Nonminimal Supersymmetric Standard Model Research Articles

Prospects of neutral Higgs boson decays in the NMSSM

In this paper, we present the branching ratios of the two lightest CP-even Higgses, $h_1$ and $h_2$, and of the lightest CP-odd Higgs, $a_1$, in the context of the Non-Minimal Supersymmetric Standard Model (NMSSM). We find that for some regions of the parameter space, the branching fractions of $a_1$ into the lightest charginos ($a_1\to \chi^+_1\chi^-_1)$ and neutralinos ($a_1\to \chi^0_1\chi^0_1)$ are larger than $50\%$, and can reach a $100 \%$ level in the latter case. Furthermore, the branching ratio of the $h_2\to a_1a_1$ can be equal to unity for all masses of $h_2$ when it is a pure singlet. The above unusual channels are hallmarks of the existence of the NMSSM.

Invisible decays of low mass Higgs bosons in supersymmetric models

The discovery of a 126 GeV Higgs-like scalar at the LHC along with the nonobservation of the supersymmetric particles has in turn led to constraining various supersymmetric models through the Higgs data. We here consider the case of both the minimal supersymmetric standard model (MSSM) as well its extension containing an additional chiral singlet superfield, the next-to-minimal or nonminimal supersymmetric standard model (NMSSM). A lot of work has been done in the context of the lightest scalar of these models being identified as the 126 GeV state discovered at the LHC. We here, however, concentrate on the case where we identify the second lightest Higgs boson as the 126 GeV state discovered at the CERN LHC and consider the invisible decays of the low mass Higgs bosons in both the MSSM and NMSSM. In the case of the MSSM we consider $H\ensuremath{\approx}126\text{ }\text{ }\mathrm{GeV}$ and $h\ensuremath{\approx}98\text{ }\text{ }\mathrm{GeV}$, known as the nondecoupling regime, whereas in the case of the NMSSM ${h}_{2}\ensuremath{\approx}126\text{ }\text{ }\mathrm{GeV}$, with ${m}_{{h}_{1}}$ and ${m}_{{a}_{1}}$ varying depending on the parameter space. We find that, in the case of the MSSM with universal boundary conditions at the grand unified theory (GUT) scale, it is not possible to have light neutralinos leading to the decay channel $H\ensuremath{\rightarrow}{\stackrel{\texttildelow{}}{\ensuremath{\chi}}}_{1}^{0}{\stackrel{\texttildelow{}}{\ensuremath{\chi}}}_{1}^{0}$. The invisible decay mode is allowed in the case of certain $SO(10)$ and ${E}_{6}$ grand unified models with large representations and nonuniversal gaugino masses at the GUT scale. In the case of the NMSSM, for the parameter space considered it is possible to have the invisible decay channel with universal gaugino masses at the GUT scale. We furthermore consider the most general case, with ${M}_{1}$ and ${M}_{2}$ as independent parameters for both the MSSM and NMSSM. We isolate the regions in parameter space in both cases where the second lightest Higgs boson has a mass of 126 GeV and then concentrate on the invisible decay of Higgs bosons to lighter neutralinos. The other nonstandard decay mode of the Higgs boson is also considered in detail. The invisible Higgs branching ratio being constrained by the LHC results, we find that, in this case with the second lightest Higgs boson being the 126 GeV state, more data from the LHC are required to constrain the neutralino parameter space, compared to the case when the lightest Higgs boson is the 126 GeV state.

Natural supersymmetry and implications for Higgs physics

We reanalyze the LHC bounds on light third-generation squarks in natural supersymmetry, where the sparticles have masses inversely proportional to their leading-log contributions to the electroweak symmetry breaking scale. Higgsinos are the lightest supersymmetric particles; top and bottom squarks are the next-to-lightest sparticles that decay into both neutral and charged Higgsinos with well-defined branching ratios determined by Yukawa couplings and kinematics. The Higgsinos are nearly degenerate in mass, once the bino and wino masses are taken to their natural (heavy) values. We consider three scenarios for the stop and sbottom masses: (I) ${\stackrel{\texttildelow{}}{t}}_{R}$ is light; (II) ${\stackrel{\texttildelow{}}{t}}_{L}$ and ${\stackrel{\texttildelow{}}{b}}_{L}$ are light; and (III) ${\stackrel{\texttildelow{}}{t}}_{R}$, ${\stackrel{\texttildelow{}}{t}}_{L}$, and ${\stackrel{\texttildelow{}}{b}}_{L}$ are light. Dedicated stop searches are currently sensitive to scenarios II and III but not scenario I. Sbottom-motivated searches ($2b+\mathrm{MET}$) impact both squark flavors due to $\stackrel{\texttildelow{}}{t}\ensuremath{\rightarrow}b{\stackrel{\texttildelow{}}{\ensuremath{\chi}}}_{1}^{+}$ as well as $\stackrel{\texttildelow{}}{b}\ensuremath{\rightarrow}b{\stackrel{\texttildelow{}}{\ensuremath{\chi}}}_{1,2}^{0}$, constraining scenarios I and III with somewhat weaker constraints on scenario II. The totality of these searches yields relatively strong constraints on natural supersymmetry. Two regions that remain are (1) the ``compressed wedge,'' where $({m}_{\stackrel{\texttildelow{}}{q}}\ensuremath{-}|\ensuremath{\mu}|)/{m}_{\stackrel{\texttildelow{}}{q}}\ensuremath{\ll}1$ and (2) the ``kinematic limit'' region, where ${m}_{\stackrel{\texttildelow{}}{q}}\ensuremath{\gtrsim}600--750\text{ }\text{ }\mathrm{GeV}$, at the kinematic limit of the LHC searches. We calculate the correlated predictions for Higgs physics, demonstrating that these regions lead to distinct predictions for the lightest Higgs couplings that are separable with $\ensuremath{\simeq}10%$ measurements. We show that these conclusions remain largely unchanged once the minimal supersymmetric standard model is extended to the nonminimal supersymmetric standard model in order to naturally obtain a large enough mass for the lightest Higgs boson consistent with LHC data.

Invisible decays of the lightest Higgs boson in supersymmetric models

We consider supersymmetric models in which the lightest Higgs scalar can decay invisibly consistent with the constraints on the $126$~GeV state discovered at the CERN LHC. We consider the invisible decay in the minimal supersymmetric standard model~(MSSM), as well its extension containing an additional chiral singlet superfield, the so-called next-to-minimal or nonminimal supersymmetric standard model~(NMSSM).We consider the case of MSSM with both universal as well as nonuniversal gaugino masses at the grand unified scale, and find that only an $E_6$ grand unified model with unnaturally large representation can give rise to sufficiently light neutralinos which can possibly lead to the invisible decay $h^0 \rightarrow \tilde \chi_1^0 \tilde \chi_1^0$. Following this, we consider the case of NMSSM in detail, where also we find that it is not possible to have the invisible decay of the lightest Higgs scalar with universal gaugino masses at the grand unified scale. We delineate the regions of the NMSSM parameter space where it is possible to have the lightest Higgs boson to have a mass of about $126$ GeV, and then concentrate on the region where this Higgs can decay into light neutralinos, with the soft gaugino masses $M_1$ and $M_2$ as two independent parameters, unconstrained by grand unification. We also consider, simultaneously, the other important invisible Higgs decay channel in the NMSSM, namely the decay into the lightest CP odd scalars, $h_1 \to a_1 a_1$, which is studied in detail. With the invisible Higgs branching ratio being constrained by the present LHC results, we find that $\mu_{eff} < 170$~GeV and $M_1 < 80$~GeV is disfavored in NMSSM for fixed values of the other input parameters. The dependence of our results on the parameters of NMSSM is discussed in detail.

Radiative neutralino production in low energy supersymmetric models. II. The case of beam polarization

We study the production of the lightest neutralinos in the radiative process ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\stackrel{\texttildelow{}}{\ensuremath{\chi}}}_{1}^{0}{\stackrel{\texttildelow{}}{\ensuremath{\chi}}}_{1}^{0}\ensuremath{\gamma}$ in low energy supersymmetric models for the International Linear Collider energies with longitudinally polarized electron and positron beams. For this purpose we consider the case of nonminimal supersymmetric standard model as well as the case of minimal supersymmetric standard model. At the first stage of a linear collider, with $\sqrt{s}=500\text{ }\text{ }\mathrm{GeV}$, the radiative production of the lightest neutralinos may be a viable channel to study supersymmetric partners of the standard model particles, especially if the other supersymmetric particles are too heavy to be pair produced. We consider in detail the effect of beam polarization on the production cross section. We compare and contrast the dependence of the signal cross section on the parameters of the neutralino sector of the nonminimal and minimal supersymmetric standard model when the electron and positron beams are longitudinally polarized. In order to assess the feasibility of experimentally observing the radiative neutralino production process, we consider the background to this process coming from the standard model process ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\nu}\overline{\ensuremath{\nu}}\ensuremath{\gamma}$ with longitudinally polarized electron and positron beams. We also consider the supersymmetric background to the radiative neutralino production process coming from the radiative production of the scalar partners of the neutrinos (sneutrinos) ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\stackrel{\texttildelow{}}{\ensuremath{\nu}}{\stackrel{\texttildelow{}}{\ensuremath{\nu}}}^{*}\ensuremath{\gamma}$, with longitudinally polarized beams. This process can be a background to the radiative neutralino production when the sneutrinos decay invisibly.

CP violation in the neutral Higgs sector of a non-minimal supersymmetric standard model with multiple Higgs singlets

The possibility of CP violation is studied in the Higgs sector of a supersymmetric standard model with multiple Higgs singlets. The tree-level Lagrangian in this model is assumed to conserve the CP symmetry. We flnd that CP violation is viable in this model at the one-loop level, in an explicit way, if the radiative corrections from the third generation of quarks and squarks are taken into account. In the presence of explicit CP violation, at the one-loop level, the upper bound on the mass of the lightest neutral Higgs boson and the productions of the neutral Higgs bosons via the Higgsstrahlung process in high-energy e + e i collisions are calculated. We flnd that the upper bound on the mass of the lightest neutral Higgs boson increases as the number of Higgs singlets increases in a regulated manner. The production cross sections of the neutral Higgs bosons also show a reasonable increasing behavior with respect to the number of Higgs singlets.

Neutral Higgs bosons in the MNMSSM with explicit CP violation

Within the framework of the minimal non-minimal supersymmetric standard model (MNMSSM) with tadpole terms, CP violation effects in the Higgs sector are investigated at the one-loop level, where the radiative corrections from the loops of the quark and squarks of the third generation are taken into account. Assuming that the squark masses are not degenerate, the radiative corrections due to the stop and sbottom quarks give rise to CP phases which trigger the CP violation explicitly in the Higgs sector of the MNMSSM. The masses, the branching ratios for dominant decay channels, and the total decay widths of the five neutral Higgs bosons in the MNMSSM are calculated in the presence of explicit CP violation. The dependence of these quantities on the CP phases is quite recognizable, for given parameter values.

Supersymmetric Higgs singlet effects onB-meson flavor-changing neutral current observables at largetanβ

Higgs singlet superfields are usually present in most extensions of the minimal supersymmetric standard model that address the {mu}-problem, such as the next-to-minimal supersymmetric standard model and the minimal nonminimal supersymmetric standard model. Employing a gauge- and flavor- covariant effective Lagrangian formalism, we show how the singlet-Higgs bosons of such theories can have significant contributions to B-meson flavor-changing neutral current observables for large values of tan{beta} > or approx. 50 at the 1-loop level. Illustrative results are presented including effects on the B{sub s} and B{sub d} mass differences and on the rare decay B{sub s}{yields}{mu}{sup +}{mu}{sup -}. In particular, we find that depending on the actual value of the lightest singlet pseudoscalar mass in the next-to-minimal supersymmetric standard model, the branching ratio for B{sub s}{yields}{mu}{sup +}{mu}{sup -} can be enhanced or even suppressed with respect to the standard model prediction by more than 1 order of magnitude.

Theoretical upper bound on the mass of the LSP in the MNSSM

We study the neutralino sector of the Minimal Non-minimal Supersymmetric Standard Model (MNSSM) where the μ problem of the Minimal Supersymmetric Standard Model (MSSM) is solved without accompanying problems related with the appearance of domain walls. In the MNSSM as in the MSSM the lightest neutralino can be the absolutely stable lightest supersymmetric particle (LSP) providing a good candidate for the cold dark matter component of the Universe. In contrast with the MSSM the allowed range of the mass of the lightest neutralino in the MNSSM is limited. We establish the theoretical upper bound on the lightest neutralino mass in the framework of this model and obtain an approximate solution for this mass.

Implications of vacuum stability constraints on the nonminimal supersymmetric standard model with lepton number violation

We carry out a detailed analysis of the scalar sector of the nonminimal supersymmetric standard model with lepton number violation, and study the constraints imposed on it by the stability of the electroweak symmetry breaking vacuum. The model contains a trilinear lepton number violating term in the superpotential together with the associated supersymmetry breaking interactions which can give rise to neutrino masses. We evaluate the mass matrices for the various boson and fermion modes and then discuss the effect that the lepton number violating interactions have on the mass spectra using a phenomenological prescription to implement the experimental constraints on the light neutrinos mass matrix. We also discuss qualitatively the conditions on the lepton number violating parameters set by the unbounded from below directions, and from the absence of the charge and color breaking minima in this model.

Nonminimal supersymmetric standard model with lepton number violation

We carry out a detailed analysis of the nonminimal supersymmetric standard model with lepton number violation. The model contains a unique trilinear lepton number violating term in the superpotential which can give rise to neutrino masses at the tree level. We search for the gauged discrete symmetries realized by cyclic groups which preserve the structure of the associated trilinear superpotential of this model, and which satisfy the constraints of the anomaly cancellation. The implications of this trilinear lepton number violating term in the superpotential and the associated soft supersymmetry breaking term on the phenomenology of the light neutrino masses and mixing is studied in detail. We evaluate the tree and loop level contributions to the neutrino mass matrix in this model. We search for possible suppression mechanism which could explain large hierarchies and maximal mixing angles.

Coupling unifications in gauge-Higgs unified orbifold models

Supersymmetric gauge theories, in higher dimensions compactified in an orbifold, give a natural framework to unify the gauge bosons, Higgs fields, and even the matter fields in a single multiplet of the unifying gauge symmetry. The extra dimensions and the supersymmetry are the two key ingredients for such an unification. In this work, we investigate various scenarios for the unification of the three gauge couplings and the Yukawa couplings in the minimal supersymmetric standard model (MSSM), as well as the trilinear Higgs couplings $\ensuremath{\lambda}$ and $\ensuremath{\kappa}$ of the nonminimal supersymmetric standard model (NMSSM). We present an $SU(8)$ model in six dimensions with $N=2$ supersymmetry, compactified in a ${T}^{2}/{Z}_{6}$ orbifold which unifies the three gauge couplings with $\ensuremath{\lambda}$ and $\ensuremath{\kappa}$ of NMSSM. Then we present an $SU(9)$ model in 6D, which, in addition, includes partial unification of Yukawa couplings, either for the up-type (top quark and Dirac tau neutrino) or down-type (bottom quark and tau lepton). We also study the phenomenological implications of these various unification scenarios using the appropriate renormalization group equations and show that such unification works very well with the measured low energy values of the couplings. The predicted upper bounds for the lightest neutral Higgs boson mass in our model is higher than those in MSSM but lower than those in the general NMSSM (where the couplings $\ensuremath{\lambda}$ and $\ensuremath{\kappa}$ are arbitrary). Some of the predictions of our models can be tested in the upcoming Large Hadron Collider.

Electroweak phase transition in a nonminimal supersymmetric model

The Higgs potential of the minimal nonminimal supersymmetric standard model (MNMSSM) is investigated within the context of electroweak phase transition. We investigate the allowed parameter space yielding correct electroweak phase transitoin employing a high temperature approximation. We devote to phenomenological consequences for the Higgs sector of the MNMSSM for electron-positron colliders. It is observed that a future $e^+ e^-$ linear collider with $\sqrt{s} = 1000$ GeV will be able to test the model with regard to electroweak baryogenesis.

Quasifixed-point scenario in a modified nonminimal supersymmetric standard model

The simplest extension of the MSSM that does not contradict LEP II experimental bound on the lightest Higgs boson mass at $\tan\beta\sim 1$ is the modified Next-to-Minimal Supersymmetric Standard Model (MNSSM). We investigate the renormalization of Yukawa couplings and soft SUSY breaking terms in this model. The possibility of $b$-quark and $\tau$-lepton Yukawa coupling unification at the Grand Unification scale $M_X$ is studied. The particle spectrum is analysed in the vicinity of the quasi-fixed point where the solutions of renormalization group equations are concentrated at the electroweak scale.

Renormalization of parameters of a soft breakdown of supersymmetry in the regime of strong yukawa coupling within a nonminimal supersymmetric standard model

Within a nonminimal supersymmetric (SuSy) model, the renormalization of trilinear coupling constants A i(t) for scalar fields and of specific combinations \(\mathfrak{M}_i^2 (t)\) of the scalar-particle masses is investigated in the regime of strong Yukawa coupling. The dependence of these parameters on their initial values at the Grand Unification scale disappears as solutions to the renormalization-group equations approach infrared quasifixed points with increasing Y i(0). In the vicinities of quasifixed points for \(\tilde \alpha _{GUT} \ll Y_i (0) \ll 1\), all solutions A i(t) and \(\mathfrak{M}_i^2 (t)\) are concentrated near some straight lines or planes in the space of parameters of a soft breakdown of supersymmetry. This behavior of the solutions in question is explained by a sufficiently slow disappearance of the A i(0) and \(\mathfrak{M}_i^2 (t)\) dependence of the trilinear coupling constants and combinations of the scalar-particle masses. A method is proposed for deriving equations describing the aforementioned straight lines and planes, and the process of their formation is discussed by considering the example of exact and approximate solutions to the renormalization-group equations within a nonminimal supersymmetric standard model.

Nonminimal supersymmetric standard model with baryon and lepton number violation

We carry out a comprehensive analysis of the nonminimal supersymmetric standard model (NMSSM) with baryon and lepton number violation. We catalogue the baryon and lepton number violating dimension four and five operators of the model. We then study the renormalization group evolution and infrared stable fixed points of the Yukawa couplings and the soft supersymmetry breaking trilinear couplings of this model with baryon and lepton number (and R-parity) violation involving the heaviest generations. We show analytically that in the Yukawa sector of the NMSSM there is only one infrared stable fixed point. This corresponds to a non-trivial fixed point for the top-, bottom-quark Yukawa couplings and the $B$ violating coupling $\lambda_{233}''$, and a trivial one for all other couplings. All other possible fixed points are either unphysical or unstable in the infrared region. We also carry out an analysis of the renormalization group equations for the soft supersymmetry breaking trilinear couplings, and determine the corresponding fixed points for these couplings. We then study the quasi-fixed point behaviour, both of the third generation Yukawa couplings and the baryon number violating coupling, and those of the soft supersymmetry breaking trilinear couplings. From the analysis of the fixed point behaviour, we obtain upper and lower bounds on the baryon number violating coupling $\lambda_{233}''$, as well as on the soft supersymmetry breaking trilinear couplings. Our analysis shows that the infrared fixed point behavior of NMSSM with baryon and lepton number violation is similar to that of MSSM.

Infrared quasifixed solutions in a nonminimal supersymmetric standard model

The considerable part of the parameter space in the MSSM corresponding to the infrared quasi fixed point scenario is almost excluded by LEP II bounds on the lightest Higgs boson mass. In the NMSSM the mass of the lightest Higgs boson reaches its maximum value in the strong Yukawa coupling limit when Yukawa couplings are essentially larger than gauge ones at the Grand Unification scale. In this limit the solutions of the renormalisation group equations are attracted to the infrared and Hill type effective fixed lines or surfaces in the Yukawa coupling parameter space. They are concentrated in the vicinity of quasi fixed points for $Y_i(0)\to\infty$. However the solutions are attracted to such points rather weakly. For this reason when all $Y_i(0)\sim 1$ the solutions of the renormalisation group equations are gathered near a line in the Hill type effective surface. In the paper the approximate solutions for the NMSSM Yukawa couplings are given. The possibility of $b$--quark and $\tau$--lepton Yukawa coupling unification at the scale $M_{X}$ is also discussed.

Light charged Higgs boson and supersymmetry

A possible discovery of a relatively light charged Higgs boson H + in near future experiments, with a mass M H + ≲110 GeV, together with the present LEP2 direct limits on the chargino and neutral Higgs sectors, would disfavour the minimal supersymmetric standard model as well as its frequently discussed next-to-minimal supersymmetric extension. We show that a supersymmetric origin can naturally be ascribed to the existence of such a light charged Higgs scalar within the context of the recently introduced minimal nonminimal supersymmetric standard model.

Higgs scalars in the minimal nonminimal supersymmetric standard model

We consider the simplest and most economic version among the proposed non-minimal supersymmetric models, in which the $\mu$-parameter is promoted to a singlet superfield, whose all self-couplings are absent from the renormalizable superpotential. Such a particularly simple form of the renormalizable superpotential may be enforced by discrete $R$-symmetries which are extended to the gravity-induced non-renormalizable operators as well. We show explicitly that within the supergravity-mediated supersymmetry-breaking scenario, the potentially dangerous divergent tadpoles associated with the presence of the gauge singlet first appear at loop levels higher than 5 and therefore do not destabilize the gauge hierarchy. The model provides a natural explanation for the origin of the $\mu$-term, without suffering from the visible axion or the cosmological domain-wall problem. Focusing on the Higgs sector of this minimal non-minimal supersymmetric standard model, we calculate its effective Higgs potential by integrating out the dominant quantum effects due to stop squarks. We then discuss the phenomenological implications of the Higgs scalars predicted by the theory for the present and future high-energy colliders. In particular, we find that our new minimal non-minimal supersymmetric model can naturally accommodate a relatively light charged Higgs boson, with a mass close to the present experimental lower bound.

Particle spectrum in the modified nonminimal supersymmetric standard model in the strong Yukawa coupling regime

A theoretical analysis of solutions of renormalization group equations in the minimal supersymmetric standard model, which lead to a quasi-fixed point has shown that the mass of the lightest Higgs boson in these models does not exceed 94 ± 5 GeV. This implies that a considerable part of the parameter space in the minimal supersymmetric model is in fact eliminated by existing LEPII experimental data. In the nonminimal supersymmetric standard model the upper bound on the mass of the lightest Higgs boson reaches its maximum in the strong Yukawa coupling regime when the Yukawa constants are substantially greater than the gauge constants on the grand unification scale. In the present paper the particle spectrum is studied using the simplest modification of the nonminimal supersymmetric standard model which gives a self-consistent solution in this region of parameter space. This model can give m h ∼ 125 GeV even for comparatively low values of β ≥ 1.9. The spectrum of Higgs bosons and neutralinos is analyzed using the method of diagonalizing mass matrices proposed earlier. In this model the mass of the lightest Higgs boson does not exceed 130.5 ± 3.5 GeV.