A Markov Chain Monte Carlo Analysis of the CMSSM

We perform a comprehensive exploration of the Constrained MSSM parameters using a Markov Chain Monte Carlo technique and a Bayesian analysis. We compute superpartner masses and other collider observables as well as a cold dark matter abundance, and compare them with experimental data. We include uncertainties arising from theoretical approximations as well as from residual experimental errors on relevant SM parameters. We delineate probability distributions of the CMSSM parameters, the collider and cosmological observables as well as a dark matter direct detection cross section. The 68% probability intervals of the CMSSM parameters are: 0.52 TeV < m_{1/2} < 1.26 TeV, m_0 <2.10 TeV, -0.34 TeV < A_0 < 2.41 TeV and 38.5< tan(beta) <54.6. Generally, large fractions of high probability ranges of the superpartner masses will be probed at the LHC. We highlight a complementarity between LHC and WIMP dark matter searches in exploring the CMSSM parameter space. We further expose a number of correlations among the observables, in particular between BR(B_s \to \mu^+ \mu^-) and BR({\bar B}\to X_s\gamma) or sigma_p^{SI}. Once SUSY is discovered, this and other correlations may prove helpful in distinguishing the CMSSM from other supersymmetric models. The robustness of our results is investigated in terms of the assumed ranges of CMSSM parameters and the effect of the (g-2)_mu anomaly which shows some tension with the other observables. We find that the results for m_0, and the observables which strongly depend on it, are sensitive to our assumptions, while our conclusions for the other variables are robust.