Supersymmetric Dark Matter in Light of WMAP

TL;DR

This study re-evaluates the constrained MSSM (CMSSM) in light of the WMAP-reported cold dark matter density, $0.094\le \Omega_{CDM} h^2 \le 0.129$, to obtain a significantly tighter upper bound on the lightest SUSY particle mass. The authors show that the CMSSM parameter space—particularly the coannihilation strips and rapid-annihilation funnels—shrinks substantially, yielding $m_\chi \lesssim 500$ GeV for $\tan\beta \lesssim 45$ with $\mu>0$ (or $\tan\beta \lesssim 30$ with $\mu<0$), and even stronger limits when the $g_\mu-2$ constraint is applied ($m_\chi \lesssim 370$ GeV). These tighter bounds improve SUSY discovery prospects at the LHC and increase the likelihood that a 1 TeV linear collider could access relevant sleptons and other sparticles. The results also imply a narrowed CMSSM parameter space, with the potential to determine $\tan\beta$ from measurements of $m_{1/2}$ and $m_0$, while highlighting sensitivity to $m_t$ and $m_h$ calculations. Overall, the paper illustrates how precision cosmology reshapes supersymmetric phenomenology and experimental strategies.

Abstract

We re-examine the parameter space of the constrained minimal supersymmetric extension of the Standard Model (CMSSM), taking account of the restricted range of Ω_{CDM} h^2 consistent with the WMAP data. This provides a significantly reduced upper limit on the mass of the lightest supersymmetric particle LSP: m_χ< 500 GeV for \tan β< 45 and μ> 0, or \tan β< 30 and μ< 0, thereby improving the prospects for measuring supersymmetry at the LHC, and increasing the likelihood that a 1-TeV linear e^+ e^- collider would be able to measure the properties of some supersymmetric particles.

Figures (3)

• Figure 1: The $(m_{1/2}, m_0)$ planes for (a) $\tan\beta = 10, \mu > 0$, (b) $\tan\beta = 10, \mu < 0$, (c) $\tan\beta = 35, \mu < 0$, and (d) $\tan\beta = 50, \mu > 0$. In each panel, the region allowed by the older cosmological constraint $0.1 \le \Omega_\chi h^2 \le 0.3$ has medium shading, and the region allowed by the newer cosmological constraint $0.094 \le \Omega_\chi h^2 \le 0.129$ has very dark shading. The disallowed region where $m_{\tilde{\tau}_1} < m_\chi$ has dark (red) shading. The regions excluded by $b \rightarrow s \gamma$ have medium (green) shading, and those in panels (a,d) that are favoured by $g_\mu - 2$ at the 2-$\sigma$ level have medium (pink) shading. A dot-dashed line in panel (a) delineates the LEP constraint on the $\tilde{e}$ mass and the contours $m_{\chi^\pm} = 104$ GeV ($m_h = 114$ GeV) are shown as near-vertical black dashed (red dot-dashed) lines in panel (a) (each panel).
• Figure 2: The strips display the regions of the $(m_{1/2}, m_0)$ plane that are compatible with $0.094 < \Omega_\chi h^2 < 0.129$ and the laboratory constraints for $\mu > 0$ and $\tan \beta = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55$. The parts of the strips compatible with $g_\mu - 2$ at the 2-$\sigma$ level have darker shading.
• Figure 3: The ranges of $m_\chi$ allowed by cosmology and other constraints, for (a) $\mu > 0$ and (b) $\mu < 0$. Upper limits without (red solid line) and with (blue dashed line) the $g_\mu - 2$ constraint are shown for $\mu > 0$: the lower limits are shown as black solid lines. Note the sharp increases in the upper limits for $\tan \beta \mathrel{\hbox{$>$} {\hbox{$\sim$}}} 50, \mu > 0$ and $\tan \beta \mathrel{\hbox{$>$} {\hbox{$\sim$}}} 35, \mu < 0$ due to the rapid-annihilation funnels. Also shown as dotted lines are the ${\tilde{e}_L}$ and $\chi^\pm$ masses at the tips of the coannihilation tails.