The Three-loop Quark Jet Function

TL;DR

This paper presents the first complete three-loop calculation of the massless quark jet function, a key component in high-precision collider physics, enabling advanced resummation and subtraction techniques at N$^3$LO.

Contribution

It provides the first full three-loop result for a collinear radiation factorization ingredient, advancing precision calculations in QCD for collider processes.

Findings

First complete three-loop quark jet function calculation.

Enhances resummation accuracy to N$^3$LL$^ extprime$.

Supports N$^3$LO fully-differential cross section computations.

Abstract

We calculate the massless quark jet function to three-loop order. The quark jet function is a universal ingredient in SCET factorization for many collider and decay processes with quark initiated final state jets. Our three-loop result contributes to the resummation for observables probing the invariant mass of final state quark jets at N$^3$LL$^\prime$. It represents the first complete three-loop result for a factorization ingredient describing collinear radiation. Furthermore it constitutes a major component of the $N$-jettiness subtraction/slicing method at N$^3$LO, which eventually may enable the calculation of fully-differential cross sections with a colorful final state at this order.