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The Higgs-boson production channel $gg\to h$ mediated by light-quark loopsreceives large logarithmic corrections in QCD, which can be resummed usingfactorization formulae derived in soft-collinear effective theory. In thesefactorization formulae the radiative gluon jet function appears, which is acentral object in the study of factorization beyond the leading order in scaleratios. We calculate this function at two-loop order for the first time andpresent the subtleties that come along with this.

The Two-Loop Radiative Gluon Jet Function for $gg\to h$ via a Light Quark Loop