Endpoint factorization and next-to-leading power resummation of gluon thrust

TL;DR

This paper develops a new factorization framework to resum large logarithmic power-suppressed corrections in gluon thrust distributions, overcoming endpoint divergence issues in collider physics.

Contribution

It introduces an operatorial endpoint factorization approach that allows for the first resummation of endpoint-divergent SCET$_{ m I}$ observables at leading logarithmic accuracy.

Findings

Derived a divergence-free factorization formula for gluon thrust

Enabled resummation using only renormalization-group methods

Achieved first resummation of endpoint-divergent observables

Abstract

Endpoint divergences in the convolution integrals appearing in next-to-leading-power factorization theorems prevent a straightforward application of standard methods to resum large logarithmic power-suppressed corrections in collider physics. We study the power-suppressed configuration of the thrust distribution in the two-jet region, where a gluon-initiated jet recoils against a quark-antiquark pair. With the aid of operatorial endpoint factorization conditions, we derive a factorization formula where the individual terms are free from endpoint divergences and can be written in terms of renormalized hard, (anti) collinear, and soft functions in four dimensions. This framework enables us to perform the first resummation of the endpoint-divergent SCET$_{\rm I}$ observables at the leading logarithmic accuracy using exclusively renormalization-group methods.