wbosons, and participate together with these bosons in the electromagnetic
interaction. Gluons themselves have no electric charge and are not directly
associated with the electromagnetic field, but nevertheless can produce
quarkantiquark pairs, carrying the charge. This is possible due to the
assumption existing in the standard theory that energy is a) can be converted
into mass; b) can exist only in the form of particleantiparticle. However, the
conversion of energy into mass contradicts to the law of conservation of
matter, which is part of the law of conservation and change of carriers. ^{[19]} On the other hand, in the theory of Infinite
Hierarchical Nesting of Matter the strong interaction is associated mainly with
the strong gravitation and the gravitational torsion fields, but not with the
gluon field. In turn, gravitation, including strong gravitation, as well as
weak interaction are explained as a result of electromagnetic radiation at the
lower spatial levels of matter. ^{[5]}
15) How could leptons, that in
the standard theory do not participate in the strong interaction, produce at
their collisions quarks and hadrons, which are the objects of strong
interaction? According to the theory of strong
gravitation, it is the basic part of the strong interaction. In addition,
contribution into the strong interaction is made by the forces from
gravitational torsion fields and the electromagnetic forces, acting between the
particles. Just like ordinary gravitation, the strong gravitation is
responsible for the integrity of elementary particles and the attraction of
their matter, regardless of whether the matter is part of hadrons or leptons
(such as electrons and muons). Therefore, strong interaction must exist in
leptons, though in electrons it is much weaker than the electromagnetic
interaction due to the low mass to charge ratio. However, in interaction
between two muons the action of strong gravitetion exceeds the electrical force
23 times, which leads to similarity of interaction between muons and between
hadrons. Thus in 2005 the dimuonium state with energy 214.3 MeV, which decays
into positive and negative muons, was studied at the research center Fermilab. ^{[20]} As it was described above for the tau lepton, in
collisions of electrons and positrons of sufficient energy, under action of
strong gravitation the muon and pion phases of matter arise from the matter of
these leptons. The high density of matter of muon and pion phases is achieved
due to the energy of collision. At the level of stars, this corresponds to
transition of the planetary matter in collisions with relativistic velocities
into the state of matter of white dwarfs, and then after merging of white
dwarfs into the state of matter of neutron stars.
16) Why do mesons of two quarks
and baryons of three quarks prevail, and not hadrons of an arbitrary number of
quarks? From the point of view of spin symmetry, all particles have either
integer spin (bosons) or halfinteger spin, as fermions. Accordingly, in
interactions of elementary particles either mesons with integer spin or baryons
with halfinteger spin are produced. If we assume that quarks have spin ½, then
two quarks always have an integer spin, and three quarks have halfinteger
spin. Taking into account the orbital angular momenta, which are multiple of an
integer number in units of Dirac constant, does not change the baryon or meson
status of particles. Therefore, in the simplest case it is sufficient to assume
that all mesons are composed of two quarks, and baryons – of three quarks. This
allows us to cover all possible hadrons, and the particles of an arbitrary
number of quarks in the standard theory are simply unnecessary. However, if we
assume that division of particles on the basis of an integer or noninteger
spin is conventional, and that there are hadron states with intermediate values
of spin, then the idea of quarks with halfinteger spin also becomes
conventional. In this case, the desired spin of certain quarks should decrease,
and the possible number of quarks in hadrons should increase. The fact, that
the quark approach to explanation of the composition of mesons and baryons is
simplified, is proved by the states with inconsistent and contradictory quantum
numbers that are periodically found in different mass ranges. One recent
example is production of unaccounted muon jets at the Tevatron collider in
protonantiproton collisions at the total energy of 1.96 GeV. ^{[21]} In collisions with protons not only unaccounted
baryon have been found for a long time, but also meson states with such
energies as 62 MeV, 80 MeV and 100 MeV, etc. ^{[22]}
17) What is the meaning of the
observed exotic hadrons that do not fit into the standard quark scheme due to
the ambiguity of division into quarks? This situation occurs probably due to
the incompleteness of the quark theory that considers the particles as real
systems of two or three quarks. However, if quarks are only quasiparticles,
indirectly reflecting the symmetry of the interaction of particles, many hadron
states, instead of revealing certain symmetry, will give quasisymmetries that
do not comply with the idea of quarks.
For example, there are reports
about the discovery of hadrons, consisting of four or five quarks; besides,
there is assumed the existence of glueballs – the particles, in which the main
role is played not by quarks but by gluons G. ^{[7]}
For example, in experiments with negative pions and protons at energies 18 GeV,
mesons π_{1}(1400) and π_{1}(1600) with quantum numbers J^{PC}
= 1^{–+} were obtained. The analysis of experiments shows that π_{1}(1400)
looks like a fourquark state of the type qqqq, and π_{1}(1600) is a
hybrid of quarks and gluons in the form qqG. The discovered charged meson Z^{±}(4430)
counts in favor of multiquark states, it could have the structure in the form or ^{[23]}
The baryon resonances – the
candidates for fivequark states (pentaquarks) include Φ(1860) with the level
width less than 18 MeV and possible quark composition Θ^{+}(1540) with the mass 1533.6 MeV
and the level width 0.9 MeV, ^{[24]} as well as Θ^{0}_{c}(3100)
with an estimated quark composition
The wellknown organization
Particle Data Group has been collecting for a long time the data on the
properties of elementary particles and their annual updates. It has gathered a
significant collection of references to experimental works, according to which
a great number of states of particles is discovered that clearly do not fit
into the standard quark model. ^{[25]}
18) What prevents the virtual
quarks from the quark sea from being combined, like valence quarks, and from
forming new hadrons, thus creating mesons, nucleons and matter? According to
the standard model, quark or gluon that have a color charge, in case they have
excess energy, can transfer this energy to the quark sea with production of a
real quarkantiquark pair. Thus, the process of formation of matter from energy
is admitted. The philosophical contradiction consists in the fact that energy
is a characteristic or a quality of the matter, which therefore cannot produce
matter without involving some other source of matter. If we assume that virtual
particles are the source of matter, they should have the properties of real
matter in order to produce real particles. In this case, how can this virtual
matter be hidden from observation in the experiment? It is obvious that this
question has no answer, and we can only guess what is the mechanism of matter
conversion from the virtual status into the real one, why the sea of quarks and
antiquarks does not disappear in the process of selfannihilation or does not
spontaneously generate hadrons. We can avoid contradictions in the theory of
Infinite Hierarchical Nesting of Matter, in which instead of the sea of quarks
(quark vacuum), gluon vacuum or electromagnetic vacuum, etc., there are many
sources of real matter, each of which is a level of matter, nested in one
another.
19) What is the mechanism that
keeps the quarks and antiquarks of same or different flavors in some mesons
from annihilation? Some hadrons consist of a quark and an antiquark of the same
flavor, for example: η_{c} with the energy of 2980.5 MeV and the
composition of the charmed cquark and cantiquark, and χ_{b} with the
energy of 9859.44 MeV and the composition of the beautiful bquark and
bantiquark (see quarkonium). Other hadrons are assumed to consist of
combinations of pairs of quarks and antiquarks of the same flavor, in the form
of quantum superpositions of these pairs. Quarkonium decay to charmonium and
bottomium is considered similarly to the decay of positronium, the bound state
of electron, and its antiparticle – positron, existing until their
annihilation. Due to the absence in the standard theory of clear justification
of interaction between the quarks, taking into account the origin and nature of
their color charges, the problem of annihilation cannot be solved completely.
20) Is there a relationship
between the symmetry of quarks, leading to combining of hadrons in multiplets
and supermultiplets, and the ChewFrautschi families, built on the basis of the
dependence between the spins and the square of the hadron mass? The hadron
multiplets include the particles of approximately equal mass, with equal spin
and intrinsic parity, but with different electrical charges and the internal
quantum numbers similar to strangeness. These multiplets reflect the
combinatorics of quark at constant spin of hadrons. If we consider the hadrons
of the same type with their resonance states, then in the plane “spin – squared
mass” we obtain smooth curves. They are approximately parallel for different
types of hadrons, even including mesons and baryons. The reason of parallel
curves, the socalled ChewFrautschi plots, in the standard theory is unknown,
as well as their relationship with quarks and multiplets. If we analyze the
dependences of the hadron spin on the square of their mass using strong
gravitation, then we find a formula for the slope of the ChewFrautschi plots,
which turns out coinciding with the experimental values. ^{[2]} For the resonances it is shown that their spin
is not associated with the limiting rotation of hadrons as some spheres, but
rather with the orbital angular momentum of the particles, which form the
resonance. Simple multiplets can be understood not as a consequence of symmetry
of udsquarks, but as a result of combinations of αphase and βphase of
hadrons’ matter, that are part of nucleons and pions, with the property of
combining of these particles in hadron states that are characteristic of
strange particles. ^{[5]}
21) How does strong interaction
between the quarks inside hadrons turns into strong interaction between the
quarks of different hadrons, for example in the atomic nucleus? As the model of
interaction of quarks inside hadrons gluon strings are often used which connect
the quarks and do not allow them to leave the hadron. It is believed that the
potential of such an interaction is shortrange. This means that if a quark
from the outside will acquire sufficient energy and fly out of the hadron, then
the energy density of the gluon string at some point will exceed the limit, the
string will be broken with formation of a quarkantiquark pair from gluons,
after that hadronization of all quarks into new hadrons will take place. The
problem with the strong interaction between hadrons results from the fact that
quarks and gluons in the unexcited state do not leave hadrons because of the
color confinement. How then are gluon connections between quarks of different
hadrons established, which are necessary for the strong interaction between
hadrons? In this case, the standard theory involves the idea of using not
gluons, but whole hadrons (mostly pions) as the field quanta of strong
interaction. This idea is not new, since it repeats the quantum theory, in
which electromagnetic interactions between the charges are performed by
photons. The significant difference however is that the electromagnetic
interaction is a priori potential (the work in the field depends only on the
initial and final points, but not on the path of charge transfer), and the fact
that the same holds for the strong interaction performed by exchange of gluons
or hadrons is not proven. In addition, photons have zero mass, and their range
is not restricted, while pions have significant mass. Since there are no real
pions between the interacting hadrons, it is assumed that the strong
interaction is performed by virtual pions as well as by other hadrons with
various degrees of their contribution to the interaction. From this, we can see
that the strong interaction between hadrons again is reduced to hadrons, so
that there is inadmissible from the point of view of philosophy selfclosure of
theory and the absence of essential explanation of phenomena. The situation
changes if we use the theory of strong gravitation, in which the strong
interaction between hadrons and in the hadrons’ matter occurs by the same laws.
22) Is it possible in the
framework of quantum chromodynamics to derive from the first principles the
description of quarks’ interaction, which leads to confinement? It has not been
done so far, because the first principles for quarks are secondary – they are
derived from the properties of hadrons, but not from the properties of quarks
as such, due to unobservability of quarks. Besides, in the model of quark quasiparticles
the definition of quarks’ interactions does not have the meaning of primary
matter and can be used only for qualitative estimates of interactions, but not
for precise predictions.
23) How do the axisymmetric
properties of hadrons with respect to the preferred direction arise from the
discrete symmetry of the quark structure of hadrons (two quarks inside mesons
and three quarks inside baryons)? We will consider a positive pion, consisting
of uquark with the charge (⅔ e) and dantiquark with the charge (⅓ e), where e
is the elementary charge. Block massenergies of these quarks, based on their
content in the nucleon, are approximately the same and equal to 310 MeV.
However, their current massenergies, manifested in interactions with other
hadrons, are different and much less – about 3 MeV and 5 MeV, respectively. The
massenergy of a pion is equal to 139.567 MeV, which causes the block values of
quark masses no more than 70 MeV. Consequently, it is assumed that gluons
should bear the main part of the hadron mass instead of quarks.
On the other hand, the hadron
spin is determined by the quark spins. Thus, in a pion the quark spins must be
opposite, giving zero spin (on condition there is no orbital motion of quarks).
In this regard, there is a question – how can almost point quarks with low mass
have a spin equal to ħ/2? This spin is so great that even a much more massive
proton, taken in the form of a ball uniformly filled with matter with the
radius 0.87 fm, in case of such spin at the equator, would have the velocity of
matter rotation that reaches the value of 0.26 of the speed of light. For a
quark in this case the equatorial velocity is much greater than the speed of
light, which has no explanation. This situation is similar to the situation with
electron, the spin of which in the framework of quantum mechanics also has no
rational explanation and is only postulated. An alternative solution for the
electron spin is found in the substantial
electron model, similarly we should expect another solution for the spin of
quarks and hadrons. In particular, calculation of the quantum spin of a pion
gives a small but nonzero value, without use of the concept of quarks. ^{[5]}
As for the quarks’ combination in
hadrons other questions arise. For example, what supports the direction of
quark spins all the time so that their sum gives the hadron spin? Why is it
more suitable for the quark spins in the ground state of a pion to have
opposite directions? It can be assumed that there must be spinspin forces
between the quarks that ensure spin orientation in one direction or another and
keep them in this state. However, in a simple model of gluon exchange between
the quarks such forces are not supposed to exist. Due to the absence of spin,
the pion should not have a magnetic moment. Since both pion quarks have no the
same mass and their charges differ two times, it remains unclear how the spins
of these quarks generate equal and opposite magnetic moments. Moreover, these
magnetic moments must have significant size, which is indicated by the magnetic
moment of the proton that results from three quarks.
Baryons contain not two, but
three quarks, and in contrast to abstract theory, in practice, there is a
problem of determining their location in space relative to each other. For
example, inside a proton quarks must have some combination uud. Should they be
located on the same axis and lie in a plane so that their spins would be
perpendicular to this plane? Or can quarks be moving freely relative to each
other? In the standard model, there no answers to these questions due to
incompleteness of the theory, which follows from the symmetry of hadrons, but
not from their essential model.
24) In collisions of highenergy
particles new quarkantiquark pairs should be formed that are divided and are
included in new hadrons in the processes with multiple production of particles.
How are color quarks (antiquarks) combined into new particles, so that these
particles are always colorless and the number of quarks in them is such, as is
required for mesons and baryons (hadronization problem)? Formally, during
formation and subsequent division of a quarkantiquark pair, the quark (and the
antiquark) can form by means of gluons new quarkantiquark pairs, which then
somehow, according to their color charges, gather together to form hadrons.
Hadronization of jets, generated by initial quarks, is called fragmentation.
During fragmentation the color charge of the initial quark or gluon, when
combined with secondary quarks, should become discolored. This is expected in
the theory due to the symmetrical properties of hadrons and quarks anticipated
in them, but there is no single specific mechanism of the fragmentation
phenomenon.
25) Why do hadron states, formed
in different ways but having identical decays, differ from each other in their
energy? Example: a) The resonance Δ (1232), that appears in the scattering of
pions by nucleons and decays into a nucleon and a pion; b) Interaction of a
gammaquantum with the energy of 300 MeV with a stationary proton leads to
formation of a neutron and a pion with invariant energy of the state 1200 MeV;
c) The scattering of protons by protons produces a number of narrow resonances,
such as the 1004 MeV, 1044 MeV, 1094 MeV, 1136 MeV, 1173 MeV, 1210 MeV, 1249
MeV, etc. ^{[26]} In the standard theory the hadron
states are associated with a set of quarks, which have certain quantum states,
regardless of the way of their formation. In this case, the observed difference
in energies requires further explanation and is simulated by various
approximations. If, however, in the energy balance of a hadron state we take
into account not only energy, according to the definition of special theory of
relativity, but also strong gravitation, then due to different contributions to
the energy balance, different ways of hadron production will inevitably cause
different energy states, as it is observed. ^{[5]}
26) How can we understand the
fact that in the standard theory some hadrons should consist not only of a
particular set of two or three valence quarks (and indefinite number of virtual
quarks and gluons), but are considered to be quantum superpositions of valence
quarks, which contain different proportions of combinations of quarks and
hence, on the average, fractional by time number of quarks? The examples of
such hadrons are Λhyperon with the energy of 1115.68 MeV and neutral Σhyperon
with the energy of 1192.6 MeV, consisting of two triplets of quarks of the form
uds ± dus in different states, as well as neutral pion with the energy of
134.97 MeV and meson η with the energy of 547.8 MeV, consisting of
quarkantiquark pairs (with u, d, squarks).
This is a consequence of the
quantumwave approach and the use of unitary symmetry for dividing particles
into multiplets, where various combinations of the wave functions of quarks and
their combinations are admitted. If we use a probabilistic approach, which is
generally accepted in quantum mechanics, it turns out that, for example, some
neutral pion, taken at random, can be a quarkantiquark pair of utype and
another similar pion can be a quarkantiquark pair of dtype. In this case,
these pairs of quarks inside pions should periodically be annihilated, transforming
into each other. The situation for the strange meson η is even more
complicated, since the existence of three quarkantiquark pairs is admitted in
it, which are annihilated and transformed into each other. From a physical
point of view, the meaning of superpositions of quark states in some hadrons
and their absence in other hadrons is not clear enough. The specific mechanism
of hypothetical oscillations of quark pairs in mesons and quark triples in
baryons, as well as the proof of the existence of quark superpositions require
complete theoretical justification and experimental confirmation.
Elementary particles have a set
of quantum numbers, some of them are unique to hadrons and quarks. For example,
the baryon number of quarks is equal to ⅓, the baryon number of baryons is
equal to 1, and the baryon number of other particles, including mesons, is
zero. We can assume that central parts of baryons are responsible for the
conservation of baryon number, their nuclei that do not change or get destroyed
in any known reaction, except for annihilation of baryons and antibaryons. The
mass, charge and other properties of baryon shells change in reactions with
baryons, but not the nuclei. In this case, the nuclei of all baryons consist of
the matter of α – phase, which is inherent in the nuclei of neutron and proton.
In the state of α  phase the matter is maximally ordered by the magnetic
fields and gravitational torsion fields, and therefore it is stable, which
leads to conservation of the baryon number. Mesons do not have stable baryon
nuclei, so that only nucleon nuclei and the total baryon number are conserved
in the interaction with nucleons. In the table above of mesons, for kaon K^{+}
the matter composition in the form of α – phase is indicated. This follows from
the theory of quark quasiparticles and the idea that all quarks can be formally
represented as certain combinations of two phases of hadrons’ matter. However,
this is not enough to assign a nonzero baryon number to a particle. For
example, kaons can be considered as complexes of three pions, each of which and
the kaon itself have the baryon number equal to zero.
Isospin quantum number (isotopic
spin) I determines the number 2I +1 of the charge states characteristic of
hadrons of the same type, which are part of the respective isospin multiplet.
Nucleons have I = ½ and two isospin states – the proton and neutron.
The pion isospin is equal to 1
and corresponds to three charge states of pions. The interaction of pions with
nucleons can give not more than four charge states, resulting in isospin equal
to 3/2 for resonances Δ. By analogy with hadron isospin, reflecting
independence of strong interaction from the charge of particles and the value
of their electromagnetic interaction, weak isospin is also introduced for
quarks, which differentiates three up quarks and three down quarks. This means
that transformations or decays in weak interactions of the quarks of one type
are only possible to the quarks of the other type (up quarks transform into
down and vice versa). Strong and weak isospins were originally introduced for
nucleons and quarks that they consist of. Since the quark composition of proton
is uud, and the quark composition of neutron is udd, then replacing uquark by
dquark (or vice versa) would change the nucleon of one type to another
nucleon. This shows that weak isospin of quarks is closely associated with
strong isospin of hadrons, which is similar to a relationship between the parts
and the whole. In the substantial neutron
model, neutron betadecay and its transformation into proton results from
the transformation of neutron matter under influence of weak interaction, that
is followed by rearrangement of internal fluxes of electric and magnetic
fields. Therefore, weak isospin underlines the relative independence of the
weak interaction reactions that occur in the hadrons’ matter due to the strong
and electromagnetic interactions in this matter.
The quantum numbers of quarks
associated with their spin and charge are determined entirely by and result
from the quantitative quark composition and the spins of mesons and baryons. As
for the quark masses, they are not determined precisely neither in the quark
model, nor in the model of quark quasiparticles, which gives the properties of
quasiparticles to the quarks. Let us now consider the differences between the
quarks, determined by such a property as flavor. There are four types (flavors)
of quarks: s, c, b, t, which are associated with the quantum numbers of:
strangeness s, charm c, beauty (bottomness) b, truth (topness) t. For u and
dquarks there are no special quantum numbers, associated with the flavor.
In the model of quark
quasiparticles all quarks and hadrons are expressed as combinations of two
phases of hadrons’ matter. This allows us to get closer to the possible
structure of hadrons’ matter and shows that quarks are the material
representation of symmetry inherent in hadrons and their resonant states. In particular,
the difference between the properties of hadrons can be due to the fact that
they have different amounts of hadrons’ matter in its two states (αphase and
βphase), which can be differently charged and magnetized with respect to each
other and located in different spatial configurations. The latter is important
for strange hadrons, in which there is at least one squark. As it was shown in
the section devoted to strange hadrons, the presence of squark in a hadron can
be interpreted as an indication that this hadron has quasiequilibrium,
spatially separated state, which can be decomposed into simpler hadrons. The
long lifetime of strange particles results from the way of their production,
stability of particles is achieved due to the strong gravitation and the forces
from the gravitational torsion fields of particles.
The massive charmed and beautiful
hadrons differ from ordinary strange hadrons due to more complex composition of
constituent particles, as well as increased energy of their interaction. The
hadron states with tquarks arising at high energies exist for a short time, so
that tquark has time to decay to a less massive bquark before it becomes part
of some hadron. In a sense, tquark is similar to an intermediate virtual
particle. In the model of quark quasiparticles, tquark is interpreted as
manifestation of such a state of hadrons’ matter, in which the threshold
velocities are achieved, close to the maximum permissible for this matter.
Another quantum characteristic of
quarks, the color charge (color), appeared in order to explain the resonance Δ^{++},
in which three quarks uuu must be in the same state, contradicting the Pauli
exclusion principle for fermions. Hence we conclude that the maximum number of
different color charges should be the same as the maximum number of valence
quarks in a hadron, that is three quarks (in baryons) and three colors. In
contrast to isospin described by the symmetry group SU(2), rotation in the
color space forms the group SU(3). Based on the color charge the strong
interaction of quarks in hadrons is explained, which results from exchange of
colored gluons between quarks, leading to a change in the color charge and to
emerging of attraction forces. However, the idea of force interaction between
quarks by means of exchange of gluons, which resembles a quantummechanical
pattern of interaction between the electric charges by means of exchange of
photons, contradicts to the law of conservation of momentum, since two bodies,
exchanging neutral particles, can only repel.
In addition to the specific
quantum numbers of quarks, in quantum chromodynamics there are a lot of
hypotheses and auxiliary quantities, which are necessary for validation of the
theory and consistency with the experiment. We can mention anticipated
violations of the symmetry of quarks’ interaction due to differences in quark
masses, leading to a large difference in the masses of hadrons in each
multiplet, as well as to the idea of superposition of neutral quarkantiquark
pairs to represent the quark structure of some hadrons (these pairs must
annihilate periodically due to the strong interaction, transforming into each
other). To match the theoretical results with the experiment various mixing
angles in wave functions are introduced, a number of constant coefficients in
the terms presumably responsible for certain effects.
Based on the symmetry of color,
the existence of eight colored gluons is postulated, so that they could change
their color charge in exchange with quarks, without changing the quark flavor.
The unique properties of gluons are such that carrying their color charge they
can interact not only with quarks but also with each other, which is
inexplicable, if we assume that gluons are massless wave quanta. In this case,
isn’t it easier to refuse from quarks at all, replacing them with gluons?
Though in this case, the hadron masses would be entirely reduced to the
massenergy of massless gluons and the matter would become merely a
manifestation of the field. Anyway the expected strong interaction of gluons
among themselves is nothing but ultimate absolutization of de Broglie’s idea,
according to which the wave–particle duality of particles is performed. With
this duality the photons, for example, carry energy and momentum and thus they
have the properties of corpuscles as matter particles, but they do not carry an
electrical charge, they are involved in electromagnetic and gravitational
interactions, but not in the strong or weak interaction. The difference of
gluons from corpuscles like quarks consists only in the fact that gluons have
zero rest mass, and eight types of charges. Few physicists believe in the full
wave–particle duality between matter particles and field quanta at the level of
microparticles, assuming that it is valid only in part, in respect of the de
Broglie waves and the formulas for the energymomentum of the special theory of
relativity. Accordingly, the idea of gluons, which are even closer in their
properties to particles, is viewed with suspicion and skepticism.
Quite unusual is the hypothesis
of color confinement in quarks and gluons, since it is unclear how the color
charge can be both in quarks as matter particles and in massless gluons as the
field quanta. The result is the socalled confinement and the absence of free
quarks and gluons in nature. On the other hand, from the point of view of
experiment, the quarks are point (less than 10^{–18} m) structureless
formations inside hadrons, although the hadrons themselves have a radius of the
order of 10^{–15} m. Then what must the space inside a hadron be filled
with and should it be considered as almost absolutely empty? It is assumed that
quarks must be surrounded by clouds of virtual quarkantiquark pairs, and the
same applies to gluons, thus quark and gluon vacuums are introduced. It turns
out that hadrons mostly are filled with unobserved, obviously virtual
particles. This picture clearly contradicts the Infinite Hierarchical Nesting of Matter
and the theory of similarity of matter
levels, in which each hadron has corresponding analogues at every level of
matter, including the level of stars. In particular, in a neutron star as the
analogue of nucleon we don’t need to search for objects like quarks or gluons,
because the physical structure of stars is fairly well known.
Besides quarks and gluons, in QCD
in order to explain the weak decays of quarks and transformations of their
flavors the massive vector W and Z bosons are required. Although they are
considered as quanta – the carriers of weak interaction, they have nonzero
rest mass, ensuring very short range of weak interaction. Charged vector bosons
can change the electric charge of the quark that emits them to one elementary
charge, as well as change the spin to the quantity ħ. The quark emitting such a
boson changes its flavor and the boson decays into a lepton and a neutrino or
into a quark and an antiquark. Acquiring mass by vector bosons is assumed the
result of violation of the symmetry, which is theoretically considered
electroweak, and all known particles, in principle, should not have mass,
similarly to gluon, except for the hypothetical Higgs boson. But in the real
world the symmetry is spontaneously broken, and leptons, quarks and vector
bosons acquire mass by interacting with the Higgs bosons.
As we can see, in the standard
theory the mass is still reduced to energy and the matter particles – to the
field quanta, assuming the latter to be primary. This postulate contradicts the
philosophical basis of the matter structure and the theory of Infinite
Hierarchical Nesting of Matter. Besides, instead of the standard theory, with
shortrange massive vector bosons, there is another approach to explaining the
weak interaction. According to it, the weak interaction essentially is not a
force interaction, like gravitational or electromagnetic interaction, but the
result of a longterm transformation of the matter of elementary particles. At
the level of stars, this corresponds to phase transitions in the stellar
matter, similar to the transformation of the ordinary star matter into the
matter of white dwarfs and neutron stars, and the inverse transformation of
this matter at the masses of stars, exceeding the limits of the matter
stability in the gravitational field. These transitions are accompanied by the
collapse of stellar objects, ejection of shells and emission of neutrinos,
corresponding to the similar processes in weak decays of elementary particles.
A major role in these phase transitions in the stellar matter is played by
reactions with elementary particles and nuclear reactions with emission of
leptons and neutrinos, as well as breaking of the balance of forces of gravity
and pressure in the matter. Therefore, the weak interaction of hadrons and
leptons can be reduced again to the weak interaction and matter instability,
but at a lower level of elementary particles’ matter. ^{[2]} In this case, the weak interaction is not a
field interaction, so to describe it we actually do not need to introduce any
special field quanta. But if we introduce formally the field quanta of weak
interaction, such as gauge W and Z bosons, then they would have various
extraordinary properties, like mass. Moreover, it becomes necessary to
postulate the electroweak symmetry breaking, as well as to introduce the Higgs
mechanism.
Since in some cases there are
alternative models to describe the properties of hadrons and there is no need
to involve the idea of quarks, we can assume that quarks are not real particles
inside hadrons, but some quasiparticles, reproducing the physical laws and the
properties of symmetry inherent in hadrons.
In particular, during hadrons
production in reactions of interaction between elementary particles we should
take into account the following factors:
The additional factors making the
internal structure of hadrons more complicated can be the following:
A significant part of hadrons,
discovered in experiments, are the bound states of lowmass hadrons, such as
nucleons and pions. Some of these states can be called dynamically bound,
because the interaction time in them is almost equal to the time of flight of
the particles near each other. The dynamic states include almost all the
resonance states of hadrons. The typical examples are the baryons N and Δ, as a
result of the interaction between nucleons and mesons such as pions and kaons,
and the mesons f and ρ as twopion states. Due to the smallness of
electromagnetic interaction in comparison to strong interaction, the symmetry
with respect to the charge of identical hadrons is manifested in the form of
isotopic invariance (isospin).
Another symmetry associated with
the independence of weak interaction in the hadrons’ matter from strong
interaction (forming hadrons under the influence of strong gravitation) and
electromagnetic interaction (giving charges and magnetic moments to hadrons),
is reflected in the concept of the weak isospin of quarks. The special
properties of hadrons also include quantization of their properties and
discreteness of their states. As a rule, quantization and discreteness follow
from the way of hadrons production, the behavior of their matter in the
fundamental physical fields. A typical example is neutron stars, which are the
analogues of nucleons at the stellar level of matter. The method of formation
of neutron stars and the equation for the state of their matter are such that
the masses of the majority of these stars fall within a narrow range of
acceptable values. The same applies to the formation and evolution of nucleons,
which are the basis of matter observed in the Universe.
From the stated above it is clear
that considering quarks and hadrons as some compositions of hadrons’ matter in
αphase and βphase helps to understand phenomenologically different
characteristics of elementary particles. The formal substitution of six quarks
with two new entities, the matter phases, implies the possibility of further
simplification of the theory of hadron structure, generally based on the idea
of symmetry of particle interactions and involving the methods of quantum
mechanics. In hadron interactions, the matter phases are transformed into each
other, so that quarks as compositions of phases are not selfsufficient and
therefore unobservable as individual particles. This assigns to the quarks the
physical meaning of quasiparticles that do not exist outside of elementary
particles. In this case, the theory of confinement loses its sense, since in it
unobservability of free quarks is explained by the fact that separation of
quarks requires large amount of energy. Another consequence is that the
methodology of study of elementary particles needs revision. For example, we
need not mathematicaldescriptive theories of particles’ structure and
interaction, but real essentialmaterial models, including the origin and
evolution of particles in a single process of the world evolution. Such models
can be presented in the framework of the theory of Infinite Hierarchical
Nesting of Matter.
Source: http://sergf.ru/mkken.htm