We examine the effect of a prior that favours low values of fine-tuning on Bayesian multi-dimensional fits of the constrained minimal supersymmetric standard model ( CMSSM or mSUGRA ) to current data .
The dark matter relic density , the anomalous magnetic moment of the muon and the branching ratio of b \rightarrow s \gamma are all used to constrain the model via a Markov Chain Monte Carlo sampler .
As a result of the naturalness prior , posterior probability distributions skew towards lighter higgs and sparticle masses , the effect being most pronounced in the gaugino sector .
Interestingly , slepton masses are an exception and skew towards heavier masses .
The lightest CP-even Higgs h ^ { 0 } -pole annihilation mechanism becomes allowed at the 2 \sigma level for the latest combination of measurements of m _ { t } = 172.7 \pm 2.9 GeV , provided we allow for a theoretical error in the prediction of its mass m _ { h ^ { 0 } } . m _ { h ^ { 0 } } is constrained to be less than 120 GeV at the 95 \% C.L .
Probing the branching ratio of B _ { s } \rightarrow \mu ^ { + } \mu ^ { - } to the level of 2 \times 10 ^ { -8 } , as might be achieved by the Tevatron experiments , would cover 32 \% of the probability density , irrespective of which of the two priors is used .