Unitarity methods for Mellin moments of Drell-Yan cross sections

TL;DR

This paper introduces a unitarity-based method to compute Mellin moments of Drell-Yan cross sections directly from forward diagrams, efficiently isolating physical contributions and validated at one- and two-loop levels.

Contribution

It presents a novel, diagram-independent approach using cutting equations to extract Mellin moments from forward scattering diagrams, improving computational efficiency.

Findings

Validated method at one- and two-loop diagrams

Accurately isolates physical cuts in Mellin moments

Provides a systematic approach for Drell-Yan processes

Abstract

We develop a method for computing Mellin moments of single inclusive cross sections such as Drell-Yan production directly from forward scattering diagrams, by invoking unitarity in the form of cutting equations. We provide a diagram-independent prescription for eliminating contributions from unwanted cuts at the level of an expansion in the reciprocal omega=1/z variable. The modified sum over powers of omega produces the result from physical cuts only, with the nth coefficient precisely equal to the nth Mellin moment of the cross section. We demonstrate and validate our method for representative one- and two-loop diagrams.