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We study the properties of the constrained minimal supersymmetric standardmodel (mSUGRA) by performing fits to updated indirect data, including the relicdensity of dark matter inferred from WMAP5. In order to find the extent towhich mu < 0 is disfavoured compared to mu > 0, we compare the Bayesianevidence values for these models, which we obtain straightforwardly and withgood precision from the recently developed multi-modal nested sampling('MultiNest') technique. We find weak to moderate evidence for the mu > 0branch of mSUGRA over mu < 0 and estimate the ratio of probabilities to be P(mu> 0)/P(mu < 0) = 6-61 depending on the prior measure and range used. There isthus positive (but not overwhelming) evidence that mu > 0 in mSUGRA. TheMultiNest technique also delivers probability distributions of parameters andother relevant quantities such as superpartner masses. We explore thedependence of our results on the choice of the prior measure used. We also usethe Bayesian evidence to quantify the consistency between the mSUGRA parameterinferences coming from the constraints that have the largest effects: (g-2)_mu,BR(b -> s gamma) and cold dark matter (DM) relic density Omega_{DM}h^2.

Bayesian Selection of sign(mu) within mSUGRA in Global Fits Including WMAP5 Results