Exponentiation of the Drell-Yan cross section near partonic threshold in the DIS and MSbar schemes

TL;DR

Problem: threshold-region Drell–Yan cross sections contain large logarithms and important constant terms that challenge fixed-order perturbation theory. Method: apply refactorization and RG-based exponentiation to both DIS and MSbar schemes to exponentiate N-independent terms and separate virtual and real contributions. Findings: in DIS, exponentiation arises from the ratio of timelike to spacelike Sudakov form factors; in MSbar, a finite, exponentiated structure is achieved via pure counterterms with F and D functions, and two-loop analysis shows partial agreement and constraints between real and virtual pieces. Significance: provides a scheme-dependent, systematic framework to estimate higher-order corrections near threshold, improve predictions, and extend to other threshold phenomena and multi-leg cross sections.

Abstract

It has been observed that in the DIS scheme the refactorization of the Drell-Yan cross section leading to exponentiation of threshold logarithms can also be used to organize a class of constant terms, most of which arise from the ratio of the timelike Sudakov form factor to its spacelike counterpart. We extend this exponentiation to include all constant terms, and demonstrate how a similar organization may be achieved in the MSbar scheme. We study the relevance of these exponentiations in a two-loop analysis.