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We compute the mixed QCD-electroweak corrections to the cross section for theproduction of a Higgs boson via gluon fusion, in the limit of a small mass ofthe electroweak gauge bosons. This limit is regular and we calculate it bysetting the W, Z masses to zero in the Feynman rules for their propagators. Ouranalytic results provide an independent check, in a non-trivial limit, of arecent exact computation for the three-loop mixed QCD and electroweak virtualcorrections and the corresponding contribution to the cross section in thesoft-virtual approximation. From our calculation in the small massapproximation, we can infer the second term in the expansion of the crosssection around the threshold limit with its exact dependence on the masses ofthe W, Z bosons. Furthermore we find that in the small mass approximation thenon-factorizable contributions from the real radiation, so far unknown for fullgauge boson mass dependence, are modest in comparison to the known factorizableand virtual contributions to the full ${\cal O}(\alpha_s^3 \alpha^2)$ mixed QCDand electroweak cross-section. This furnishes a new phenomenological test ofestimates for the mixed QCD and electroweak corrections, which were based onthe hypothesis of factorization of QCD and electroweak corrections.

Mixed QCD-electroweak corrections to Higgs production via gluon fusion in the small mass approximation