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Abstract The described Dark Abelian Sector Model (DASM) extends the Standard Model (SM) by a “dark” sector containing a spontaneously broken U(1)d gauge group. Keeping this dark sector quite generic we only add one additional Higgs boson, one Dirac fermion, and right-handed SM-like neutrinos to the SM. Using the only two singlet operators of the SM with dimension less than 4 (the U(1)Y field-strength tensor and the SM Higgs mass operator |Φ|2) as well as the right-handed neutrino fields we open up three portals to the dark sector. Dark sectors, such as the one of the DASM, that introduce an additional Higgs boson H as well as an additional Z′ gauge boson can have a large influence on the predictions for electroweak precision observables and even accommodate possible dark matter candidates. We consider one of the two Higgs bosons to be the known 125 GeV Higgs boson and parameterize the extension of the scalar sector by the mass of the second Higgs boson, the Higgs mixing angle, and a Higgs self-coupling. We do not assume any mass hierarchy in the gauge sector and use the mass of the additional Z′ boson and a corresponding gauge-boson mixing angle to parameterize the extension of the gauge sector. The fermion sector is parameterized by the mass of the additional fermion and a fermion mixing angle. We describe an on-shell as well as an MS ¯ $$ \overline{\textrm{MS}} $$ renormalization scheme for the DASM sectors and give explicit results for the renormalization constants at the 1-loop level, and, thus, prepare the ground for full NLO predictions for collider observables in the DASM. As a first example, we provide the DASM prediction for the W-boson mass derived from muon decay.

Abstract In supersymmetric theories the Higgs boson masses are derived quantities where higher-order corrections have to be included in order to match the measured Higgs mass value at the precision of current experiments. Closely related through the Higgs potential are the Higgs self-interactions. In addition, the measurement of the trilinear Higgs self-coupling provides the first step towards the reconstruction of the Higgs potential and the experimental verification of the Higgs mechanism sui generis. In this paper, we advance our prediction of the trilinear Higgs self-couplings in the CP-violating Next-to-Minimal Supersymmetric extension of the SM (NMSSM). We provide the $$\mathcal{O}(\alpha _t^2)$$ O ( α t 2 ) corrections in the gaugeless limit at vanishing external momenta. The higher-order corrections turn out to be larger than the corresponding mass corrections but show the expected perturbative convergence. The inclusion of the loop-corrected effective trilinear Higgs self-coupling in gluon fusion into Higgs pairs and the estimate of the theoretical uncertainty due to missing higher-order corrections indicate that the missing electroweak higher-order corrections may be significant.

Abstract We calculate the Higgs-boson mass spectrum and the corresponding mixing of the Higgs states in the Minimal Supersymmetric Standard Model (MSSM). We assume a mass-hierarchy with heavy SUSY particles and light Higgs bosons. To investigate this scenario, we employ an effective-field-theory approach with a low-energy Two-Higgs-Doublet Model (2HDM) where both Higgs doublets couple to right-handed up- as well as right-handed down-type fermions. We perform a one-loop matching of the MSSM to the 2HDM and evolve the parameters to the low energy scale by exploiting two-loop renormalization group equations, taking the complex parameters into account. For the calculation of the pole mass, we compare three different options: one suitable for large charged Higgs mass, one for low charged Higgs mass, and one approximation that interpolates between these scenarios. The phase dependence of the mass of the lightest neutral Higgs boson can be sizeable, i.e. of the order of a couple of GeV depending on the scenario. In addition, we discuss the CP composition of the neutral Higgs bosons.

Abstract A recently proposed scheme for a gauge-invariant treatment of tadpole corrections in spontaneously broken gauge theories — called Gauge-Invariant Vacuum expectation value Scheme (GIVS) — is applied to a singlet Higgs extension of the Standard Model and to the Two-Higgs Doublet Model. In contrast to previously used tadpole schemes, the GIVS unifies the gauge-invariance property with perturbative stability. For the Standard Model this was demonstrated for the conversion between on-shell and MS ¯ $$ \overline{\mathrm{MS}} $$ renormalized masses, where the GIVS leads to very moderate, gauge-independent electroweak corrections. In models with extended scalar sectors, issues with tadpole renormalization exist if Higgs mixing angles are renormalized with MS ¯ $$ \overline{\mathrm{MS}} $$ conditions, which is the major subject of this article. In detail, we first formulate non-linear representations of the extended scalar sectors, which is an interesting subject in its own right. Then we formulate the GIVS which employs these non-linear representations in the calculation of the tadpole renormalization constants, while actual higher-order calculations in the GIVS proceed in linear representations as usual. Finally, for the considered models we discuss the next-to-leading-order (electroweak and QCD) corrections to the decay processes h/H → WW/ZZ → 4 fermions of the CP-even neutral Higgs bosons h and H using MS ¯ $$ \overline{\mathrm{MS}} $$ -renormalized Higgs mixing angles with the GIVS and previously used tadpole treatments.

Abstract The renormalization of vacuum expectation value parameters, such as v in the Standard Model (SM), is an important ingredient in electroweak renormalization, where this issue is connected to the treatment of tadpoles. Tadpole counterterms can be generated in two different ways in the Lagrangian: in the course of parameter renormalization, or alternatively via Higgs field redefinitions. The former typically leads to small corrections originating from tadpoles, but in general suffers from gauge dependences if MS ¯ $$ \overline{\mathrm{MS}} $$ renormalization conditions are used for mass parameters. The latter is free from gauge dependences, but is prone to very large corrections in MS ¯ $$ \overline{\mathrm{MS}} $$ schemes, jeopardizing perturbative stability in predictions. In this paper we propose a new scheme for tadpole renormalization, dubbed Gauge-Invariant Vacuum expectation value Scheme (GIVS), which is a hybrid scheme of the two mentioned types, with the benefits of being gauge independent and perturbatively stable. The GIVS is based on the gauge-invariance property of Higgs fields, and the corresponding parameters like v, in non-linear representations of Higgs multiplets. We demonstrate the perturbative stability of the GIVS in the SM by discussing the conversion between on-shell and MS ¯ $$ \overline{\mathrm{MS}} $$ renormalized masses.

Abstract We present our computation of the O $$ \mathcal{O} $$ ((α t + α λ + α κ )2) two-loop corrections to the Higgs boson masses of the CP-violating Next-to-Minimal Supersymmetric Standard Model (NMSSM) using the Feynman-diagrammatic approach in the gaugeless limit at vanishing external momentum. We choose a mixed DR ¯ $$ \overline{\mathrm{DR}} $$ -on-shell (OS) renormalisation scheme for the Higgs sector and apply both DR ¯ $$ \overline{\mathrm{DR}} $$ and OS renormalisation in the top/stop sector. For the treatment of the infrared divergences we apply and compare three different regularisation methods: the introduction of a regulator mass, the application of a small momentum expansion, and the inclusion of the full momentum dependence. Our new corrections have been implemented in the Fortran code NMSSMCALC that computes the Higgs mass spectrum of the CP-conserving and CP-violating NMSSM as well as the Higgs boson decays including the state-of-the-art higher-order corrections. Our numerical analysis shows that the newly computed corrections increase with rising λ and κ, remaining overall below about 3% compared to our previously computed O $$ \mathcal{O} $$ (α t (α t + α s )) corrections, in the region compatible with perturbativity below the GUT scale. The renormalisation scheme and scale dependence is of typical two-loop order. The impact of the CP-violating phases in the new corrections is small. We furthermore show that the Goldstone Boson Catastrophe due to the infrared divergences can be treated in a numerically efficient way by introducing a regulator mass that approximates the momentum-dependent results best for squared mass values in the permille range of the squared renormalisation scale. Our results mark another step forward in the program of increasing the precision in the NMSSM Higgs boson observables.

Abstract Predictions for the Higgs masses are a distinctive feature of supersymmetric extensions of the Standard Model, where they play a crucial role in constraining the parameter space. The discovery of a Higgs boson and the remarkably precise measurement of its mass at the LHC have spurred new efforts aimed at improving the accuracy of the theoretical predictions for the Higgs masses in supersymmetric models. The “Precision SUSY Higgs Mass Calculation Initiative” (KUTS) was launched in 2014 to provide a forum for discussions between the different groups involved in these efforts. This report aims to present a comprehensive overview of the current status of Higgs-mass calculations in supersymmetric models, to document the many advances that were achieved in recent years and were discussed during the KUTS meetings, and to outline the prospects for future improvements in these calculations.

Abstract Recently, the Higgs boson masses in the Minimal supersymmetric standard model (MSSM) and their mixing have been calculated using the complex two-Higgs-doublet model (cTHDM) as an effective field theory (EFT) of the MSSM. Here, we discuss the implementation of this calculation, which we improve in several aspects, into the hybrid framework of FeynHiggs by combing the cTHDM-EFT calculation with the existing fixed-order calculation. This combination allows accurate predictions also in the intermediate regime where some SUSY particles are relatively light, some relatively heavy and some in between. Moreover, the implementation provides precise predictions for the Higgs decay rates and production cross-sections.

Abstract We present our calculation of the two-loop corrections of O $$ \mathcal{O} $$ ( α t 2 $$ {\alpha}_t^2 $$ ) to the neutral Higgs boson masses of the CP-violating Next-to-Minimal Supersymmetric extension of the Standard Model (NMSSM). The calculation is performed in the Feynman diagrammatic approach in the gaugeless limit at vanishing external momentum. We apply a mixed DR ¯ $$ \overline{\mathrm{DR}} $$ -on-shell (OS) renormalization scheme for the NMSSM input parameters. Furthermore, we exploit a DR ¯ $$ \overline{\mathrm{DR}} $$ as well as an OS renormalization in the top/stop sector. The corrections are implemented in the Fortran code NMSSMCALC for the calculation of the Higgs spectrum both in the CP-conserving and CP-violating NMSSM. The code also provides the Higgs boson decays including the state-of-the-art higher-order corrections. The corrections computed in this work improve the already available corrections in NMSSMCALC which are the full one-loop corrections without any approximation and the two-loop O $$ \mathcal{O} $$ (α t α s ) corrections in the gaugeless limit and at vanishing external momentum. Depending on the chosen parameter point, we find that the O(α t α s + α t 2 $$ {\alpha}_t^2 $$ ) corrections add about 4-7% to the one-loop mass of the SM-like Higgs boson for DR ¯ $$ \overline{\mathrm{DR}} $$ renormalization in the top/stop sector and they reduce the mass by about 6-9% if OS renormalization is applied. For an estimate of the theoretical uncertainty we vary the renormalization scale and change the renormalization scheme and show that care has to be taken in the corresponding interpretation.

Abstract We discuss the parameter spaces of supersymmetry (SUSY) scenarios taking into account the improved Higgs-mass prediction provided by FeynHiggs 2.14.1. Among other improvements, this prediction incorporates three-loop renormalization-group effects and two-loop threshold corrections, and can accommodate three separate mass scales: $$m_{{{\tilde{q}}}}$$ mq~ (for squarks), $$m_{\tilde{g\,}\!}$$ mg~ (for gluinos) and $$m_{{{\tilde{\chi }}}}$$ mχ~ (for electroweakinos). Furthermore, it contains an improved treatment of the $$\overline{\mathrm {DR}}$$ DR¯ scalar top parameters avoiding problems with the conversion to on-shell parameters, that yields more accurate results for large SUSY-breaking scales. We first consider the CMSSM, in which the soft SUSY-breaking parameters $$m_0$$ m0 and $$m_{1/2}$$ m1/2 are universal at the GUT scale, and then sub-GUT models in which universality is imposed at some lower scale. In both cases, we consider the constraints from the Higgs-boson mass $$M_h$$ Mh in the bulk of the $$(m_0, m_{1/2})$$ (m0,m1/2) plane and also along stop coannihilation strips where sparticle masses may extend into the multi-TeV range. We then consider the minimal anomaly-mediated SUSY-breaking scenario, in which large sparticle masses are generic. In all these scenarios the substantial improvements between the calculations of $$M_h$$ Mh in FeynHiggs 2.14.1 and FeynHiggs 2.10.0, which was used in an earlier study, change significantly the preferred portions of the models’ parameter spaces. Finally, we consider the pMSSM11, in which sparticle masses may be significantly smaller and we find only small changes in the preferred regions of parameter space.

Abstract We have calculated the next-to-leading-order electroweak and QCD corrections to the decay processes h → WW/ZZ → 4 fermions of the light CP-even Higgs boson h of various types of Two-Higgs-Doublet Models (Types I and II, “lepton-specific” and “flipped” models). The input parameters are defined in four different renormalization schemes, where parameters that are not directly accessible by experiments are defined in the M S ¯ $$ \overline{\mathrm{MS}} $$ scheme. Numerical results are presented for the corrections to partial decay widths for various benchmark scenarios previously motivated in the literature, where we investigate the dependence on the M S ¯ $$ \overline{\mathrm{MS}} $$ renormalization scale and on the choice of the renormalization scheme in detail. We find that it is crucial to be precise with these issues in parameter analyses, since parameter conversions between different schemes can involve sizeable or large corrections, especially in scenarios that are close to experimental exclusion limits or theoretical bounds. It even turns out that some renormalization schemes are not applicable in specific regions of parameter space. Our investigation of differential distributions shows that corrections beyond the Standard Model are mostly constant offsets induced by the mixing between the light and heavy CP-even Higgs bosons, so that differential analyses of h→4f decay observables do not help to identify Two-Higgs-Doublet Models. Moreover, the decay widths do not significantly depend on the specific type of those models. The calculations are implemented in the public Monte Carlo generator Prophecy4f and ready for application.

Abstract We perform the renormalization of different types of Two-Higgs-Doublet Models for the calculation of observables at next-to-leading order. In detail, we suggest four different renormalization schemes based on on-shell renormalization conditions as far as possible and on M S ¯ $$ \overline{\mathrm{MS}} $$ prescriptions for the remaining field-mixing parameters where no distinguished on-shell condition exists and make contact to existing schemes in the literature. In particular, we treat the tadpole diagrams in different ways and discuss issues of gauge independence and perturbative stability in the considered schemes. The renormalization group equations for the M S ¯ $$ \overline{\mathrm{MS}} $$ parameters are solved in each scheme, so that a consistent renormalization scale variation can be performed. We have implemented all Feynman rules including counterterms and the renormalization conditions into a FeynArts model file, so that amplitudes and squared matrix elements can be generated automatically. As an application we compute the decay of the light, CP-even Higgs boson of the Two-Higgs-Doublet Model into four fermions at next-to-leading order. The comparison of different schemes and the investigation of the renormalization scale dependence allows us to test the perturbative consistency in each of the renormalization schemes, and to get a better estimate of the theoretical uncertainty that arises due to the truncation of the perturbation series.

Abstract We analyze the Higgs-boson masses and mixing matrices in the NMSSM based on an on-shell (OS) renormalization of the gauge-boson and Higgs-boson masses and the parameters of the top/scalar top sector. We compare the implementation of the OS calculations in the codes NMSSMCALC and NMSSM-FeynHiggs up to $${\mathcal {O}}(\alpha _t\alpha _s)$$ O ( α t α s ) . We identify the sources of discrepancies at the one- and at the two-loop level. Finally we compare the OS and $$\overline{\mathrm {DR}}$$ DR ¯ evaluation as implemented in NMSSMCALC. The results are important ingredients for an estimate of the theoretical precision of Higgs-boson mass calculations in the NMSSM.