Journal of Physical Studies 23(1), Article 1101 [12 pages] (2019)
DOI: https://doi.org/10.30970/jps.23.1101

THE CALCULATION OF THE DIFFERENTIAL CROSS SECTION OF HADRON ELASTIC SCATTERING BY TRANSFERRED FOUR-MOMENTUM WITHIN THE PERTURBATION THEORY

N. O. Chudak, K. K. Merkotan, D. A. Ptashynskiy, O. S. Potiienko, I. V. Sharph, V. I. Bregid

Odesa National Polytechnic University, 1, Shevchenko Ave., Odesa, 65044, Ukraine
e-mail: nata.podolyan@gmail.com

Existing field theories consider multi-particle states from the Fock space are considered, but field operators are purely single-particle operators. As a result, all known quantum field theories are formulated in terms of the filling numbers of the single-particle states. Such a situation is acceptable for the theories (for example, QED), in which in the initial and final states there are quanta of the same fields that interact. But when we describe the hadron scattering processes, a known problem arises. Through the gluons' exchange an interaction occurs between the quarks that are in the hadron, but in the initial and final states of the scattering process, only the bound states of the quarks, which are hadrons, can be observed. This leads to the conclusion that when we consider the interaction between the quarks and gluons, we cannot ``turn on'' the interaction in the initial phase of the scattering process and ``turn off'' it in the final phase, as in the usual $\hat{S}$ -- matrix consideration. Namely, the asymptotic quark and gluon states are not single-particle and cannot, in principle, be expressed in terms of one-particle states due to the requirement of relativistic invariance. Indeed, it is impossible to realize a purely spatial shift in a relativistic theory, as each single-particle state cannot be characterized only by the particleТs momentum, but must be characterized by the energy-momentum four-vector. Therefore, as a result of working with the filling numbers of such states, we will have the energy-momentum conservation law for the quarks and gluons four-momenta, not for hadrons, as in the experiment.

We propose to solve these problems by using the model of multi-particle fields. After quantization, the operator-marking functions of the multi-particle fields describe the creation and annihilation of hadrons. When we describe the hadron processes with these operators, the hadrons energy-momentum is conserved, not the constituent particles, as it should be.

The differential cross section of proton elastic scattering by the square of the transferred four-momentum is calculated by the model of the multi-particle fields, namely three-particle bispinor field and two-particle gauge field. The contribution from the simplest pole diagrams and the contribution from the two-particle branching point are taken into account.

Comparison with experimental data showed a qualitative reproduction of these data. The nonmonotonе effect of the differential cross section dependence on the square of the transmitted four-momentum with increasing energy in the center of the mass system is described.

In the considered model, the nonmonotonе effect is a consequence of the proton spin properties. In our opinion, if we want to reproduce the quantitative experimental data, we will have to include the contributions from inelastic processes to the unitarity condition, but this requires a large amount of calculation.

PACS number(s): 12.38.Bx, 12.38.Cy, 25.40.Cm, 13.85.-t

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