Mellin Moments of the Next-to-next-to Leading Order Coefficient Functions for the Drell-Yan Process and Hadronic Higgs-Boson Production

TL;DR

This work develops a Mellin-space framework for NNLO coefficient functions in Drell–Yan and hadronic Higgs production, recasting intricate x-space expressions into a compact basis of finite harmonic sums up to weight 4. By exploiting algebraic and structural relations among harmonic sums and analytic continuation to complex N, the authors reduce a large function basis to five basic sums plus standard functions, enabling fast and precise numerical evaluations. They provide explicit N-space representations for both unpolarized and polarized DY and Higgs cross sections, with a streamlined path from Mellin moments to x-space via contour inversion. The approach reveals a common mathematical structure across massless two-loop Wilson coefficients, improving theoretical precision and computational efficiency for phenomenology and data fitting.

Abstract

We calculate the Mellin moments of the next-to-next-to leading order coefficient functions for the Drell--Yan and Higgs production cross sections. The results can be expressed in terms of multiple finite harmonic sums of maximal weight w = 4. Using algebraic and structural relations between harmonic sums one finds that besides the single harmonic sums only five basic sums and their derivatives w.r.t. the summation index contribute. This representation reduces the large complexity being present in x-space calculations and is well suited for fast numerical implementations.