Relativistic Coulomb S-factor of Two Spinor Particles with Arbitrary Masses

TL;DR

This paper introduces a new relativistic resummation method for the Coulomb S-factor in systems of two spin-1/2 particles with arbitrary masses, analyzing spin effects near threshold and in the relativistic regime.

Contribution

It develops a novel relativistic quasipotential approach to compute the S-factor for arbitrary mass spinor particles, including spin dependence and threshold behavior.

Findings

Spin significantly reduces the Sommerfeld effect at threshold.

At ultrarelativistic velocities, spin effects become negligible.

The new S-factor connects previous models for spinless and equal-mass spinor particles.

Abstract

A new resummation of the $S$-factor of a composite system of two relativistic spin-1/2 particles of arbitrary masses interacting via a Coulomb-like chromodynamical potential is presented. The analysis is performed in the framework of a relativistic quasipotential approach based on the Hamiltonian formulation of the covariant quantum field theory in the relativistic configuration representation. The pseudoscalar, vector, and pseudovector systems are considered and the behaviour of the $S$-factor near the threshold and in the relativistic limit is investigated in detail. The spin dependence of the $S$-factors is discussed as well. It is argued that at the threshold the contribution of spins significantly reduces the Sommerfeld effect, while at ultrarelativistic velocities their role diminishes and the $S$-factor becomes basically the same as for the spinless systems. A connection between the new and previously obtained S-factors for spinless particles of arbitrary masses and for relativistic spinor particles of equal masses is established.