Soft and Jet functions for SCET at four loops in QCD

TL;DR

This paper presents four-loop calculations of soft and jet functions in Soft-Collinear Effective Theory, advancing high-precision QCD predictions and enabling more accurate cross section computations at N^4LO accuracy.

Contribution

It provides the first four-loop predictions for soft and jet functions in SCET using recent anomalous dimension results, enhancing precision in QCD calculations.

Findings

Four-loop soft and jet functions computed for quarks and gluons.

Results enable N^4LO accuracy in the N-jettiness subtraction method.

Facilitates calculation of fully-differential cross sections at higher orders.

Abstract

Soft-Collinear Effective Theory is a framework for systematically organizing and resumming the logarithmic contributions that occur in high-energy reactions. It provides a factorized description of cross sections in terms of hard, jet, soft, and beam functions. As the latter are universal, they can be obtained from the well-known perturbative results in quantum chromodynamics (QCD) for deep-inelastic scattering, Drell-Yan and Higgs boson productions. Using the recent results ~\cite{Kniehl:2025ttz} on four-loop eikonal $(f^I)$ and collinear anomalous dimensions $(B^I)$ for quarks and gluons, $I=q,g$, as well as perturbative results from previous orders, we present four-loop predictions for the quark and gluon soft and jet functions. They constitute an important component of the $N$-jettiness subtraction method at $\rm{N^4LO}$ accuracy in QCD, which eventually may enable the calculation of fully-differential cross sections at higher orders.