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We present an estimate of the next-to-leading order QCD corrections to mixedQCD-electroweak contribution to Higgs boson production cross section in gluonfusion, combining the recently computed three-loop virtual corrections and theapproximate treatment of real emission in the soft approximation. We find thatthe NLO QCD corrections to mixed QCD-electroweak contributions are nearlyidentical to NLO QCD corrections to QCD Higgs production. Our result confirmsan earlier estimate of these ${\cal O}\left( \alpha\, \alpha_s^2 \right)$effects in arXiv:0811.3458 [hep-ph] and provides further support for thefactorization approximation of QCD and electroweak corrections.

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