Non-global and rapidity logarithms in narrow jet broadening

TL;DR

This paper develops a comprehensive factorization theorem for narrow jet broadening, a non-global observable sensitive to soft and collinear radiation, revealing that rapidity logarithms can be incorporated without added complexity, and identifying the structure of non-global logarithms.

Contribution

First factorization analysis of narrow jet broadening, showing rapidity logarithms are manageable and linking non-global logarithms to known jet functions.

Findings

Rapidity logarithms can be tied to the jet function, simplifying their treatment.

Leading non-global logarithms are encoded in the same factor as other soft functions.

This work provides a foundation for resummation of non-global observables.

Abstract

We derive an all-order factorization theorem for the narrow jet broadening event shape, a measure of the transverse momentum in jet events. This is a non-global observable which receives logarithmically enhanced contributions associated with the large rapidity difference between soft and collinear radiation and which is also sensitive to soft recoil effects. Our work is the first factorization analysis of an observable of this type and we show that with regard to the non-global nature, the rapidity logarithms do not constitute an essential complication since they can be tied to the jet function, which is the same as for global observables. As a consequence, the leading non-global logarithms in narrow jet broadening are encoded in the same overall factor relevant for the hemisphere soft function and light jet mass.