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

## TL;DR

This paper introduces a systematic algorithm and a new software package for calculating two-loop soft functions in quantum chromodynamics, applicable to various collider observables, and confirms existing results while providing new predictions.

## Contribution

The authors develop a universal parametrisation method and a software tool, SoftSERVE, enabling efficient two-loop calculations of soft functions for different collider observables.

## Key findings

- Confirmed existing two-loop soft function results.
- Provided new predictions for C-parameter and angularities.
- Demonstrated applicability to both SCET-1 and SCET-2 soft functions.

## 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.