Soft and Jet functions for SCET at four loops in QCD

TL;DR

This work derives four-loop soft and jet functions for quarks and gluons within Soft-Collinear Effective Theory by leveraging the latest four-loop eikonal and collinear anomalous dimensions and the KG equation framework. It connects full QCD results for Drell–Yan, Higgs production, and DIS to SCET building blocks, extracting SV and NSV components and predicting $ ext{O}(a_s^4)$ contributions, including $delta(1-z)$ terms and logarithmic structures. The rapidity-distribution sector is treated similarly, yielding SV/NSV rapidity functions with some coefficients left as ancillary data. The results provide essential ingredients for $N$-jettiness subtraction at $N^4LO$ and for high-precision threshold resummation, advancing precision collider phenomenology and informing future EIC studies.

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.