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 mt → ∞. We use our result to improve the known NNLO order result obtained at mt → ∞. We estimate the effect of the high energy NNLO mt dependence on the K factor to be of the order of a few per cent. CERN-PH-TH/2008-009 January 2008 On leave from INFN, Sezione di Torino, Italy 1 The cross section in the soft limit and in the hard limit The determination of higher–order corrections to collider processes [1], and specifically Higgs production [2] in perturbative QCD is becoming increasingly important in view of forthcoming phenomenology at the LHC. The dominant Higgs production mechanism in the standard model is inclusive gluon–gluon fusion (gg → H + X) through a top loop. The next–to–leading order corrections to this process were computed several years ago [3, 4] and turn out to be very large (of order 100%). The bulk of this large correction comes from the radiation of soft and collinear gluons [5], which give the leading contribution in the soft limit in which the partonic center-ofmass energy ŝ tends to the Higgs mass mH , and which at LHC energies turns out to dominate the hadronic cross section after convolution with the parton distributions. This dominant contribution does not resolve the effective gluon-gluon-higgs (ggH) coupling induced by the top loop. As a consequence, the NLO correction can be calculated [6, 7] quite accurately in the limit mt → ∞, where it simplifies considerably because the ggH coupling becomes pointlike and the corresponding Feynman diagrams have one less loop. Recently, the NNLO corrections to this process have been computed in the mt → ∞ limit [8]. The NNLO result appears to be perturbatively quite stable, and this stability is confirmed upon inclusion [9] of terms in the next few orders which are logarithmically enhanced as ŝ → mH , which can be determined [10] using soft resummation methods. This suggests that also at NNLO the large mt approximation should provide a good approximation to the yet unknown exact result. However, this is only true for the total inclusive cross section: for example, if one looks at the production of Higgs plus jets, if the transverse momentum is large the infinite mt approximation fails [11]. Indeed, even though the mt–independent contribution from soft and collinear radiation turns out to dominate the cross section at the hadronic level, it does not necessarily provide a good approximation to the partonic cross section in a fixed kinematical region. In particular, the infinite mt approximation, which becomes exact in the soft limit, fails in the opposite (hard) limit of large center–of–mass energy. This is due to the fact that the ggH vertex is pointlike in the infinite mt limit, whereas for finite mt the quark loop provides a form factor (as we shall see explicitly below). Clearly, a point–like interaction has a completely different high energy behaviour than a resolved interaction which is softened by a form factor: in fact one can show [12] that a point–like interaction at n–th perturbative order has double energy logs while a resolved interaction has only single logs. This means that as ŝ → ∞ the gg → H +X partonic cross section σ̂ behaves as σ̂ ∼ ŝ→∞ 