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

TL;DR

The paper analyzes the NMSSM neutralino sector by introducing a singlet superfield and deriving a 5×5 neutralino mass/mixing framework. Using a perturbative approach valid for small doublet–singlet mixing ($\\mu_\\lambda$), it provides analytic expressions for masses and mixings across MSSM-like and singlino-dominated states, and explores several limiting cases (large gaugino mass, large higgsino mass, large singlino mass, and a symmetric point $M_1=M_2$, $\\tan\\beta=1$). It then details neutralino production in $e^+e^-$ collisions and various decay channels, including decays to a singlino with and without Higgs bosons, as well as implications for sfermion cascades and Higgs decays, with explicit formulae for widths and couplings in terms of the NMSSM mixing matrices. The work shows how a slightly broken Peccei–Quinn symmetry can yield a light singlino while preserving MSSM-like dynamics, and discusses potential observability at LHC and future linear colliders depending on the parameter regime. Overall, the study provides a comprehensive analytical and phenomenological framework for the NMSSM neutralino sector and its collider signatures.

Abstract

The Next-to-Minimal Supersymmetric Standard Model (NMSSM) includes a Higgs iso-singlet superfield in addition to the two Higgs doublet superfields of the minimal extension. If the Higgs fields remain weakly coupled up to the GUT scale, as naturally motivated by the concept of supersymmetry, the mixing between singlet and doublet fields is small and can be treated perturbatively. The mass spectrum and mixing matrix of the neutralino sector can be analyzed analytically and the structure of this 5-state system is under good theoretical control. We also determine decay modes and production channels in sfermion cascade decays to these particles at the LHC and pair production in e+e- colliders.

Figures (8)

• Figure 1: The exact numerical solution (solid) and the approximate solution (dashed) for the masses of the five neutralino states in the NMSSM as a function of $\mu_\lambda$ for the parameter set $\mathbb{P}=\{\mu_\kappa=120$ GeV, $M_1=250$ GeV, $M_2=500$ GeV, $\mu=170$ GeV, $\tan \beta=3\}$. The ordering of the mass spectrum is $m_5, m_1, m_2, m_3$, and $m_4$ in increasing mass, i.e. the state $\tilde{\chi}^0_5$ is the lightest neutralino for the given parameter set.
• Figure 2: The exact numerical solution (solid) and the approximate solution (dashed) for the gaugino/higgsino and singlino components, $\{|N^5_{51}|, |N^5_{53}|, |N^5_{55}|\}$, of the lightest singlino--dominant neutralino as a function of $\mu_\lambda$ for the same parameter set $\mathbb{P}$ as in Fig.\ref{['fig:fig1']}.
• Figure 3: (a) The neutralino masses $|m_i|$, mapped onto positive values, and (b) the tangent values of the mixing angles $\theta_{g/h}$ and $\theta_{h/s}$ as a function of the higgsino mass parameter $\mu$ for the parameter set: $M=200$ GeV, $\mu_\kappa=120$ GeV, $\mu_\lambda=100$ GeV.
• Figure 4: The production cross sections of neutralino pairs, $\{51\}$ (dashed), $\{55\}$ (thin--solid), $\{53\}$ (dotted) and $\{11\}$ (thick--solid), in $e^+e^-$ collisions with the center-of-mass energy $\sqrt{s}=500$ GeV as a function of $\mu_\lambda$ for the parameter set $\mathbb{P}$ [Fig.\ref{['fig:fig1']}] with $m_{\tilde{e}_R}=200$ GeV and $m_{\tilde{e}_L}=250$ GeV.
• Figure 5: The widths, lifetimes and flight distances [broken lines] of the decays $\tilde{\chi}^0_1\rightarrow \tilde{\chi}^0_5\, l^+l^-$ and $\tilde{l}_R\rightarrow \tilde{\chi}^0_5 l$ as a function of $\mu_\lambda$ for the parameter set $\mathbb{P}$[Fig.\ref{['fig:fig1']}]. The mass of the right--handed slepton is taken to be $m_{\tilde{l}_R}=200 \, {\rm GeV} > m_{\tilde{\chi}_1^0}$ for the 3--body neutralino decays (upper panels) and to be $m_{\tilde{l}_R}=130 \, {\rm GeV} < m_{\tilde{\chi}_1^0}$ for the 2--body slepton decays (lower panels). The masses of the squarks are assumed to be $m_{\tilde{q}_L}=250$ GeV and $m_{\tilde{q}_R}=200$ GeV. Right: flight distances for $\sqrt{s}=500$ GeV are shown by broken lines. The kink in the $\tilde{\chi}_1^0$ lifetime and flight distance in the upper right panel is caused by accidental cancellations between sfermion and $Z$ exchange diagrams. [The value of the lower bound, expected from cosmological arguments on $\mu_\lambda$ is presently not yet known.]