The Next-to-Minimal Supersymmetric extension of the Standard Model reviewed

TL;DR

The NMSSM addresses the MSSM μ-problem by generating μ_eff dynamically via μ_eff = λ⟨S⟩ and expands the Higgs and neutralino sectors with a gauge-singlet. The paper systematically derives the NMSSM superpotential, the Higgs potential and mass matrices (including one-loop corrections), and analyzes CP properties, domain-wall issues, and the no-lose theorems for LHC Higgs discovery. It surveys theoretical and experimental constraints, cosmology (relic density and dark matter detection), and parameter scans, highlighting regions with a singlino-like LSP and potential displaced-vertex signatures. A Groebner-basis algebraic approach is presented to determine the global minimum of the Higgs potential, revealing rich stationary-point structures and substantial portions of parameter space compatible with current data. Overall, the NMSSM emerges as a viable, testable extension of the SM with distinctive collider and cosmological predictions that differ meaningfully from the MSSM.

Abstract

The next-to-minimal supersymmetric extension of the Standard Model (NMSSM) is one of the most favored supersymmetric models. After an introduction to the model, the Higgs sector and the neutralino sector are discussed in detail. Theoretical, experimental, and cosmological constraints are studied. Eventually, the Higgs potential is investigated in the approach of bilinear functions. Emphasis is placed on aspects which are different from the minimal supersymmetric extension.

Figures (20)

• Figure 1: Higgs-boson production via Higgs-strahlung and subsequent decay into a $b\bar{b}$ quark pair, as searched for at the LEP experiment Schael:2006cr. The coupling of the Higgs boson to the $Z$ bosons is denoted by $g_{HZZ}$ and given for the NMSSM in App. \ref{['app-feyn']}.
• Figure 2: Upper limit on the ratio $\xi^2$ given in \ref{['eq-xi']} times the branching ratio of the Higgs boson into $b \bar{b}$ according to the SM. The upper limit is gained from at LEP from LEP1 data at the $Z$ resonance as well as from LEP2 data taken at energies between 161 and 209 GeV. The dark and bright band give the 1--$\sigma$ and 2--$\sigma$ deviations from the central upper limit. The observation is shown (full line), exceeding the upper limit for a Higgs-boson mass of about 98 GeV. The horizontal line above represents the SM expectation on $\xi^2$. Figure taken from Barate:2003sz.
• Figure 3: Central exclusive production of a light CP-even Higgs boson ($H$) in proton ($p$) collisions, $pp \rightarrow ppH$, as suggested by Forshaw:2007ra. The Higgs boson $H$ decays into a pair of pseudoscalar Higgs bosons $A$. The process proceeds via a fermion loop.
• Figure 4: Neutralino masses (left) and mixings (right) depending on $\mu_\lambda \equiv \lambda v/\sqrt{2}$. The other parameters are fixed to $\sqrt{2} \kappa v_s= 120$ GeV (this is the lower diagonal entry in the mixing matrix \ref{['eq-neutralinomass']}), $M_1=250$ GeV, $M_2=500$ GeV, $\lambda v_s/\sqrt{2}=170$ GeV, $\tan(\beta)=3$. The numbering $i=1,...,5$ denotes the mass eigenstates in the mixing $\chi_i^0 = U_{j i}\, \psi_j^0$\ref{['eq-chi0mix']}, before the arrangement in ascending order. The mixing entries in the matrix $U_{j i}$ are denoted in the right plot by the indices, that is, for instance $|53|$ denotes $|U_{5 3}|$. The dashed respectively dotted curves show an approximation, in case the singlino--Higgsino mixing is suppressed, that is, for $v \ll v_s$. Figure taken from Choi:2004zx.
• Figure 5: Total cross section for singlino-like neutralino production $e^+e^- \rightarrow \tilde{\chi}_1^0 \tilde{\chi}_S^0$ depending on the vacuum-expectation-value $v_s$, here denoted by $x$ as presented by Hesselbach and Franke Hesselbach:2002nv. The electron--positron center-of-mass energy is fixed to 500 GeV. The model parameters chosen are inspired by the SPS1a scenario in the MSSM with $M_1=99$ GeV, $M_2=193$ GeV, $\tan(\beta)=10$, $\mu= \lambda v_s= 352$ GeV. The full line refers to unpolarized beams, the dashed line to beam polarizations $P_-=+0.8$, $P_+=-0.6$ and the dotted line to beam polarizations $P_-=-0.8$, $P_+=+0.6$. The mass of the neutralino $\tilde{\chi}_S^0$ is fixed at 120 GeV by the $\kappa$-parameter.

Theorems & Definitions (5)

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