Threshold resummation for electroweak annihilation from DIS data

Eric Laenen,Lorenzo Magnea

doi:10.1016/j.physletb.2005.10.038

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 MS¯ 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.

Highlights

Soft gluon resummations [1, 2, 3] have proven to be a valuable tool in perturbative QCD
We have analyzed threshold resummation for the Drell-Yan process in the MS scheme, in light of the recent results obtained for Deep Inelastic Scattering by MVV
General relationship expressing the function D(αs), responsible for threshold logarithms in the Drell-Yan cross section at single-logarithmic level, in terms of data requiring the knowledge of the virtual part of the nonsinglet splitting function, and the singular terms in the quark form factor, at the same perturbative order, plus a well-defined set of N-independent terms arising in the Drell-Yan cross section at lower orders

Summary

Introduction

Soft gluon resummations [1, 2, 3] have proven to be a valuable tool in perturbative QCD. The scope and expected precision of a range of QCD calculations have been extended in a remarkable series of papers by Moch, Vermaseren and Vogt (MVV), who computed first the three-loop contribution to the QCD splitting functions [6, 7], and the complete three-loop DIS coefficient functions [8], in what is arguably the most complex perturbative calculation ever carried out in quantum field theory Their results both test and extend the range of threshold resummation for DIS, which can be performed exactly to N2LL accuracy. These results will be useful in refining the theoretical prediction for processes of great interest at the LHC, such as Z0 production and Higgs production via gluon fusion, by extending our knowledge of soft-gluon effects, and our control of the theoretical uncertainty due to uncalculated higher-order perturbative as well as nonperturbative corrections

Factorization and exponentiation

Constraints from finiteness

Discussion