Jet mass with a jet veto at two loops and the universality of non-global structure

TL;DR

This paper calculates the two-loop soft function for jet mass with a veto, revealing detailed structure of logarithms and a surprising connection to hemisphere soft functions, advancing understanding of jet substructure in QCD.

Contribution

It provides the first two-loop calculation of the soft function for jet mass with a veto, elucidating non-global logarithms and their universality in jet observables.

Findings

Two-loop soft function for jet mass with veto calculated.

Clear structure of global and non-global logarithms identified.

Small R limit shows a universal relation to hemisphere soft functions.

Abstract

We investigate the exclusive jet mass distribution in e+e- events, defined with a veto on the out-of-jet radiation, at two-loop order. In particular, we calculate the two-loop soft function, which is required to describe this distribution in the threshold region. When combined with other ingredients using soft-collinear effective theory, this generates the complete singular distribution for jet thrust, the sum of the jet masses, at two-loop order. The result is in excellent agreement with full QCD. The integrated jet thrust distribution is found to depend in an intricate way on both the finite jet cone size, R, and the jet veto scale. The result clarifies the structure of the potentially large logarithms (both global and non- global) which arise in jet observables for the first time at this order. Somewhat surprisingly, we find that, in the small R limit, there is a precise and simple correspondence between the non-global contribution to the integrated jet thrust distribution and the previously calculated non-global contribution to the integrated hemisphere soft function, including subleading terms. This suggests that the small R limit may provide a useful expansion for studying other exclusive jet substructure observables.