Next-to-leading power endpoint factorization and resummation for off-diagonal "gluon" thrust

TL;DR

This paper develops a novel method for resumming power-suppressed logarithmic corrections in collider physics by achieving endpoint-finite factorization formulas, enabling the first resummation of certain off-diagonal gluon contributions.

Contribution

It introduces a new endpoint factorization approach that removes divergences, allowing for systematic NLP resummation using renormalization-group techniques in collider observables.

Findings

First resummation of endpoint-divergent SCET$_{ m I}$ observables at leading logarithmic accuracy.

Factorization formulas free from endpoint divergences expressed in four dimensions.

Applicable to systematic NLP resummation in various collider processes.

Abstract

The lack of convergence of the convolution integrals appearing in next-to-leading-power (NLP) factorization theorems prevents the applications of existing methods to resum power-suppressed large logarithmic corrections in collider physics. We consider thrust distribution in the two-jet region for the flavour-nonsinglet off-diagonal contribution, where a gluon-initiated jet recoils against a quark-antiquark pair, which is power-suppressed. With the help of operatorial endpoint factorization conditions, we obtain a factorization formula, where the individual terms are free from endpoint divergences in convolutions and can be expressed in terms of renormalized hard, soft and collinear functions in four dimensions. This allows us to perform the first resummation of the endpoint-divergent SCET$_{\rm I}$ observables at the leading logarithmic accuracy using exclusively renormalization-group methods. The presented approach relies on universal properties of the soft and collinear limits and may serve as a paradigm for the systematic NLP resummation for other $1\to 2$ and $2\to 1$ collider physics processes.