Neutralino Relic Density in a Supersymmetric U(1)' Model

TL;DR

This paper investigates the lightest neutralino as a cold dark matter candidate in a supersymmetric $U(1)'$ extension with a secluded breaking sector, termed the $S$-model. It analyzes the mass and composition of the LSP in the limit $M_1' \gg M_1,M_2$, showing a predominantly singlino state with $m_{\chi^0} \lesssim 100$ GeV and an enhanced $Z\chi^0\chi^0$ coupling that facilitates annihilation via the $Z$-pole. Relic density calculations, including all relevant $Z$-mediated diagrams and thermal averaging, demonstrate that $\Omega_{\chi^0} h^2$ can match the observed value across broad regions of parameter space, with three notable regions: near the $Z$ pole, an enhanced-coupling region at $\tan\beta \approx 1$, and a singlino-dominated island for $M_2<0$. The results show that the $S$-model can accommodate the measured CDM density without conflicting LEP constraints and offers a viable alternative to MSSM scenarios for dark matter phenomenology.

Abstract

We study properties of the lightest neutralino (χ) and calculate its cosmological relic density in a supersymmetric U(1)' model with a secluded U(1)' breaking sector (the S-model). The lightest neutralino mass is smaller than in the minimal supersymmetric standard model; for instance, m_χ< 100 GeV in the limit that the U(1)' gaugino mass is large compared to the electroweak scale. We find that the Z-χ-χcoupling can be enhanced due to the singlino components in the extended neutralino sector. Neutralino annihilation through the Z-resonance then reproduces the measured cold dark matter density over broad regions of the model parameter space.

Figures (5)

• Figure 1: The fraction of the lightest neutralino ($|N_{1i}|^2$) versus $M_2$ for (a) the $S$-model and (b) the MSSM. All components are presented: $|N_{11}|^2$ ($\tilde{B}$, dot), $|N_{12}|^2$ ($\tilde{W}_3$, dash), $|N_{13}|^2$ ($\tilde{H}_1^0$, solid), $|N_{14}|^2$ ($\tilde{H}_2^0$, dash-dot), and $|N_{15}|^2$ ($\tilde{S}$, dash-dot-dot). The curve for $|N_{1i}|^2$ is labeled by $i$. Fixed values of $h_s = 0.75$, $\tan\beta = 1.03$ and $s = 250$ GeV are illustrated. The difference of $|N_{13}|^2$ and $|N_{14}|^2$ is large when the singlino component is present even though $\tan\beta \sim 1$.
• Figure 2: The $Z\chi^0\chi^0$ coupling $|O"_{11}|$ versus $M_2$ for (a) $\tan\beta = 1.03$, (b) $\tan\beta = 2.0$, and (c) $\tan\beta = 2.5$, in the $S$-model (solid) and in the MSSM (dash). Fixed values of $h_s = 0.75$ and $s = 250$ GeV are used. The coupling is much larger in the $S$-model than in the MSSM in most of the parameter space.
• Figure 3: (a) The lightest neutralino mass as a function of $M_2$ and (b) the $Z\chi^0 \chi^0$ coupling ($|O"_{11}|$) versus the lightest neutralino mass in the $S$-model (solid) and the MSSM (dash). Fixed values of $h_s = 0.75$, $\tan\beta = 1.03$ and $s = 250$ GeV are used. The $S$-model has a smaller $m_{\chi^0}$ bound, and, for $M_2 > 0$, larger $Z \chi^0 \chi^0$ coupling than the MSSM.
• Figure 4: The neutralino relic density ($\Omega_{\chi^0} h^2$) versus $m_{\chi^0}$ in the $S$-model [$M_2 > 0$ (solid) and $M_2 < 0$ (dash-dot)] and the MSSM [$M_2 > 0$ (dash) and $M_2 < 0$ (dot)] for (a) $\tan\beta = 1.03$, (b) $\tan\beta = 2.0$, and (c) $\tan\beta = 2.5$. The isolated black curve corresponds to the singlino-dominated flat part of the $S$-model in Figure \ref{['fig:mass']} with $M_2 < 0$. Fixed values of $h_s = 0.75$ and $s = 250$ GeV are used. The acceptable relic density is $\Omega_{\chi^0} h^2 \sim 0.1$ .
• Figure 5: Regions of the $S$-model neutralino relic density in the $M_2$-$s$ plane (with $s$ scanned only above $100$ GeV) for $0.09 < \Omega_{\chi^0} h^2 < 0.15$ (filled square; $3 \sigma$ allowed range), $\Omega_{\chi^0} h^2 < 0.09$ (open circle), and $0.15 < \Omega_{\chi^0} h^2 < 1.0$ (cross). Three representative values of $\tan\beta$ are chosen: (a) $\tan\beta = 1.03$, (b) $\tan\beta = 2.0$, and (c) $\tan\beta = 2.5$, and a fixed value of $h_s = 0.75$ is used. The shaded region of the parameter space (bounded by solid curves) is excluded by the LEP 2 chargino mass limit ($m_{\chi^+_1} \alt 104$ GeV). There exist sizable regions (filled square) in the parameter space consistent with the relic density constraint outside of the chargino mass exclusion boundary.