Calculating Soft Radiation at One Loop

TL;DR

This paper introduces an efficient method for calculating one-loop soft QCD radiation effects, addressing divergences and complex measurements, enabling precise predictions for LHC processes at high logarithmic accuracy.

Contribution

It presents a novel approach to compute soft functions for complex jet measurements, including the first calculation of N-jettiness soft functions for generic angularities.

Findings

Successfully reproduces existing soft functions

Calculates N-jettiness soft function for generic angularities

Addresses divergences and complex jet boundary issues

Abstract

We present an efficient way to calculate the effect of soft QCD radiation at one loop, which is needed for predictions at next-to-next-to-leading logarithmic accuracy. We use rapidity coordinates and isolate the divergences in the integrand. By performing manipulations with cumulative variables, we avoid complications from plus distributions. We address rapidity divergences, divergences with an azimuthal dependence, complicated jet boundaries and multi-differential measurements. The process and measurements can be easily adjusted, as we demonstrate by reproducing many existing soft functions. The results for a general LHC process with multiple Wilson lines are obtained by treating Wilson lines that are not back-to-back using a boost. We also obtain, for the first time, the N-jettiness soft function for generic jet angularities, and the collinear-soft function for the measurement of two angularities.