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It is well known that the observed Higgs mass is more naturally explained in the NMSSM than in the MSSM. Without any violation of this success, there are variants on the NMSSM which can lead to new phenomenologies. In this study we propose a new variant of NMSSM by imposing an unbroken $R$ symmetry. We firstly identify the minimal structure of such scenario from the perspective of both simplicity and viability, then compare model predictions to current experimental limits, and finally highlight main features that differ from the well-known scenarios.
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From the current ATLAS and CMS results on Higgs boson mass and decay rates, the NMSSM is obviously better than the MSSM. To explain the fine-tuning problems such as gauge hiearchy problem and strong CP problem in the SM, we point out that supersymmetry does not need to provide a dark matter candidate, i.e., R-parity can be violated. Thus, we consider three kinds of the NMSSM scenarios: in Scenarios I and II R-parity is conserved and the lightest neutralino relic density is respectively around and smaller than the observed value, while in Scenario III R-parity is violated. To fit all the experimental data, we consider the chi^2 analyses, and find that the Higgs boson mass and decay rates can be explained very well in these Scenarios. Considering the small chi^2 values and fine-tuning around 2-3.7% (or 1-2%), we obtain the viable parameter space with light (or relatively heavy) supersymmetric particle spectra only in Scenario III (or in Scenarios I and II). Because the singlino, Higgsinos, and light stop are relatively light in general, we can relax the LHC supersymmetry search constraints but the XENON100 experiment gives a strong constraint in Scenarios I and II. In all the viable parameter space, the anomalous magnetic moment of the muon (g_{mu} - 2)/2 are generically small. With R-parity violation, we can increase (g_{mu} - 2)/2, and avoid the contraints from the LHC supersymmetry searches and XENON100 experiment. Therefore, Scenario III with R-parity violation is more natural and realistic than Scenarios I and II.
Electroweak precision measurements, encoded in the oblique parameters, give strong constraints on physics beyond the Standard Model. The oblique parameters S, T, U (V, W, X) are calculated in the next-to-minimal supersymmetric model (NMSSM). We outline the calculation of the oblique parameters in terms of one-loop gauge-boson selfenergies and find sensitive restrictions for the NMSSM parameter space.
We discuss a possibility that the domain wall problem in the next-to-minimal supersymmetric standard model is alleviated without introducing a small explicit $Z_3$ breaking term by analyzing the evolution of the singlet scalar field within an inflationary paradigm. The singlet scalar field which explains the $mu$-term tracks a time-varying minimum of the effective potential after inflation and slowly rolls down to its global minimum if there exist sufficiently large negative Hubble-induced corrections on the effective potential for the singlet field, which arise through supergravity. As a consequence, the whole Universe is confined within a single domain during and after inflation, which prevents the formation of domain walls. This will further constrain the history of the early Universe along with the Higgs-singlet coupling.
A highly bino-like Dark Matter (DM), which is the Lightest Supersymmetric Particle (LSP), could be motivated by the stringent upper bounds on the DM direct detection rates. This is especially so when its mass is around or below 100 GeV for which such a bound tends to get most severe. Requiring not so large a higgsino mass parameter, that would render the scenario reasonably natural, prompts such a bino-like state to be relatively light. In the Minimal Supersymmetric Standard Model (MSSM), in the absence of comparably light scalars, such an excitation, if it has to be a thermal relic, is unable to meet the stringent experimental upper bound on its abundance unless its self-annihilation hits a funnel involving either the $Z$-boson or the Standard Model (SM)-like Higgs boson. We demonstrate that, in such a realistic situation, a highly bino-like DM of the popular $Z_3$-symmetric Next-to-Minimal Supersymmetric Standard Model (NMSSM) is viable over an extended range of its mass, from our targeted maximum in the vicinity of the mass of the top quark down to about 30 GeV. This is facilitated by the presence of comparably light singlet-like states that could serve as funnel (scalars) and/or coannihilating (singlino) states even as the bino-like LSP receives a minimal (but optimal) tempering triggered by suitably light higgsino states that, in the first place, evade stringent lower bounds on their masses that can be derived from the Large Hadron Collider (LHC) experiments only in the presence of a lighter singlino-like state. An involved set of blind spot conditions is derived for the DM direct detection rates by considering for the very first time the augmented system of neutralinos comprising of the bino, the higgsinos and the singlino which highlights the important roles played by the NMSSM parameters $lambda$ and $tanbeta$ in delivering a richer phenomenology.
The strategy for assigning $Z_{4R}$ parity in the string compactification is presented. For the visible sector, an anti-SU(5) (flipped-SU(5)) grand unification (GUT) model with three families is used to reduce the number of representations compared to the number in the minimal supersymmetric standard models (MSSMs). The SO(32) heterotic string is used to allow a large nonabelian gauge group SU($N$), $Nge 9$, for the hidden sector such that the number of extra U(1) factors is small. A discrete subgroup of the gauge U(1)s is defined as the $Z_{4R}$ parity. Spontaneous symmetry breaking of anti-SU(5) GUT is achieved by the vacuum expectation values of two index antisymmetric tensor Higgs fields ${bf 10}_{+1}$ and $overline{bf 10}_{-1}$ that led to our word `anti-SU(5). In the illustrated example, the multiplicity 3 in one twisted sector allows the permutation symmetry $S_3$ that leads us to select the third family members and one MSSM pair of the Higgs quintets.
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