  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.
