Combining the Muon Anomalous Magnetic Moment with other Constraints on the CMSSM

Abstract

We combine the constraint suggested by the recent BNL E821 measurement of the anomalous magnetic moment of the muon on the parameter space of the constrained MSSM (CMSSM) with those provided previously by LEP, the measured rate of b to s gamma decay and the cosmological relic density Omega-hsquared. Our treatment of Omega-hsquared includes carefully the direct-channel Higgs poles in annihilation of pairs of neutralinos chi and a complete analysis of chi - slepton coannihilation. We find excellent consistency between all the constraints for tan beta > 10 and mu > 0, for restricted ranges of the CMSSM parameters m_0 and m_1/2. All the preferred CMSSM parameter space is within reach of the LHC, but may not be accessible to the Tevatron collider, or to a first-generation e^+ e^- linear collider with centre-of-mass energy below 1.2 TeV.

Figures (3)

• Figure 1: The $(m_{1/2}, m_0)$ planes for $\mu > 0$ and $\tan \beta =$ (a) 10, (b) 30, (c) 50 and (d) 55, found assuming $A_0 = 0, m_t = 175$ GeV and $m_b(m_b)^{\overline {MS}}_{SM} = 4.25$ GeV. The near-vertical (red) dot-dashed lines are the contours $m_h = 113, 117$ GeV, and the near-vertical (black) dashed line in panel (a) is the contour $m_{\chi^\pm} = 104$ GeV. The medium (dark green) shaded regions are excluded by $b \to s \gamma$. The light (turquoise) shaded areas are the cosmologically preferred regions with $0.1\leq\Omega_{\chi} h^2\leq 0.3$. In the dark (brick red) shaded regions, the LSP is the charged ${\tilde{\tau}}_1$, so this region is excluded. The regions allowed by the E821 measurement of $a_\mu$ at the 2-$\sigma$ level are shaded (pink) and bounded by solid black lines, with dashed lines indicating the 1-$\sigma$ ranges.
• Figure 2: Upper limits on $m_{1/2}$ and $m_0$ obtained as functions of $\tan \beta$ for $\mu > 0$, assuming $m_b(m_b)^{\overline {MS}}_{SM} = 4.25$, $m_t = 175$ GeV and $A_0 = 0$. We show the upper limits on $m_{1/2}$ obtained by combining cosmology with the LEP Higgs 'signal' and the E821 lower limit on $\delta a_\mu$, and the upper limits on $m_0$ imposed by cosmology alone and in association with either $a_\mu$ or the LEP Higgs 'signal'.
• Figure 3: Comparison between the $(m_{1/2}, m_0)$ planes for $\tan \beta = 50, \mu > 0$ and $A_0 = 0$, with different values of other input parameters. Panels (a) and (b) are for $m_t = 175$ GeV, $m_b(m_b)^{\overline {MS}}_{SM} = 4.0$ and $4.5$ GeV, respectively. Panels (c) and (d) are for $m_b(m_b)^{\overline {MS}}_{SM} = 4.25$ GeV and $m_t = 170$ and $180$ GeV, respectively.