Finite top mass effects for hadronic Higgs production at next-to-next-to-leading order

Abstract

The first four terms of an expansion in M 2 H /M 2 t of the total inclusive cross section for Higgs production in gluon fusion are evaluated through next-to-next-to-leading order QCD. A reliable and precise approximation of the full top mass dependence at NNLO is derived and compared to the frequently used heavy-top limit. It is found that both results agree numerically to better than 0.5% in the Higgs mass range of 100-300 GeV. This validates the higher order results for the inclusive Higgs cross section and justifies the heavy-top limit as a powerful tool for Higgs phenomenology at the LHC and the Tevatron.

Higgs production at the lHC

“…At NLO, the approximation m t ≫ M H for the contribution of the top quark in the loop is rather good for Higgs masses below the tt threshold, M H < ∼ 340 GeV, in particular when the full quark mass dependence of the leading order cross section σ LO exact is taken into account [27]. At NNLO, this approximation for the top quark contribution seems also to be accurate as studies of the effect of a finite m t value in expansions of M H /(2m t ) have shown a difference below the percent level with respect to the EFT calculation for M H 300 GeV [78][79][80][81].…”

Higgs physics: Theory

“…Luckily, one can work in an effective field theory (EFT) approach in which the heavy loop particles are integrated out, making the calculation of the contributions beyond NLO possible. While this approach is justified for the dominant top quark contribution for M H < ∼ 2m t [33], it is not valid for the b-quark loop and for those involving the electroweak gauge bosons [34]. The uncertainties induced by the use of the EFT approach at NNLO are estimated to be of O(5%) [20].…”

“…Note in passing that the choice µ 0 = 1 2 M H also improves the convergence of the perturbative series and is more appropriate to describe the kinematics of the process. Some small additional corrections beyond NNLO have been also calculated [31][32][33]. The electroweak corrections are known both in some approximations [34] and exactly at NLO [35] and contribute at the level of a few percent; there are also small mixed NNLO QCD-electroweak effects which have been calculated in an effective approach valid for M H ≪ M W [30].…”

Higgs boson production at LHC to NNLO accuracy and finite top quark mass effects

“…We found 1 In Refs. [5,7] an expansion in x = M 2 H /ŝ has been performed whereas in Ref. [6] the full x-dependence is kept.…”

“…It is thus very important to perform the NNLO calculation within full QCD in order to obtain reliable predictions up to NNLO accuracy. Recently two independent groups have completed this big enterprise [3,4,5,6,7]. In this contribution we briefly describe the calculation and results obtained in Refs.…”