Threshold factorization of the Drell-Yan process at next-to-leading power

TL;DR

This paper develops a factorization theorem for the Drell-Yan process near the threshold at next-to-leading power, identifying collinear functions and analyzing their behavior at higher orders, with implications for threshold resummation accuracy.

Contribution

It introduces a factorization framework at next-to-leading power for the Drell-Yan process, including the calculation of collinear functions and analysis of divergence issues in resummation.

Findings

Collinear functions calculated at $\\mathcal{O}(\alpha_s)$ match previous expansion-by-regions results.

Factorization is valid before dimensional regularization removal, highlighting issues in threshold resummation.

Divergent convolution arises when expanding around $d=4$, affecting resummation beyond leading-logarithmic accuracy.

Abstract

We present a factorization theorem valid near the kinematic threshold $z=Q^2/\hat{s}\to 1$ of the partonic Drell-Yan process $q\bar q\to\gamma^*+X$ for general subleading powers in the $(1-z)$ expansion. We then consider the specific case of next-to-leading power. We discuss the emergence of collinear functions, which are a key ingredient to factorization starting at next-to-leading power. We calculate the relevant collinear functions at $\mathcal{O}(\alpha_s)$ by employing an operator matching equation and we compare our results to the expansion-by-regions computation up to the next-to-next-to-leading order, finding agreement. Factorization holds only before the dimensional regulator is removed, due to a divergent convolution when the collinear and soft functions are first expanded around $d=4$ before the convolution is performed. This demonstrates an issue for threshold resummation beyond the leading-logarithmic accuracy at next-to-leading power.