Factorization for the light-jet mass and hemisphere soft function

TL;DR

This paper derives factorization formulas for the light-jet mass and hemisphere soft function, capturing all NNLO logarithms and enabling all-order resummations of non-global logarithms in collider observables.

Contribution

It introduces explicit factorization formulas for non-global observables, linking soft radiation to multi-Wilson-line operators and demonstrating their numerical significance.

Findings

Formulas capture all NNLO logarithms

Soft radiation linked to multi-Wilson-line operators

Non-global logarithms have sizeable impact

Abstract

Many collider observables suffer from non-global logarithms not captured by standard resummation techniques. Classic examples are the light-jet mass event shape in the limit of small mass and the related hemisphere soft function. We derive factorization formulas for both of these and explicitly demonstrate that they capture all logarithms present at NNLO. These formulas achieve full scale separation and provide the basis for all-order resummations. A characteristic feature of non-global observables is that the soft radiation is driven by multi-Wilson-line operators, and the ones arising here map onto those relevant for the case of narrow-cone jet cross sections. Numerically, the contributions of non-global logarithms to resummed hemisphere-mass event shapes are sizeable.