Soft Integrals and Soft Anomalous Dimensions at N$^3$LO and Beyond

TL;DR

This paper computes advanced soft integrals and anomalous dimensions at N$^3$LO and N$^4$LO in perturbative QCD, enhancing precision for processes like Drell-Yan and Higgs production, with implications for high-order theoretical predictions.

Contribution

It provides the first nine terms of soft phase-space and loop master integrals at N$^3$LO, and extracts anomalous dimensions at N$^4$LO, advancing the understanding of soft functions in QCD.

Findings

Computed soft integrals up to N$^3$LO with transcendental weight

Derived perturbative coefficient functions for Drell-Yan and Higgs production at N$^3$LO

Extracted soft and beam function anomalous dimensions at N$^4$LO

Abstract

We calculate soft phase-space and loop master integrals tor the computation of color-singlet cross sections through N$^3$LO in perturbative QCD. Our results are functions of homogeneous transcendental weight and include the first nine terms in the expansion in the dimensional regulator $\epsilon$. We discuss the application of our results to the computation of deeply-inelastic scattering and $e^+e^-$ annihilation processes. We use these results to compute the perturbative coefficient functions for the Drell-Yan and gluon-fusion Higgs boson production cross sections to higher orders in $\epsilon$ through N$^3$LO in QCD in the limit where only soft partons are produced on top of the colorless final state. Furthermore, we extract the anomalous dimension of the inclusive threshold soft function and of the $N$-Jettiness beam and jet functions to N$^4$LO in perturbative QCD.