Gravitino Dark Matter in the CMSSM

TL;DR

This paper investigates the viability of gravitino dark matter within the CMSSM by treating the gravitino as the LSP and the NSP (neutralino or lighter stau) as the unstable progenitor of gravitinos. It extends standard CMSSM relic-density calculations to compute the NSP density for both neutralino and stau NSPs, and then uses NSP decay lifetimes to apply light-element constraints from Big-Bang Nucleosynthesis and the CMB baryon-to-entropy ratio $\eta_B$. The main result is that gravitino DM is allowed only in limited regions of the $(m_{1/2}, m_0)$ plane, where the gravitino density produced by NSP decays is compatible with $\Omega_{3/2} h^2 \lesssim 0.129$ and EM cascade bounds, often requiring the NSP to be the ${\tilde{\tau}}_1$; additional gravitino production mechanisms may be needed to account for all DM. The findings have implications for collider phenomenology and highlight the need to consider gravitino DM scenarios in CMSSM studies beyond conventional neutralino DM.

Abstract

We consider the possibility that the gravitino might be the lightest supersymmetric particle (LSP) in the constrained minimal extension of the Standard Model (CMSSM). In this case, the next-to-lightest supersymmetric particle (NSP) would be unstable, with an abundance constrained by the concordance between the observed light-element abundances and those calculated on the basis of the baryon-to-entropy ratio determined using CMB data. We modify and extend previous CMSSM relic neutralino calculations to evaluate the NSP density, also in the case that the NSP is the lighter stau, and show that the constraint from late NSP decays is respected only in a limited region of the CMSSM parameter space. In this region, gravitinos might constitute the dark matter.

Figures (3)

• Figure 1: The $(m_{1/2}, m_0)$ planes for $\tan \beta =10, \mu > 0$ and the choices (a) $m_{3/2} = 10$ GeV, (b) $m_{3/2} = 100$ GeV, (c) $m_{3/2} = 0.2 m_0$ and (d) $m_{3/2} = m_0$. In each panel, we show $m_h = 114$ GeV calculated using FeynHiggsFeynHiggs, as a near-vertical (red) dot-dashed line, the region excluded by $b \to s \gamma$ is darkly shaded (green), and the region where the NSP density before decay lies in the range $0.094 < \Omega^0_{NSP} h^2 < 0.129$ is medium shaded (grey-blue). The (purple) dashed line is the contour where gravitinos produced in NSP decay have $\Omega_{3/2} h^2 = 0.129$, and the grey (khaki) solid line ($r=1$) is the constraint on NSP decays provided by Big-Bang nucleosynthesis and CMB observations. The light (yellow) shaded region is allowed by all the constraints. The contour where $m_\chi = m_{\tilde{\tau}_1}$ is shown as a (red) diagonal dotted line. Panels (a) and (c) show as a black solid line the contour beyond which $\tau_{NSP} < 10^4$ s, the case not considered here. Panels (b), (c), and (d) show black lines to whose left the gravitino is no longer the LSP.
• Figure 2: As in Fig. \ref{['fig:NSP10p']}, for $\tan \beta = 35$ and $\mu < 0$ and the choices (a) $m_{3/2} = 10$ GeV, (b) $m_{3/2} = 100$ GeV, (c) $m_{3/2} = 0.2 m_0$ and (d) $m_{3/2} = m_0$. The light (yellow) shaded regions are allowed by all the constraints.
• Figure 3: As in Figs. \ref{['fig:NSP10p']} and \ref{['fig:NSP35n']}, for $\tan \beta = 50$ and $\mu > 0$ and the choices (a) $m_{3/2} = 10$ GeV, (b) $m_{3/2} = 100$ GeV, (c) $m_{3/2} = 0.2 m_0$ and (d) $m_{3/2} = m_0$. In addition to the quantities plotted in the earlier figures, here we also plot grey solid lines where $a_\mu = 44.5 \times 10^{-10}$, which cut off at small $m_0$ the allowed regions in panels (a) and (c). The light (yellow) shaded regions are allowed by all the constraints.