Radiative Quark Jet Function with an External Gluon

TL;DR

This paper calculates the radiative quark jet function with an external gluon at one- and two-loop order, providing insights into its anomalous dimension and renormalization-group evolution relevant for soft-collinear effective theory.

Contribution

It presents the first detailed calculation of the radiative quark jet function with an external gluon at two-loop order, expanding understanding beyond the photon case.

Findings

Calculated the jet function at one- and two-loop order.

Derived the one-loop anomalous dimension.

Analyzed the renormalization-group evolution.

Abstract

Factorization theorems in soft-collinear effective theory at subleading order in power counting involve ``radiative jet functions'', defined in terms of matrix elements of collinear fields with a soft momentum emitted from inside the jet. Of particular importance are the radiative quark jet functions with an external photon or gluon, which arise e.g. in the factorization theorems for the Higgs-boson amplitudes $h\to\gamma\gamma$, $h\to gg$ and $gg\to h$ induced by light-quark loops. While the photon case has been studied extensively in previous work, we present here a detailed study of the radiative jet function with an external gluon. We calculate this jet function at one- and two-loop order, derive its one-loop anomalous dimension and study its renormalization-group evolution.