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

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