Next-to-Minimal Supersymmetric Extension Of The Standard Model Research Articles

The O(αt+αλ+ακ)2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{O}(\\alpha _t+\\alpha _\\lambda +\\alpha _\\kappa )^2$$\\end{document} correction to the ρ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\rho $$\\end{document} parameter and its effect on the W boson mass calculation in the complex NMSSM

We present the prediction of the electroweak ρ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\rho $$\\end{document} parameter and the W boson mass in the CP-violating Next-to-Minimal Supersymmetric extension of the Standard Model (NMSSM) at the two-loop order. The ρ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\rho $$\\end{document} parameter is calculated at the full one-loop and leading and sub-leading two-loop order O(α+αtαs+αt+αλ+ακ2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {O}}(\\alpha + \\alpha _t\\alpha _s + \\left( \\alpha _t+\\alpha _\\lambda +\\alpha _\\kappa \\right) ^2)$$\\end{document}. The new Δρ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta \\rho $$\\end{document} prediction is incorporated into a prediction of MW\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_W$$\\end{document} via a full supersymmetric (SUSY) one-loop calculation of Δr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta r$$\\end{document}. Furthermore, we include all known state-of-the-art SM higher-order corrections to Δr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta r$$\\end{document}. By comparing results for Δρ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta \\rho $$\\end{document} obtained using on-shell (OS) and DR¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\overline{\ ext {DR}}$$\\end{document} renormalization conditions in the top/stop sector, we find that the scheme uncertainty is reduced at one-loop order by 55%, at two-loop O(αsαt)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {O}}(\\alpha _s\\alpha _t)$$\\end{document} by 22%, and at two-loop O(αt+ακ+αλ)2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {O}}(\\alpha _t+\\alpha _\\kappa +\\alpha _\\lambda )^2$$\\end{document} by 16%, respectively. The influence of the two-loop results on the MW\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_W$$\\end{document} mass prediction is found to be sub-leading. The new calculation is made public in the computer program NMSSMCALC. We perform an extensive comparison in the W-mass, Higgs boson mass and the muon anomalous magnetic moment prediction between our calculation and three other publicly available tools and find very good agreement provided that the input parameters and renormalization scales are treated in the same way. Finally, we study the impact of the CP-violating phases on the W-mass prediction which is found to be smaller than the overall size of the SUSY corrections.

Leptonic anomalous magnetic and electric dipole moments in the CP-violating NMSSM with and without inverse seesaw mechanism

The new results on the muon anomalous magnetic moment (AMM) published by Fermilab in 2021 did not lead to a reduction of its long-pending deviation from the Standard Model (SM) value by more than 4sigma . The explanation of this discrepancy by adding new particles to the theory puts many new physics models under tension when combined with the null results of the LHC direct searches for new particles. In this paper, we investigate the CP-violating Next-to-Minimal Supersymmetric extension of the SM (NMSSM) with and without an inverse seesaw mechanism. We compute the one-loop supersymmetric contributions to the AMM and the two-loop Barr–Zee-type diagrams with effective Higgs couplings to photons for the leptonic electric dipole moments (EDMs). The effects of the extended (s)neutrino sector on the muon AMM and on the mass of the SM-like Higgs boson can be significant. Complex phases can have an important impact on the AMM. On the other hand, the stringent limits from the EDMs on the complex phases have to be taken into account. Our calculations have been implemented in the Fortran codes NMSSMCALC and NMSSMCALC-nuSS which are publicly available. Besides the leptonic AMMs and EDMs, these programs can compute the Higgs boson masses and mixings, together with Higgs boson decay widths and branching ratios taking into account the most up-to-date higher-order corrections in the NMSSM with and without inverse seesaw mechanism.

One-loop corrections to the two-body decays of the charged Higgs bosons in the real and complex NMSSM

We evaluate the full next-to-leading order supersymmetric (SUSY) electroweak and SUSY-QCD corrections to the on-shell two-body decays of the charged Higgs bosons in the framework of the next-to-minimal supersymmetric extension of the Standard Model (NMSSM) allowing also for CP violation. We furthermore provide the possibility to choose between different renormalization schemes in the electroweakino and the squark and slepton sectors. Our corrections are implemented in the code NMSSMCALCEW and thus complete the one-loop corrections of the charged Higgs boson decays which so far only included the state-of-the-art QCD corrections and the resummed SUSY-electroweak and SUSY-QCD corrections. We investigate the impact of the NLO corrections including the newly computed higher-order corrections for each decay mode in a wide range of the parameter space that is allowed by the theoretical and experimental constraints as well as the effect of CP violation and the dependence on the choice of the renormalization scheme. The new version of NMSSMCALCEW is made publicly available.

One-loop corrections to the two-body decays of the neutral Higgs bosons in the complex NMSSM

Since no direct signs of new physics have been observed so far indirect searches in the Higgs sector have become increasingly important. With the discovered Higgs boson behaving very standard model (SM)-like, however, indirect new physics manifestations are in general expected to be small. On the theory side, this makes precision predictions for the Higgs parameters and observables indispensable. In this paper, we provide in the framework of the CP-violating next-to-minimal supersymmetric extension of the SM (NMSSM) the complete next-to-leading order (SUSY-)electroweak corrections to the neutral Higgs boson decays that are on-shell and non-loop induced. We also investigate possible gauge-dependence issues in the decays of light Higgs bosons into fermion pairs. Together with the also provided SUSY-QCD corrections to colored final states, the newly calculated SUSY-electroweak corrections are implemented in the Fortran code NMSSMCALC which already includes the state-of-the art QCD corrections. The new code is called NMSSMCALCEW. This way we provide the NMSSM Higgs boson decays and branching ratios at presently highest possible precision and thereby contribute to the endeavor of searching for New Physics at present and future colliders.

Two-loop mathcal{O} ( {alpha}_t^2 ) corrections to the neutral Higgs boson masses in the CP-violating NMSSM

We present our calculation of the two-loop corrections of mathcal{O} ( {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 overline{mathrm{DR}} -on-shell (OS) renormalization scheme for the NMSSM input parameters. Furthermore, we exploit a 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 mathcal{O} (αtαs) corrections in the gaugeless limit and at vanishing external momentum. Depending on the chosen parameter point, we find that the O(αtαs + {alpha}_t^2 ) corrections add about 4-7% to the one-loop mass of the SM-like Higgs boson for 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.

Higgs portals for thermal Dark Matter. EFT perspectives and the NMSSM

We analyze a low energy effective model of Dark Matter in which the thermal relic density is provided by a singlet Majorana fermion which interacts with the Higgs fields via higher dimensional operators. Direct detection signatures may be reduced if blind spot solutions exist, which naturally appear in models with extended Higgs sectors. Explicit mass terms for the Majorana fermion can be forbidden by a Z3 symmetry, which in addition leads to a reduction of the number of higher dimensional operators. Moreover, a weak scale mass for the Majorana fermion is naturally obtained from the vacuum expectation value of a scalar singlet field. The proper relic density may be obtained by the s-channel interchange of Higgs and gauge bosons, with the longitudinal mode of the Z boson (the neutral Goldstone mode) playing a relevant role in the annihilation process. This model shares many properties with the Next-to-Minimal Supersymmetric extension of the Standard Model (NMSSM) with light singlinos and heavy scalar and gauge superpartners. In order to test the validity of the low energy effective field theory, we compare its predictions with those of the ultraviolet complete NMSSM. Extending our framework to include Z3 neutral Majorana fermions, analogous to the bino in the NMSSM, we find the appearance of a new bino-singlino well tempered Dark Matter region.

Enhanced Higgs associated production with a top quark pair in the NMSSM with light singlets

Precision measurements of the 125 GeV Higgs resonance recently discovered at the LHC have determined that its properties are similar to the ones of the Standard Model (SM) Higgs boson. However, the current uncertainties in the determination of the Higgs boson couplings leave room for significant deviations from the SM expectations. In fact, if one assumes no correlation between the top-quark and gluon couplings to the Higgs, the current global fit to the Higgs data lead to central values of the Higgs couplings to the bottom-quark and the top-quark that are about 2 σ away from the SM predictions. In a previous work, we showed that such a scenario could be realized in the Next to Minimal Supersymmetric extension of the SM (NMSSM), for heavy singlets and light MSSM-like Higgs bosons and scalar top quarks, but for couplings that ruined the perturbative consistency of the theory up to the GUT scale. In this work we show that a perturbative consistent scenario, for somewhat heavier stops, may be obtained in the presence of light singlets. An interesting bonus of this scenario is the possibility of explaining an excess of events observed in CP-even Higgs searches at LEP2.

Alignment limit of the NMSSM Higgs sector

The Next-to-Minimal Supersymmetric extension of the Standard Model (NMSSM) with a Higgs boson of mass 125 GeV can be compatible with stop masses of order of the electroweak scale, thereby reducing the degree of fine-tuning necessary to achieve electroweak symmetry breaking. Moreover, in an attractive region of the NMSSM parameter space, corresponding to the "alignment limit" in which one of the neutral Higgs fields lies approximately in the same direction in field space as the doublet Higgs vacuum expectation value, the observed Higgs boson is predicted to have Standard-Model-like properties. We derive analytical expressions for the alignment conditions and show that they point toward a more natural region of parameter space for electroweak symmetry breaking, while allowing for perturbativity of the theory up to the Planck scale. Moreover, the alignment limit in the NMSSM leads to a well defined spectrum in the Higgs and Higgsino sectors, and yields a rich and interesting Higgs boson phenomenology that can be tested at the LHC. We discuss the most promising channels for discovery and present several benchmark points for further study.

The order O α t α s $$ \mathcal{O}\left({\alpha}_t{\alpha}_s\right) $$ corrections to the trilinear Higgs self-couplings in the complex NMSSM

A consistent interpretation of the Higgs data requires the same precision in the Higgs boson masses and in the trilinear Higgs self-couplings, which are related through their common origin from the Higgs potential. In this work we provide the two-loop corrections at order ${\cal O}(\alpha_t \alpha_s)$ in the approximation of vanishing external momenta to the trilinear Higgs self-couplings in the CP-violating Next-to-Minimal Supersymmetric extension of the Standard Model (NMSSM). In the top/stop sector two different renormalization schemes have been implemented, the OS and the $\overline{\text{DR}}$ scheme. The two-loop corrections to the self-couplings are of the order of 10\% in the investigated scenarios. The theoretical error, estimated both from the variation of the renormalization scale and from the change of the top/stop sector renormalization scheme, has been shown to be reduced due to the inclusion of the two-loop corrections.

Exploring the CP-violating NMSSM: EDM constraints and phenomenology

The Next-to-Minimal Supersymmetric extension of the Standard Model (NMSSM) features extra new sources for CP violation. In contrast to the MSSM CP violation can already occur at tree level in the Higgs sector. We investigate the range of possible allowed CP-violating phases by taking into account the constraints arising from the measurements of the Electric Dipole Moments (EDMs) and the latest LHC Higgs data. Our analysis shows that large CP-violating phases, that are NMSSM-specific, are not in conflict with the EDMs. They are dominantly constrained by the Higgs data in this case. We use our results to investigate the prospects of measuring CP violation through the combined measurement of Higgs rates, on the one hand, and in observables based on CP-violating Higgs couplings to tau leptons on the other hand.

Improved prediction for the mass of the W boson in the NMSSM

Electroweak precision observables, being highly sensitive to loop contributions of new physics, provide a powerful tool to test the theory and to discriminate between different models of the underlying physics. In that context, the $W$ boson mass, $M_W$, plays a crucial role. The accuracy of the $M_W$ measurement has been significantly improved over the last years, and further improvement of the experimental accuracy is expected from future LHC measurements. In order to fully exploit the precise experimental determination, an accurate theoretical prediction for $M_W$ in the Standard Model (SM) and extensions of it is of central importance. We present the currently most accurate prediction for the $W$ boson mass in the Next-to-Minimal Supersymmetric extension of the Standard Model (NMSSM), including the full one-loop result and all available higher-order corrections of SM and SUSY type. The evaluation of $M_W$ is performed in a flexible framework, which facilitates the extension to other models beyond the SM. We show numerical results for the $W$ boson mass in the NMSSM, focussing on phenomenologically interesting scenarios, in which the Higgs signal can be interpreted as the lightest or second lightest CP-even Higgs boson of the NMSSM. We find that, for both Higgs signal interpretations, the NMSSM $M_W$ prediction is well compatible with the measurement. We study the SUSY contributions to $M_W$ in detail and investigate in particular the genuine NMSSM effects from the Higgs and neutralino sectors.

Higher order corrections to the trilinear Higgs self-couplings in the real NMSSM

After the discovery of a Higgs-like boson by the LHC experiments ATLAS and CMS, it is of crucial importance to determine its properties in order to not only identify it as the boson responsible for electroweak symmetry breaking but also to clarify the question if it is a Standard Model (SM) Higgs boson or the Higgs particle of some extension beyond the SM as e.g. supersymmetry. In this context, the precise prediction of the Higgs parameters as masses and couplings plays a crucial role for the proper distinction between different models. In extension of previous works on the loop-corrected Higgs boson masses of the Next-to-Minimal Supersymmetric Extension of the SM (NMSSM), we present here the calculation of the loop-corrected trilinear NMSSM Higgs self-couplings. The loop corrections turn out to have a substantial impact on the decay widths of Higgs-to-Higgs decays and on the production cross section of Higgs pairs via gluon fusion. They are therefore indispensable for the correct interpretation of the experimental Higgs results.

Higgs boson masses in the complex NMSSM at one-loop level

Abstract The Next-to-Minimal Supersymmetric Extension of the Standard Model (NMSSM) with a Higgs sector containing five neutral and two charged Higgs bosons allows for a rich phenomenology. In addition, the plethora of parameters provides many sources of CP violation. In contrast to the Minimal Supersymmetric Extension, CP violation in the Higgs sector is already possible at tree-level. For a reliable understanding and interpretation of the experimental results of the Higgs boson search, and for a proper distinction of Higgs sectors provided by the Standard Model or possible extensions, the Higgs boson masses have to be known as precisely as possible including higher-order corrections. In this paper we calculate the one-loop corrections to the neutral Higgs boson masses in the complex NMSSM in a Feynman diagrammatic approach adopting a mixed renormalization scheme based on on-shell and $ \overline{\mathrm{DR}} $ conditions. We study various scenarios where we allow for tree-level CP-violating phases in the Higgs sector and where we also study radiatively induced CP violation due to a non-vanishing phase of the trilinear coupling A t in the stop sector. The effects on the Higgs boson phenomenology are found to be significant. We furthermore estimate the theoretical error due to unknown higher-order corrections by both varying the renormalization scheme of the top and bottom quark masses and by adopting different renormalization scales. The residual theoretical error can be estimated to about 10%.

THE NEXT-TO-MINIMAL SUPERSYMMETRIC EXTENSION OF THE STANDARD MODEL REVIEWED

The next-to-minimal supersymmetric extension of the Standard Model (NMSSM) is one of the most favored supersymmetric models. After an introduction to the model, the Higgs sector and the neutralino sector are discussed in detail. Theoretical, experimental, and cosmological constraints are studied. Eventually, the Higgs potential is investigated in the approach of bilinear functions. Emphasis is placed on aspects which are different from the minimal supersymmetric extension.

Supersymmetric radiative corrections onμ−τneutrino refraction including possible R-parity breaking interactions

In this paper we investigate the one-loop radiative corrections to the neutrino indices of refraction from supersymmetric models. We consider the Next-to Minimal Supersymmetric extension of the Standard Model (NMSSM) which happens to be a better supersymmetric candidate than the MSSM for both theoretical and experimental reasons. We scan the relevant SUSY parameters and identify regions in the parameter space which yield interesting values for V_{mu tau}. If R-parity is broken there are significant differences between MSSM and NMSSM contributions contrary to the R-parity conserved case. Finally, for a non-zero CP-violating phase, we show analytically that the presence of V_{mu tau} will explicitly imply CP-violation effects on the supernova electron (anti-) neutrino fluxes.

SuperIso v3.0, flavor physics observables calculations: extension to NMSSM

SuperIso v3.0 is a public program for evaluation of flavor physics observables in the minimal supersymmetric extension of the Standard Model (MSSM) and the next to minimal supersymmetric extension of the Standard Model (NMSSM). SuperIso v3.0 incorporates many flavor observables such as the inclusive branching ratio of B → X s γ , the isospin asymmetry of B → K ∗ γ , the branching ratio of B s → μ + μ − , the branching ratio of B → τ ν τ , the branching ratio of B → D τ ν τ , the branching ratio of K → μ ν μ and the branching ratios of D s → τ ν τ and D s → μ ν μ . The calculation of the branching ratio of B → X s γ includes NNLO Standard Model contributions. The program also computes the muon anomalous magnetic moment ( g − 2 ) . Seven sample models are included in the package, namely mSUGRA, NUHM, AMSB and GMSB for the MSSM, and CNMSSM, NGMSB and NNUHM for the NMSSM. SuperIso uses a SUSY Les Houches Accord file (SLHA1 or SLHA2) as input, which can be either generated automatically by the program via a call to external spectrum calculators (SOFTSUSY, ISAJET or NMSSMTools), or provided by the user. New version program summary Program title: SuperIso v3.0 Catalogue identifier: AEAN_v3_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEAN_v3_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public Licence No. of lines in distributed program, including test data, etc.: 6869 No. of bytes in distributed program, including test data, etc.: 42 627 Distribution format: tar.gz Programming language: C (C99 Standard compliant) Computer: 32- or 64-bit PC, Mac Operating system: Linux, MacOS RAM: less than 1 MB Classification: 11.6 External routines: ISASUGRA/ISAJET, SOFTSUSY and/or NMSSMTools Does the new version supersede the previous version?: Yes Nature of problem: Calculation of flavor physics observables as well as the muon anomalous magnetic moment in the Minimal Supersymmetric Standard Model with minimal flavor violation and in the Next to Minimal Supersymmetric Standard Model, in order to derive constraints on the supersymmetric parameter spaces. Solution method: SuperIso uses a SUSY Les Houches Accord (SLHA1 or SLHA2) file, which can be either generated automatically via a call to SOFTSUSY, ISAJET or NMSSMTools, or provided by the user. This file contains the masses, mixings and couplings of the supersymmetric particles. SuperIso then computes the most constraining flavor physics observables and the muon ( g − 2 ). SuperIso is able to perform the calculations in different supersymmetry breaking scenarios, such as mSUGRA, NUHM, AMSB and GMSB, as well as constrained NMSSM scenarios such as CNMSSM, NNUHM and NGMSB. Reasons for new version: SuperIso has been extended to the next to minimal supersymmetric extension of the Standard Model (NMSSM). The implemented routines are therefore extensively modified. Summary of revisions: • Improvement of the SLHA2 reader. • Replacement of “float” variables by “double”. • Implementation of an interface with NMSSMTools. • Extension of the calculation of flavor observables as well as the muon anomalous magnetic moment to NMSSM. • Addition of three different NMSSM scenarios: CNMSSM, NGMSB and NNUHM. • Three sample main programs have been added: cnmssm.c, ngmsb.c and nnuhm.c. Additional instructions to use them are given when running them without arguments. Unusual features: The code is very flexible, and new observables can be added easily. Running time: Less than 1 sec

Determining the global minimum of Higgs potentials via Groebner bases – applied to the NMSSM

Determining the global minimum of Higgs potentials with several Higgs fields like the next-to-minimal supersymmetric extension of the standard model (NMSSM) is a non-trivial task already at the tree level. The global minimum of a Higgs potential can be found from the set of all its stationary points defined by a multivariate polynomial system of equations. We introduce here the algebraic Groebner basis approach to solve this system of equations. We apply the method to the NMSSM with CP-conserving as well as CP-violating parameters. The results reveal an interesting stationary-point structure of the potential. Requiring the global minimum to give the electroweak symmetry breaking observed in Nature excludes large parts of the parameter space.