Higgs production via gluon-gluon fusion with finite top mass beyond next-to-leading order

We present a computation of the cross section for inclusive Higgs production in gluon-gluon fusion for finite values of the top mass in perturbative QCD to all orders in the limit of high partonic center-of-mass energy. We show that at NLO the high energy contribution accounts for most of the difference between the result found with finite top mass and that obtained in the limit of infinite top mass. We use our result to improve the known NNLO order result obtained with infinite top mass. We estimate the effect of the high energy NNLO top mass dependence on the K factor to be of the order of a few per cent.