Color Exchange in Near-forward Hard Elastic Ecattering

TL;DR

This paper develops a color-flow factorization for near-forward quark-quark elastic scattering, revealing that the hard exchange reorganizes into singlet and octet channels in the $t$-channel as $s\to\infty$. The octet exchange reggeizes through Sudakov suppression, producing a Regge-like energy dependence, while the singlet exchange carries a distinct, $s$-independent Sudakov factor and a finite hard part $H_s$ after infrared subtractions. The authors formulate the RG evolution of the soft and hard pieces, derive the one-loop anomalous-dimension structure, and show how IR subtractions yield a finite, scheme-dependent but well-defined $H_s$. These results connect fixed-angle factorization to forward scattering and offer a path to applications in proton-proton elastic scattering and jet processes, with potential links to BFKL-like dynamics for the singlet sector.

Abstract

We study the large-$t$ small angle behavior of quark-quark elastic scattering. We employ a factorization procedure previously developed for fixed angle scattering, which depends on the color structure of the factorized hard subprocess. We find an evolution in $t$ that (in leading logarithmic approximation) becomes diagonal in a singlet-octet basis in the $t$-channel as $s\rightarrow \infty$. Octet exhange in the hard scattering is associated with the familiar `reggeized', $s^{α_g(t)}$ behavior, which arises from $s$-dependence in Sudakov suppression. In contrast, Sudakov suppression for $t$-channel singlet exchange in the hard scattering is $s$-independent. In general, these contributions are mixed by soft corrections, which, however, cancel in many experimental amplitudes and cross sections.