Higher order corrections to mixed QCD-EW contributions to Higgs production in gluon fusion

We present an estimate of the next-to-leading-order (NLO) QCD corrections to mixed QCD-electroweak contributions to the Higgs boson production cross section in gluon fusion, combining the recently computed three-loop virtual corrections and the approximate treatment of real emission in the soft approximation. We find that the NLO QCD corrections to the mixed QCD-electroweak contributions are nearly identical to NLO QCD corrections to QCD Higgs production. Our result confirms an earlier estimate of these O(ααs2) effects by Anastasiou et al. [J. High Energy Phys. 04 (2009) 003JHEPFG1029-847910.1088/1126-6708/2009/04/003] and provides further support for the factorization approximation of QCD and electroweak corrections.