Precision Predictions for Higgs decays in the (N)MSSM

The signal that was discovered in the Higgs searches at ATLAS and CMS at a massof ∼ 125 GeV [1–3] is, within the current theoretical and experimentaluncertainties, compatible with the properties of the Higgs boson predictedwithin Standard-Model (SM) of particle physics. No conclusive signs of physicsbeyond the SM have been reported so far. However, the measurements of Higgssignal strengths for the various channels leave considerable room for BeyondStandard Model (BSM) interpretations. Consequently, the investigation of theprecise properties of the discovered Higgs boson will be one of the prime goalsat the LHC and beyond. While the mass of the observed particle is already knownwith excellent accuracy [4, 5], significant improvements of the informationabout the couplings of the observed state are expected from the upcoming runs ofthe LHC [3,6–9] and even more so from the high-precision measurements at afuture e + e − collider [10–18]. For the accurate study of the properties of theHiggs boson, precise predictions for the various partial decay widths, thebranching ratios (BRs) and the Higgs-boson production cross sections along withtheir theoretical uncertainties are indispensable. Motivated by the " HierarchyProblem " , Supersymmetry (SUSY)-inspired extensions of the SM play a prominentrole in the investigations of possible new physics. As such, the MinimalSupersymmetric Standard Model (MSSM) [19, 20] or its singlet extension, theNext-to-MSSM (NMSSM) [21,22], have been the object of many studies in the lastdecades. Despite this attention, these models are not yet prepared for an era ofprecision tests as the uncertainties at the level of the Higgs-mass calculation[23–25] are about one order of magnitude larger than the experimentaluncertainty. At the level of the decays, the theoretical uncertainty arisingfrom unknown higher-order corrections has been estimated for the case of theHiggs boson of the SM (where the Higgs mass is treated as a free inputparameter) in Refs. [26, 27] and updated in Ref. [28]: depending on the channeland the Higgs mass, it typically falls in the range of ∼ 0.5–5%. To ourknowledge, no similar analysis has been performed in SUSY-inspired models (orother BSM models), but one can expect the uncertainties from missing higher-order corrections to be larger in general—with many nuances depending on thecharacteristics of the Higgs state and the considered point in parameter space:we provide some discussion of this issue at the end of this paper. In addition,parametric uncertainties that are induced by the experimental errors of theinput parameters should be taken into account as well. For the case of the SMdecays those parametric uncertainties have been discussed in the referencesabove. In the SUSY case the parametric uncertainties induced by the (known) SMinput parameters can be determined in the same way as for the SM, while thedependence on unknown SUSY parameters can be utilised for setting constraints onthose parameters. While still competitive today, the level of accuracy of thetheoretical predictions of Higgs-boson decays in SUSY models should soon becomeoutclassed by the achieved experimental precision (in particular at future e + e− colliders) on the decays of the observed Higgs signal. Without comparableaccuracy of the theoretical predictions, the impact of the exploitation of theprecision data will be diminished—either in terms of further constraining theparameter space or of interpreting deviations from the SM results. Furtherefforts towards improving the theoretical accuracy are-251