Higgs boson gluon–fusion production at threshold in N 3 LO QCD

Abstract

We present the cross-section for the threshold production of the Higgs boson at hadron-colliders at next-to-next-to-next-to-leading order (N 3 LO) in perturbative QCD. We present an analytic expression for the partonic cross-section at threshold and the impact of these corrections on the numerical estimates for the hadronic cross-section at the LHC. With this result we achieve a major milestone towards a complete evaluation of the cross-section at N 3 LO which will reduce the theoretical uncertainty in the determination of the strengths of the Higgs boson interactions.High precision theoretical predictions for the production rate of the Higgs boson are crucial in the study of the recently discovered particle from the ATLAS and CMS Collaborations [1] and for inferring the existence of phenomena beyond the Standard Model. With the collection of further data at the upgraded LHC, the theoretical uncertainty for the gluon-fusion cross-section will become soon dominant. It is thus highly timely to improve the theoretical accuracy of the cross-section predictions.The quest for accurate Higgs boson cross-sections has been long-standing and it is paralleled with major advances in perturbative QCD. State-of-the-art calculations of the gluon-fusion cross-section (for a review, see Ref.[2] and references therein) comprise next-to-leading-order (NLO) QCD corrections in the full Standard-Model theory, next-to-next-to-leading order (NNLO) QCD corrections as an expansion in inverse powers of the top-quark mass 1/m t , two-loop electroweak corrections and mixed QCD/electroweak corrections. To improve upon the present accuracy, the most significant correction is expected from the N 3 LO QCD contribution in the leading order of the 1/m t expansion.Universal factorization of radiative corrections due to soft emissions, as well as knowledge of the three-loop splitting functions [3], have made possible the derivation of logarithmic contributions to the cross-section beyond NNLO [4]. However, further progress in determining the N 3 LO correction can only be achieved by direct evaluation of the Feynman diagrams at this order.

Two-loop splitting amplitudes and the single-real contribution to inclusive Higgs production at N3LO

“…Following the derivation of the three-loop virtual corrections [27][28][29][30][31], of the required renormalization and factorization counterterm contributions [32,33], and of expansions of single and multiple real radiation contributions around the soft limit [25,26,[34][35][36], the threshold approximation of this coefficient function was computed earlier this year [37]. We use our results for the two-loop splitting amplitudes to derive a closed analytic expression for the two-loop single-real contribution to the inclusive N 3 LO coefficient function for Higgs production.…”

“…We used our result to analytically compute the two-loop single-real contribution to the coefficient function of inclusive Higgs boson production in gluon fusion, improving upon the previously available soft approximation [25,26] of this function. When combined with either expanded or full results for the other channels (one-loop double-real and triple-real), our expression will allow to derive further terms in the threshold expansion [37] or to complete an exact calculation of the full N 3 LO coefficient function for Higgs production in gluon fusion.…”

On the calculation of soft phase space integral

“…In this work we have presented the calculation of soft triple-emission phase space integrals, which are relevant for soft-virtual corrections to Higgs production at N 3 LO [10,11]. The major techniques used in this calculation are differential equation for auxiliary integrals, and integration of harmonic polylogarithms.…”

“…[10,11], in which the soft-virtual corrections are obtained. The soft-virtual corrections are cross section in the threshold limit, where radiation in the final state is constrained to have low energy.…”

“…Perhaps the most important example is the soft-virtual corrections for Higgs production [10,11]. Consider the process…”