Bayesian Selection of sign μ within mSUGRA in Global Fits Including WMAP5 Results

We study the properties of the constrained minimal supersymmetric standard model (mSUGRA) by performing fits to updated indirect data, including the relic density of dark matter inferred from WMAP5. In order to find the extent to which μ < 0 is disfavoured compared to μ > 0, we compare the Bayesian evidence values for these models, which we obtain straightforwardly and with good precision from the recently developed multi–modal nested sampling (‘MultiNest’) technique. We find weak to moderate evidence for the μ > 0 branch of mSUGRA over μ < 0 and estimate the ratio of probabilities to be P (μ > 0)/P (μ < 0) = 6−61 depending on the prior measure and range used. There is thus positive (but not overwhelming) evidence that μ > 0 in mSUGRA. The MultiNest technique also delivers probability distributions of parameters and other relevant quantities such as superpartner masses. We explore the dependence of our results on the choice of the prior measure used. We also use the Bayesian evidence to quantify the consistency between the mSUGRA parameter inferences coming from the constraints that have the largest effects: (g − 2)μ, BR(b → sγ) and cold dark matter (DM) relic density ΩDMh.