Two-Loop QCD Amplitude forgg→h,Hin the Minimal Supersymmetric Standard Model

Abstract

We present the two-loop QCD amplitude for the interaction of two gluons and a CP-even Higgs boson in the Minimal Supersymmetric Standard Model. We apply a novel numerical method for the evaluation of Feynman diagrams with infrared, ultraviolet and threshold singularities. We discuss subtleties in the ultraviolet renormalization of the amplitude with conventional dimensional regularization, dimensional reduction, and the four dimensional helicity scheme. Finally, we show numerical results for scenarios of supersymmetry breaking with a rather challenging phenomenology in which the Higgs signal in the MSSM is suppressed in comparison to the Standard Model.The loop-mediated interaction of a Higgs boson and gluons is the main production mechanism for a Higgs boson at hadron colliders. Depending on the decay channels in which a Standard Model Higgs boson may be discovered, the measurement of the signal cross-sections can be achieved with a precision of about ±10% or better [1]. Amid the discovery of a Higgs boson, the signal crosssection will be an independent precision test of the Standard Model and its extensions.The gluon-fusion Higgs boson production cross-section is sensitive to higher order QCD corrections [2,3,4]. At the LHC, the signal cross-sections are known to change up to a factor of two when perturbative corrections from O α 2 s through O α 4 s are included [5,6]. The accuracy of these theoretical predictions is about ±10%. The partonic decay width to gluons also increases by a factor of two when including the known higher order QCD corrections. This quantity is now computed through order O α 5 s with an accuracy better than 1% [7]. Theoretical uncertainties in the ggh interaction within the Standard Model are currently adequately small for a future comparison with LHC data at a 10% precision level.Extensions of the Standard Model (SM) postulate diverse mechanisms for breaking the electroweak symmetry. A different Higgs boson sector than the one in the Standard Model and additional new particles are often introduced. The effects of undiscovered particles on the gluon-fusion cross-section are rather unconstrained from experimental data. Novel colored particles can change the Higgs and gluon interaction dramatically. For example, an additional heavy-quark with SM-like Yukawa coupling to the Higgs boson would contribute almost as much as the top-quark to the ggh amplitude. Recent examples in well motivated models were shown in [8].The complexity of the two-loop SM computations at O α 3 s in the full theory and at O α 4 s in the limit of a heavy top-quark is serious. The methods that have been employed are powerful and may be employed in other models. In especially simple modifications of the SM Lagrangian, for example adding a fourth generation with heavy leptons and quarks, the existing calculations are already sufficient. However, it will be important to know the gluon-fusion cross-section through at least order O α 3 s in all models which aspire to explain LHC data. Many viable extensions of the SM contai...

Supersymmetric next-to-next-to-leading order corrections to Higgs boson production in gluon fusion

“…Within the effective-theory framework, which constitutes an excellent approximation for Higgs boson masses below about 200 GeV, the production cross section has first been computed in Refs. [22,23] and has been confirmed analytically [24] and numerically [21] (see also Ref. [25]).…”

“…We define it to be proportional to the deviations of the approximated results based on the criteria in Eqs. (21) and (22) to their average. Since this term could by chance be small an additional factor is introduced which takes into account the size of δ 1 and δ 2 .…”

“…[19,20] (see also Ref. [21] for numerical results). The contribution from the top quark/top squark sector is available already since a few years.…”

Higgs production at the lHC

“…However, for heavy enough squarks and gluinos, as is the case for the benchmark scenarios that are in general discussed and which have M S ≫ M max h , these contributions are rather small as the SUSY states decouple from the amplitudes (their couplings to the Higgs bosons are not proportional to their masses). These SUSY contributions, including even the known QCD corrections [118][119][120][121][122][123][124][125][126][127], can be nevertheless evaluated exactly using the program HIGLU for instance.…”

NLO QCD bottom corrections to Higgs boson production in the MSSM

“…In particular, the full squark-gluon contribution is known in a closed analytic form [33][34][35], while the full quark-squark-gluino contribution has been computed in ref. [36] via a combination of analytic and numerical methods.…”