Beam functions for $N$-jettiness at N$^3$LO in perturbative QCD

TL;DR

This paper computes the N$^3$LO matching coefficients for $N$-jettiness beam functions in perturbative QCD using advanced multi-loop techniques, providing an independent verification of previous results.

Contribution

It presents a novel calculation of N$^3$LO beam function matching coefficients employing reverse unitarity and differential equations, independently confirming prior findings.

Findings

Computed N$^3$LO beam function coefficients

Established a new reduction method for master integrals

Validated previous results through independent calculation

Abstract

We present a calculation of all matching coefficients for $N$-jettiness beam functions at next-to-next-to-next-to-leading order (N$^3$LO) in perturbative quantum chromodynamics (QCD). Our computation is performed starting from the respective collinear splitting kernels, which we integrate using the axial gauge. We use reverse unitarity to map the relevant phase-space integrals to loop integrals, which allows us to employ multi-loop techniques including integration-by-parts identities and differential equations. We find a canonical basis and use an algorithm to establish non-trivial partial fraction relations among the resulting master integrals, which allows us to reduce their number substantially. By use of regularity conditions, we express all necessary boundary constants in terms of an independent set, which we compute by direct integration of the corresponding integrals in the soft limit. In this way, we provide an entirely independent calculation of the matching coefficients which were previously computed in arXiv:2006.03056.