On relativization of the Sommerfeld-Gamow-Sakharov factor

TL;DR

This paper generalizes the Sommerfeld-Gamow-Sakharov factor to arbitrary masses and energies, analyzing the Coulomb singularity in radiative corrections and proposing ways to extend the factor beyond traditional limits.

Contribution

It introduces a comprehensive treatment of the Sommerfeld-Gamow-Sakharov factor for arbitrary masses and energies, including the role of scalar triangular diagrams in Coulomb singularities.

Findings

Scalar triangular diagrams produce Coulomb singularity at threshold.

The singular correction factorizes at the complete Born cross section.

Different methods to generalize the factor are discussed.

Abstract

The Sommerfeld-Gamow-Sakharov factor is considered for the general case of arbitrary masses and energies. It is shown that the scalar triangular one-loop diagram gives the Coulomb singularity in radiative corrections at the threshold. The singular part of the correction is factorized at the complete Born cross section regardless of its partial wave decomposition. Different approaches to generalize the factor are discussed.