Generic dijet soft functions at two-loop order: correlated emissions

Guido Bell,Jim Talbert,Rudi Rahn

doi:10.1007/jhep07(2019)101

Abstract

We present a systematic algorithm for the perturbative computation of soft functions that are defined in terms of two light-like Wilson lines. Our method is based on a universal parametrisation of the phase-space integrals, which we use to isolate the singularities in Laplace space. The observable-dependent integrations can then be performed numerically, and they are implemented in the new, publicly available package SoftSERVE that we use to derive all of our numerical results. Our algorithm applies to both SCET-1 and SCET-2 soft functions, and in the current version it can be used to compute two out of three NNLO colour structures associated with the so-called correlated-emission contribution. We confirm existing two-loop results for about a dozen e+e− and hadron-collider soft functions, and we obtain new predictions for the C-parameter as well as thrust-axis and broadening-axis angularities.

Highlights

As long as the underlying scale of the soft interactions is large enough, the soft functions can be calculated order-by-order in perturbation theory
The relevant resummation ingredients for Soft-Collinear Effective Theory (SCET)-1 soft functions were defined in section 4.1, and we present our results in the form γ0S = γ0CF CF, γ1S = γ1CA CF CA + γ1nf CF TF nf + γ1CF CF2
As all soft functions we consider obey the non-Abelian exponentiation (NAE) theorem, we have γ1CF = 0, cC2 F = 1/2(cC1 F )2, and the missing NNLO coefficients can entirely be determined from the correlated-emission contribution

Summary

Introduction

As long as the underlying scale of the soft interactions is large enough, the soft functions can be calculated order-by-order in perturbation theory. For observables that obey the non-Abelian exponentiation (NAE) theorem [28, 29], a dedicated calculation of the uncorrelated-emission contribution is not needed, and we can present complete NNLO results for a number of e+e− and hadron-collider soft functions already in this work. This is, not true for observables that violate the NAE theorem, like jet-veto or grooming observables, which we will address in [27] (preliminary results can be found in [30])

Objectives

Results

Conclusion