The Complete Two-Loop Integrated Jet Thrust Distribution In Soft-Collinear Effective Theory

In this work, we complete the calculation of the soft part of the two-loop integrated jet thrust distribution in e+e− annihilation. This jet mass observable is based on the thrust cone jet algorithm, which involves a veto scale for out–of–jet radiation. The previously uncomputed part of our result depends in a complicated way on the jet cone size, r, and at intermediate stages of the calculation we actually encounter a new class of multiple polylogarithms. We employ an extension of the coproduct calculus to systematically exploit functional relations and represent our results concisely. In contrast to the individual contributions, the sum of all global terms can be expressed in terms of classical polylogarithms. Our explicit two-loop calculation enables us to clarify the small r picture discussed in earlier work. In particular, we show that the resummation of the logarithms of r that appear in the previously uncomputed part of the two-loop integrated jet thrust distribution is inextricably linked to the resummation of the non-global logarithms. Furthermore, we find that the logarithms of r which cannot be absorbed into the non-global logarithms in the way advocated in earlier work have coefficients fixed by the two-loop cusp anomalous dimension. We also show that, given appropriate L-loop contributions to the integrated hemisphere soft function, one can straightforwardly predict a number of potentially large logarithmic contributions at L loops not controlled by the factorization theorem for jet thrust. Work supported in part by US Department of Energy under contract DE-AC02-76SF00515.