We perform a forecast of the CMSSM for the LHC based in an improved Bayesian analysis taking into account the present theoretical and experimental wisdom about the model 1 . In this way we obtain a map of the preferred regions of the CMSSM parameter space and show that fine-tuning penalization arises from the Bayesian analysis itself when the experimental value of MZ is considered. The results are remarkable stable when using different priors.The start of the LHC has motivated a lot of effort to try to anticipate which kind of physics beyond the Standard Model is more likely to be there. Since the present experimental data are not powerful enough to select a small region of the parameter space of SUSY models, Bayesian Statistics becomes a very powerful tool to try to make an inference of the probability of certain regions of parameters of these models, where the choice of judicious prior probability for the parameters becomes more relevant.

Abstract:We perform a forecast of the MSSM with universal soft terms (CMSSM) for the LHC, based on an improved Bayesian analysis. We do not incorporate ad hoc measures of the fine-tuning to penalize unnatural possibilities: such penalization arises from the Bayesian analysis itself when the experimental value of M Z is considered. This allows to scan the whole parameter space, allowing arbitrarily large soft terms. Still the low-energy region is statistically favoured (even before including dark matter or g-2 constraints). Contrary to other studies, the results are almost unaffected by changing the upper limits taken for the soft terms. The results are also remarkable stable when using flat or logarithmic priors, a fact that arises from the larger statistical weight of the low-energy region in both cases. Then we incorporate all the important experimental constrains to the analysis, obtaining a map of the probability density of the MSSM parameter space, i.e. the forecast of the MSSM. Since not all the experimental information is equally robust, we perform separate analyses depending on the group of observables used. When only the most robust ones are used, the favoured region of the parameter space contains a significant portion outside the LHC reach. This effect gets reinforced if the Higgs mass is not close to its present experimental limit and persits when dark matter constraints are included. Only when the g-2 constraint (based on e + e − data) is considered, the preferred region (for µ > 0) is well inside the LHC scope. We also perform a Bayesian comparison of the positive-and negative-µ possibilities.