The Higgs Sector of the Next-to-Minimal Supersymmetric Standard Model

TL;DR

The paper analyzes the Higgs sector of the NMSSM, which extends the MSSM by adding a singlet S to address the μ problem via μ = λ v_s/√2. It derives the tree- and loop-level Higgs potentials, mass matrices, and Z-boson couplings, and explores how the spectrum and couplings depend on the PQ-breaking parameter κ and related soft terms. By examining three PQ-breaking regimes (unbroken, slightly broken, strongly broken) and performing analytic approximations valid for large SUSY scales and moderate tanβ, the authors show distinct Higgs mass patterns and Z-coupling behaviors, with vacuum stability and RG running constraining the viable parameter space. The results indicate potential collider signatures that could distinguish the NMSSM from the MSSM, particularly through light Higgs states with reduced couplings to the Z boson and altered mass hierarchies, underscoring the importance of searches at future linear colliders and careful consideration of LEP constraints.

Abstract

The Higgs boson spectrum of the Next-to-Minimal Supersymmetric Standard Model is examined. The model includes a singlet Higgs field S in addition to the two Higgs doublets of the minimal extension. `Natural' values of the parameters of the model are motivated by their renormalization group running and the vacuum stability. The qualitative features of the Higgs boson masses are dependent on how strongly the Peccei-Quinn U(1) symmetry of the model is broken, measured by the self-coupling of the singlet field in the superpotential. We explore the Higgs boson masses and their couplings to gauge bosons for various representative scenarios.

Figures (12)

• Figure 1: The dependence of $\lambda$ (left) and $\kappa$ (right) on renormalization scale, $Q$, for the top Yukawa coupling $h_t(M_{\rm GUT})=0.8$. The different curves represent different values of $\lambda$ and $\kappa$ at the GUT scale; left: $\lambda=1$, $2$ and $3$, with $\kappa=1$; right: $\kappa=1$, $2$ and $3$, with $\lambda=1$.
• Figure 2: Left: The dependence of $\sqrt{\lambda^2+\kappa^2}$ on renormalization scale, $Q$, for the top Yukawa coupling $h_t(M_{\rm GUT})=0.8$. The different curves represent different values of $\lambda$ and $\kappa$ at the GUT scale: $\lambda=\kappa=1$, $2$, and $3$. Right: The electroweak scale values of $\kappa$ and $\lambda$ for $2 \times 10^5$ different scenarios with random GUT scale values of $0<(\lambda,\kappa,h_t)<2 \pi$. Only scenarios where the running top quark mass $m_t(Q)$ falls in the bracket $165 \pm 5$ GeV at the electroweak scale are retained. Each point represents a different GUT scale parameter choice.
• Figure 3: The one-loop Higgs boson masses as a function of $A_{\kappa}$ for $\lambda=0.3$, $\kappa=0.1$, $v_s=3\,v$, $\tan \beta=3$ and $M_A=\mu \tan \beta \approx 470$ GeV. The arrows denote the physically allowed region.
• Figure 4: The one-loop Higgs boson masses, plotted as a function of $M_A$ for $\lambda=0.3$, $\kappa=0$, $v_s=3v$ and $\tan \beta=3$. The arrows denote the physically allowed region.
• Figure 5: The couplings $\mathcal{G}_{ZZH_i}$ (left) and $\mathcal{G}_{ZA_iH_j}$ (right), plotted as a function of $M_A$ for $\lambda=0.3$, $\kappa=0$, $v_s=3v$ and $\tan \beta=3$. The arrows denote the physically allowed region.