Nikolay
NOSKOV

Translated from Russian by Jury SARYCHEV

Quantum chromodynamics (QCD) is attempt to advance internal frame of elementary particles by means of a mathematical formalism of a unitary symmetry SU (3) and group theories. QCD has arisen from conclusions of a relativity theory, principle of uncertainty of the Heisenberg and quantum electrodynamics.

However "any attempts to construct the successive theory of internal frame of elementary particles invariably resulted and result in failures" (Stanjukovich, Lapchinsky [1]), and "till now it was not possible to find theoretical criterion, which one would allow to construct natural classification of all known particles" (Bransky, 1989 [2]).

On this background the expression of the leading scientists is rather symptomatic in the field of elementary particle physics (EPP). Difficulties in explanation of internal frame elementary particles arise (as well as in their systematization – N.N.), apparently, because they are considered as some mathematical points surrounded" by a cloud "from virtual electrons, mesons, nucleons etc., not identical to actual objects. However experiments of Hofshtadter on dissipation of fast electrons on atomic nuclei convincingly have shown, that the nucleons have the final spatial sizes" (Svechnikov [3]). Similar thought has stated a Mosquito, Hoods and other researchers. Here, probably, it is necessary remind to the developers of EPP that extent is one of basic nature of mass.

But "the notion about elementary particles as about extended objects
contradict the laws of a special relativity theory" (Stanjukovich,
Lapchinsky), as "The process of ideal precise measurements of length can
not be realized for an elementary particle. **It causes legal doubts in a
feasibility of application of a relativity theory «inside particles»"**
(Fainberg [4]). It means localization, relativity theory and principle of
uncertainty of the Heisenberg, or extent and waiving of the theories,
which one contradicts it.

Considering extent as fundamental property of mass, it is necessary to construct the nonlocal physically reasonable theory of elementary particles (TEP). We can make it with the help of systematization of properties of elementary particles, depended on value of their masses (as in the table of Mendelejev); with the help of dynamic spatial model performances (as in atom); on the basis of development of spatial structure. Naturally, the first attempts to systematize elementary particles were connected with the analysis of their mass numbers, but it has not allowed classifying them. Then the researchers have noted, that the mass are distributed in close group, and their number in groups is subject to a certain numerical sequence. Gell-Mann [5] and irrespective of him Tswaig [6] have supposed (in 1964), that this sequence is subject to the laws of a unitary symmetry SU (3) of group theories (mathematical theory), which one gives a numerical series 1; 8; 10; 27;... "and which one is made up three initial numbers" (Stanjukovich). The search of three particles having been undertaken by them, by help of that would be possible to compound masses of all remaining particles, was not led to success. Then Gell-Mann and Tswaig have supposed, that there are certain three prime particles – quarks, which one are not present in a free state having fractional electrical and baryon charges.

With help of the quark model, the tenth particle in the third group was retrieved. The confidence in a correctness of selected path for the researchers has increased. Some success of this model has given a hope. That was even marked by the Nobel Prize. However in due course, when quantity of particles became more than 300, and quarks – 36 {(6 quarks + 6 antiquarks) × 3 colours}, the quantum chromodynamics has turn into the impassable quark jungle. An orderly natural system of classification of elementary particles has failed. TEP has lost the way in three quarks.

Attempts to classify elementary particles with help of spatial
structure were not undertaken, so far as from very beginning it was
refused to particles to have spatial frame. The sizes of radiuses of
nucleons (proton and neutron) 0,8 Fermis (1F = 10^{–13} cm)
are obtained by Hofshtadter experimentally, therefore they could not be
disclaimed and are inserted in the reference books (as annoying exception,
on which one nobody pay attentions).

Physicist – theorist K.A. Tokhtarov (from Alma-Ata) after careful analysis of EPP problems in 1993 has considered dynamics of development of a volume of elementary particles [7, 8, 9]. For this purpose he had to make two suppositions: a spatial mass density of elementary particles is approximately identical; the shape of particles can be presented as spheres. Having determined their density with the help of radius Hofshtadter, Tokhtarov has found out, that the increment of radiuses from group to group is approximately identical. Therefore it is possible to accept it for a constant. Besides there should be one some more group of hadrons not detected experimentally for the present.

The Tokhtarov's classification of groups of hadrons looks as quantization of mass or volumes and is described by the formula:

*M _{n}* =

*M _{n}* – mass of the lightest hadrons in group having
number

*A* and *B* – constant;

*n* – number of group (*n* = 1, 2, 3 etc.).

Tokhtarov points out, that at the formula there is a direct
manifestation of quantum properties, and also signs of a unitary symmetry,
as ratio *M*_{1}/*M*_{1};
*M*_{2}/*M*_{1};
*M*_{3}/*M*_{1}...= 1; 8; 27; 64; 125... Mass of
shells correlate as *m*_{1}/*m*_{1};
*m*_{2}/*m*_{1};
*m*_{3}/*m*_{1}... = 1; 7; 19; 37... That
indicates quantity and nature of particles, which are formed in
interactions depending on what shells participate in them. If
*k*-meson collide with nucleon by the outer shells, the one k-meson
and three π-mesons or six π-mesons (without calculation of energy of
interaction) can occur. There is a weak analogy of shells to quarks
(unobserving, successive increase of mass, number of shells, their
applicability as the constituents of hadrons). If we shell prolong the
analogy we can suppose about existents same more quarks. Number of them
should be 48 {(8 quarks + 8 antiquarks) × 3 colours}.

Now it is necessary to find out regularity of change of masses of elementary particles inside groups, and also to attempt to construct their dynamic mechanism model. However it is already now possible to tell, that the first actual step to natural construction of classification of elementary particles is made on the basis of their internal structure.

The literature:

- K.P. Stanjukovich, V.G. Lapchinsky. A systematization of elementary particles. In coll. About a systematization of fundamental particles. Atoms, nuclei, elementary particles. Atomizdat M. 1970.
- V.P. Bransky. The theory of elementary particles as object of methodological research. Edition the Leningrad university, L., 1989.
- G.A. Svechnikov. The inexhaustible of a matter. In coll. Structure and form of matter. Science, M., 1967, page 106.
- E.L. Fainberg. Non-locality. In coll. A relativity theory and high-energy physics. A series: physics, mathematician and astronomy. #12, Knowledge, M., 1966, page 40.
- M. Gell – Mann. Phys. Lett., 8, 214, 1964.
- G. Zweig. CERN preprints Th. 401 and 412, 1964.
- K.A. Tokhtarov. About structure of hadrons. SPE "Print", Institute of high-energy physics, Academy of Sciences; Kaz. SSR, Alma-Ata, 1993.
- K.A. Tokhtarov. To radiuses of hadrons. SPE "Print", Institute of high-energy physics, Academy of Sciences; Kaz. SSR, Alma-Ata, 1993.
- K.A. Tokhtarov. To a spectrum of mass of hadrons. SPE "Print", Institute of high-energy physics, Academy of Sciences; Kaz. SSR, Alma-Ata, 1993.