A remark on the high--energy quark--quark scattering and the eikonal approximation

TL;DR

This paper calculates high-energy quark-quark scattering amplitudes in scalar and fermionic QCD using the eikonal approximation, extending previous results and providing a unified derivation approach.

Contribution

It offers a direct derivation of high-energy quark-quark scattering amplitudes in both scalar and fermionic QCD within the eikonal approximation, connecting and extending prior work.

Findings

Derived scalar quark propagator in an external gluon field.

Extended results to fermionic QCD, matching previous findings.

Discussed the abelian case (QED) in the appendix.

Abstract

In this paper we calculate the high--energy quark--quark scattering amplitude, first in the case of scalar QCD, using Fradkin's approach to derive the scalar quark propagator in an external gluon field and computing it in the eikonal approximation. (This approach was also recently used by Fabbrichesi, Pettorino, Veneziano and Vilkovisky to study the four--dimensional Planckian--energy scattering in gravity.) We then extend the results to the case of ``real'' ({\it i.e.} fermion) QCD, thus deriving again, in a rather direct way, the results previously found by Nachtmann. The abelian case (QED) is also discussed in the Appendix.