Likelihood analysis of the constrained minimal supersymmetric standard model parameter space

We present a likelihood analysis of the parameter space of the constrained minimal supersymmetric extension of the standard model (CMSSM), in which the input scalar masses $m_0$ and fermion masses $m_{1/2}$ are each assumed to be universal. We include the full experimental likelihood function from the CERN LEP Higgs boson search as well as the likelihood from a global precision electroweak fit. We also include the likelihoods for $\overrightarrow{b}s\gamma$ decay and (optionally) $g_{\mu }-2.$ For each of these inputs, both the experimental and theoretical errors are treated. We include the systematic errors stemming from the uncertainties in $m_t$ and $m_b,$ which are important for delineating the allowed CMSSM parameter space as well as calculating the relic density of supersymmetric particles. We assume that these dominate the cold dark matter density, with a density in the range favored by the Wilkinson Microwave Anisotropy Probe. We display the global likelihood function along cuts in the ${(m}_{1/2}{,m}_0)$ planes for $\tan \beta =10\mathrm{}$ and both signs of μ, $\tan \beta =35,$ $\mu <0,$ and $\tan \beta =50,$ $\mu >0,$ which illustrate the relevance of $g_{\mu }-2$ and the uncertainty in $m_t.$ We also display likelihood contours in the ${(m}_{1/2}{,m}_0)$ planes for these values of $\tan \beta .$ The likelihood function is generally larger for $\mu >0\mathrm{}$ than for $\mu <0\mathrm{}$ and smaller in the focus-point region than in the bulk and coannihilation regions, but none of these possibilities can yet be excluded.