Jet mass with a jet veto at two loops and the universality of nonglobal structure

Abstract

We investigate the exclusive jet mass distribution in ${e}^{+}{e}^{\ensuremath{-}}$ 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 region of small jet mass. When combined with other ingredients using the 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 quantum chromodynamics. 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 nonglobal) 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 nonglobal contribution to the integrated jet thrust distribution and the previously calculated nonglobal 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.