The hMSSM approach for Higgs self-couplings revisited

Eur. Phys. J. C (2019) 79:65 https://doi.org/10.1140/epjc/s10052-019-6594-x Regular Article - Theoretical Physics The hMSSM approach for Higgs self-couplings revisited Stefan Liebler1,a , Margarete Mühlleitner1,b , Michael Spira2,c , Maximilian Stadelmaier1,3,d 1 Institute for Theoretical Physics, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany 2 Paul Scherrer Institut, 5232, Villigen PSI, Switzerland 3 Institute for Nuclear Physics, Karlsruhe Institute of Technology, 76344 Karlsruhe, Germany Received: 11 November 2018 / Accepted: 10 January 2019 © The Author(s) 2019 Abstract We compare the decay of the heavy Higgs boson into two SM-like Higgs bosons, H → hh, calculated in a Feynman-diagrammatic approach at the one-loop level based on the one hand on the full effective potential involving the top quark and stops in the Minimal Supersymmetric Standard Model (MSSM) accompanied by the matched TwoHiggs-Doublet Model (2HDM) as its low-energy limit and on the other hand on the hMSSM approximation. We identify missing contributions due to the top quark in the Higgs self-couplings of the hMSSM, that – when taken into account – lead to a good agreement between the hMSSM and a full MSSM calculation, at least in the limit of the Higgsino mass parameter μ being small compared to the stop spectrum. We also thoroughly analyze momentum-dependent and kinetic corrections intrinsic to the Feynman-diagrammatic approach and the matching to the effective Lagrangian, respectively, for both our calculation in the MSSM and the hMSSM and for the latter suggest to include additional corrections from the top quark, which are independent of the unknown supersymmetric spectrum. 1 Introduction The discovery of the Higgs boson with a mass of (125.09 ± 0.24) GeV [1] in 2012 by the LHC experiments ATLAS [2] and CMS [3] has marked a milestone for particle physics. While this structurally completes the Standard Model (SM) the SM itself leaves open many questions that require extensions of the model. The SM is therefore considered as an effective low-energy description of a more complete model valid at high-energy scales. Since the discovered Higgs boson a e-mail: b e-mail: c e-mail: d e-mail: 0123456789().: V,-vol behaves very SM-like any such beyond-the-SM theory has to contain a SM-like Higgs boson with a mass of about 125 GeV. The Higgs sector of the Minimal Supersymmetric extension of the SM (MSSM) [4–16] consists of two complex Higgs doublets to ensure supersymmetry and the cancellation of anomalies. After electroweak symmetry breaking its Higgs sector contains five physical Higgs bosons, two neutral CP-even bosons, h, H , one neutral CP-odd boson, A, and a charged Higgs pair, H ± . The tree-level Higgs sector can be described by two parameters, usually chosen to be the mass of the CP-odd Higgs boson, M A , and the ratio of the two vacuum expectation values of the two Higgs doublets, tan β = v2 /v1 , in the case of real supersymmetric parameters. Supersymmetry restricts the tree-level mass of the lightest CP-even scalar h to values below the Z boson mass M Z . This constraint is relaxed by the inclusion of radiative corrections in the Higgs sector that can shift its value to the measured 125 GeV. The dominant corrections originate from third generation quark/squark loops. Depending on the parameter choices, the squark masses must be quite large in order to match the observed Higgs mass value for small values of tan β. Moreover, in a significant part of the MSSM parameter space the limits on the squark masses are pushed into the TeV range by the unsuccessful LHC searches for supersymmetric (SUSY) particles so far. The loop-corrected Higgs sector depends on many SUSY parameters so that the investigation of the MSSM parameter space becomes a complicated task. This triggered the introduction of benchmark scenarios that are used by the experimental collaborations for the interpretation of their results. Among these, the hMSSM presented in Refs. [17–20] exploits the fact that the dominant corrections to the lightest CP-even Higgs mass and the mixing parameters that enter the Higgs couplings have a common origin and that the dominant corrections stem from the topquark and its supersymmetric partners, the stops. In the hMSSM the measured Higgs mass value Mh is taken as an input parameter in addition to M A and tan β. 123 65 Page 2 of 18 This removes the explicit dependence of the Higgs sector on other SUSY parameters through the radiative corrections. In its region of applicability, the hMSSM approach has been shown to describe the MSSM Higgs mass spectrum and mixing angle α of the CP-even sector very well [20–22]. In particular, it allows to probe the low tan β regime where a very high SUSY scale is required for the radiative corrections to be large enough to achieve 125 GeV for the light CP-even Higgs mass. The Higgs self-couplings that are related to the Higgs masses through the Higgs potential are also affected by large radiative corrections. In order to make reliable predictions, the large logarithms that appear in the corrections in case of very large SUSY masses have to be resummed using effective field theory (EFT) methods. In physical processes containing the trilinear Higgs self-couplings, like Higgs decays into a pair of lighter Higgs bosons, momentum-dependent corrections to the vertex and to the kinetic factors can become important. These are not taken into account in the EFT approach, however, and have to be computed through a diagrammatic fixed-order calculation. In this paper, we revisit the hMSSM approach with focus on the Higgs-to-Higgs decay of the heavier H into two SMlike Higgs bosons, H → hh. We compute the decay at next-to-leading order (NLO) taking into account the dominant radiative corrections from the top-quark and stop sector. The calculation is performed in an effective low-energy 2HDM with MSSM-like quartic couplings that are properly matched to the MSSM and in the MSSM itself. In both cases the calculation is performed in the Feynman-diagrammatic approach thus including momentum-dependent corrections. Moreover, radiative corrections to the Higgs self-couplings from the top-quark contributions in the 2HDM, and the topquark and stop contributions in the MSSM, are taken into account through effective couplings. By choosing appropriate counterterms according to the low-energy limit, double counting is avoided when including the diagrammatic NLO corrections. By plugging in the effective trilinear Higgs selfcoupling of the hMSSM and comparing with the full MSSM result, we are able to disentangle the deviations due to the hMSSM approximation of the coupling from those originating from momentum-dependent contributions. In this way, we are able to properly dissect the Higgs self-coupling of the effective hMSSM approximation and to propose improvements that allow to better approximate the full result. It turns out that the bulk of the improvement does not i (...truncated)