Threshold resummation for electroweak annihilation from DIS data

TL;DR

The paper develops a framework to perform threshold resummation for electroweak annihilation using DIS results, enabling ${ m N^3LL}$ accuracy for Drell-Yan by computing the three-loop D-function from MVV's DIS data and two-loop form-factor results. It derives a general all-order relation D(α_s) = 4 B_δ(α_s) - 2 tilde G(α_s) + β_hat(α_s) d/dα_s F_MS(α_s) and explicitly evaluates D^(3) in terms of color structures and zeta values, validating the approach against renormalon and independent calculations. The analysis also extends to gluon-initiated processes, showing D_g^(3) can be obtained from D^(3) by replacing color factors, enabling ${ m N^3LL}$ resummation for Higgs production and related processes. These results enhance predictive precision for hadron collider phenomenology and provide nontrivial tests of perturbative convergence.

Abstract

We show that higher-order coefficients required to perform threshold resummation for electroweak annihilation processes, such as Drell-Yan or Higgs production via gluon fusion, can be computed using perturbative results derived in Deep Inelastic Scattering. As an example, we compute the three-loop coefficient D_3, generating most of the fourth tower of threshold logarithms for the Drell-Yan cross section in the MSbar scheme, using the recent three-loop results for splitting functions and for the quark form factor, as well as a class of exponentiating two-loop contributions to the Drell-Yan process.