The treatment of the infrared region in perturbative QCD

TL;DR

This paper addresses how to properly handle the infrared contributions in NLO QCD calculations, proposing a subtraction method that aligns with the physical interpretation of parton distribution functions and impacts global PDF analyses.

Contribution

It introduces a subtraction procedure for infrared contributions in NLO QCD, improving the consistency of perturbative calculations with phenomenological PDFs.

Findings

The proposed method removes infrared divergences in NLO matrix elements.

Differences between the new and conventional treatments are quantified.

Implications for global PDF fits are discussed.

Abstract

We discuss the contribution coming from the infrared region to NLO matrix elements and/or coefficient functions of hard QCD processes. Strictly speaking, this contribution is not known theoretically, since it is beyond perturbative QCD. For DGLAP evolution all the infrared contributions are collected in the phenomenological input parton distribution functions (PDFs), at some relatively low scale Q_0; functions which are obtained from a fit to the `global' data. However dimensional regularization sometimes produces a non-zero result coming from the infrared region. Instead of this conventional regularization treatment, we argue that the proper procedure is to first subtract from the NLO matrix element the contribution already generated at the same order in \alpha_s by the LO DGLAP splitting function convoluted with the LO matrix element. This prescription eliminates the logarithmic infrared divergence, giving a well-defined result which is consistent with the original idea that everything below Q_0 is collected in the PDF input. We quantify the difference between the proposed treatment and the conventional approach using low-mass Drell-Yan production and deep inelastic electron-proton scattering as examples; and discuss the potential impact on the `global' PDF analyses. We present arguments to show that the difference cannot be regarded as simply the use of an alternative factorization scheme.