  The Higgs-boson production channel $gg\to h$ mediated by light-quark loops
receives large logarithmic corrections in QCD, which can be resummed using
factorization formulae derived in soft-collinear effective theory. In these
factorization formulae the radiative gluon jet function appears, which is a
central object in the study of factorization beyond the leading order in scale
ratios. We calculate this function at two-loop order for the first time and
present the subtleties that come along with this.
