Renormalization group approach to soft gluon resummation

TL;DR

The paper develops an all-order renormalization-group proof that soft gluon logarithms exponentiate in perturbative QCD by tying the large logs to a single dimensionful scale and resumming with RG techniques. It provides a detailed framework relating Mellin-space (N) and momentum-space ($x$) resummations, derives an explicit all-order expression for the physical anomalous dimension, and demonstrates how resummed results can be matched with fixed-order calculations across different factorization schemes. While the approach is more general and scheme-flexible, its predictive power beyond next-to-leading log accuracy is reduced compared to previous all-order formalisms. The work also analyzes the momentum-space implementation, clarifies the origin of divergences in naive $x$-space resummations, and outlines practical schemes for combining resummed and fixed-order results, with potential extensions to other soft-resummation contexts.

Abstract

We present a simple proof of the all-order exponentiation of soft logarithmic corrections to hard processes in perturbative QCD. Our argument is based on proving that all large logs in the soft limit can be expressed in terms of a single dimensionful variable, and then using the renormalization group to resum them. Beyond the next-to-leading log level, our result is somewhat less predictive than previous all-order resummation formulae, but it does not rely on non-standard factorization, and it is thus possibly more general. We use our result to settle issues of convergence of the resummed series, we discuss scheme dependence at the resummed level, and we provide explicit resummed expressions in various factorization schemes.