Phenomenological description of spin effects in electromagnetic and strong interactions of quarks

Alexander J Silenko,Oleg V Teryaev

doi:10.1051/epjconf/201713808002

Abstract

Phenomenological description of interactions of relativistic quarks by the Dirac equation with the Cornell potential is given. The general form of the initial equation containing the vector and scalar parts of the Cornell potential is used at the arbitrary connection between these parts. The Hamiltonian in the Foldy-Wouthuysen representation is derived in the general form with allowance for the electromagnetic interactions. Unlike precedent investigations, it is relativistic and exact for terms of the zeroth and first powers in the Planck constant and also for such terms of the second power which describe contact interactions. General quantum mechanical equations of motion for the momentum and the spin are derived and the classical limit of the Hamiltonian and the equations of motion are found for the first time. A connection between the angular velocity of the quark spin precession and the force acting on it is determined. The energy of the spin-orbit interaction is rather high (of the order of 100 MeV). The terms describing the spin-orbit and contact interactions have opposite signs for the scalar and the vector parts of the Cornell potential. The evolution of the quark helicity and the spin-spin interaction of the quarks are also calculated.

Highlights

Phenomenological description of interactions of relativistic quarks by the Dirac equation with the Cornell potential is given
We have considered the strong and electromagnetic interactions of Dirac particles
The vector Cornell potential is similar to the four-vector potential of the electromagnetic field

Summary

Introduction

To solve the resulting equation only in some specific case, when the parameters of the scalar and vector potentials are very specific [3,4,5,6]. We use the both scalar and vector Cornell potentials and solve the more general problem of a strongly interacting Dirac particle (quark). Developed methods of the relativistic FW transformation [7,8,9] (see [10,11,12] and references therein) ensure fulfilling this transformation in arbitrarily strong external fields While this approach has not been used for strong interactions, it has proven itself as a powerful tool for a description of electromagnetic [11, 13, 14], gravitational [15,16,17,18,19,20,21], and weak [22, 23] interactions of single particles.

Cornell potential and its inclusion into the Dirac equation

Dirac equation with the scalar and vector Cornell potentials

Summary