N-jettiness beam functions at N3LO

TL;DR

This paper provides the first complete N$^3$LO calculation of N-jettiness beam functions in perturbative QCD, enabling higher-precision resummation and subtraction methods for collider physics.

Contribution

It introduces a novel method to compute N-jettiness beam functions at N$^3$LO using differential cross sections expanded about the collinear limit, involving complex iterated integrals.

Findings

First N$^3$LO calculation of N-jettiness beam functions.

Extension of $ au_N$ subtraction methods to N$^3$LO.

Enables resummation of $ au_N$ distributions at N$^3$LL$^ extprime$ accuracy.

Abstract

We present the first complete calculation for the quark and gluon $N$-jettiness ($\Tau_N$) beam functions at next-to-next-to-next-to-leading order (N$^3$LO) in perturbative QCD. Our calculation is based on an expansion of the differential Higgs boson and Drell-Yan production cross sections about their collinear limit. This method allows us to employ cutting edge techniques for the computation of cross sections to extract the universal building blocks in question. The class of functions appearing in the matching coefficents for all channels includes iterated integrals with non-rational kernels, thus going beyond the one of harmonic polylogarithms. Our results are a key step in extending the $\Tau_N$ subtraction methods to N$^3$LO, and to resum $\Tau_N$ distributions at N$^3$LL$^\prime$ accuracy both for quark as well as for gluon initiated processes.