Higgs Scalars in the Minimal Non-minimal Supersymmetric Standard Model

TL;DR

The paper introduces the MNSSM, a minimal non-minimal SUSY extension that generates the $\mu$-term from a singlet $S$ while forbidding singlet self-couplings at renormalizable level. Discrete ${\cal Z}_5^{R}$ and ${\cal Z}_7^{R}$ symmetries suppress dangerous gravity-induced tadpoles beyond the electroweak scale, preserving Higgs-sector stability. The authors compute the one-loop stop-dominated effective potential, derive Higgs mass matrices and couplings, and compare MNSSM predictions to NMSSM, highlighting a novel decoupling regime that allows a relatively light charged Higgs and a heavier SM-like Higgs. Phenomenologically, MNSSM favors a charged Higgs near current experimental bounds and a SM-like Higgs mass up to about $145$ GeV, with distinct collider signatures that could distinguish it from NMSSM at the LHC/Tevatron. The work provides a clean, testable benchmark for Higgs-sector phenomenology in a minimal non-minimal SUSY framework.

Abstract

We consider the simplest and most economic version among the proposed non-minimal supersymmetric models, in which the $μ$-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 $μ$-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.

Figures (12)

• Figure 1: Typical harmful tadpole divergences at the (a) six- and (b) seven- loop levels.
• Figure 2: Numerical predictions for $M_{H_1}$ as a function of $\mu$ in the MNSSM with $m^2_{12} = 0$, for $M_{H^+} = 0.1$ (solid line), 0.3 (dashed line), 0.7 (dotted line), 1 (dash-dotted line) TeV.
• Figure 3: Numerical estimates of (a) $M_{H_1}$ and $M_{H_2}$ and of (b) $g^2_{H_1ZZ}$ and $g^2_{H_2ZZ}$, as functions of $\mu$ in the MNSSM with $m^2_{12} = 0$, for $M_{H^+} = 80$ (solid line), 120 (dashed line) and 160 (dotted line) GeV.
• Figure 4: The same as in Fig. \ref{['fig:nmssm2']}, but with $\tan\beta = 20$.
• Figure 5: Numerical estimates of (a) $M_{H_1}$ and $M_{H_2}$ and of (b) $g^2_{H_1ZZ}$ and $g^2_{H_2ZZ}$, as functions of $\mu$ in the MNSSM with $m^2_{12}=0$, for $M_{H^+} = 0.2$ (solid line), 0.4 (dashed line), 0.6 (dotted line) and 0.8 (dash-dotted line) TeV.