Solving the Little Hierarchy Problem with a Singlet and ExplicitμTerms

Abstract

We present a generalization of the next-to-minimal supersymmetric standard model, with an explicit μ term and a supersymmetric mass for the singlet superfield, as a route to alleviating the little hierarchy problem of the minimal supersymmetric standard model (MSSM). Though this model does not address the μ problem of the MSSM, we are able to generate masses for the lightest neutral Higgs boson up to 140 GeV with top squarks below the TeV scale, all couplings perturbative to the gauge unification scale, and with no need to fine-tune parameters in the scalar potential. This model more closely resembles the MSSM phenomenologically than the canonical next-to-minimal supersymmetric standard model.

The fine-tuning of the generalised NMSSM

“…Interestingly it has already been noted that the presence of such additional terms can further reduce the fine-tuning needed [11][12][13]. In this paper we extend these analyses to estimate the fine-tuning needed over the full parameter space available with the additional superpotential terms and find a significant reduction in the fine-tuning, particularly for Higgs masses around 130 GeV.…”

“…In [13] a slightly restricted form of the GNMSSM was studied. Their model, referred to as the SMSSM, has a restricted set of the parameters appearing in eqs.…”

Gauge-mediated embedding of the singlet extension of the minimal supersymmetric standard model

“…[11] for an extensive review of the NMSSM.) However the NMSSM has a number of difficulties and its phenomenologically viable parameter space is highly constrained both by experiment and theory, some of which we discussed in a previous paper [12]. In particular, it is difficult for the single S-field to solve both the µ-problem and the little hierarchy problem simultaneously, though it can be done with careful choices of parameters.…”

“…In our previous paper [12], we presented an extension of the NMSSM in which we absolved the singlet of its responsibility for solving the µ-problem and found that it then solved the little hierarchy problem in a very natural way. We called this model the S-MSSM, since it is the most general version of the MSSM with one singlet superfield added 1 .…”

“…In Ref. [12] we used the stop masses as a measure of fine-tuning, arguing that if stop masses were significantly smaller than 1 TeV and there were no other obvious tunings required to make the model work, then the S-MSSM is in some sense natural. In this paper, we will explore whether the parameter choices made in Ref.…”