On the detectability of the CMSSM light Higgs boson at the Tevatron

We examine the prospects of detecting the light Higgs scalar h^0 of the Constrained MSSM at the Tevatron. To this end we explore large ranges of the CMSSM parameter space with mu>0 using a Markov Chain Monte Carlo technique, and apply all relevant collider and cosmological constraints including their uncertainties, as well as those of the Standard Model parameters. Using the formalism of Bayesian statistics we find that the 68% posterior probability region for the light Higgs mass lies between 116.0 GeV and 120.4 GeV. Otherwise, h^0 is very similar to the Standard Model Higgs boson. Nevertheless, we point out some enhancements in its couplings to bottom and tau pairs, ranging from a few per cent in most of the CMSSM parameter space, up to several per cent in the most favored region of tan(beta)~50 and the pseudoscalar Higgs mass of m_A~1 TeV. We also find that the other Higgs bosons are typically too heavy to be produced at the Tevatron. We conclude that, over the whole CMSSM light Higgs 95% posterior probability mass range, a 95% CL exclusion limit can be set with about 2/fb of integrated luminosity per experiment, or else with 4/fb (12/fb) a 3 sigma evidence (5 sigma discovery) will be guaranteed. We also emphasize that the alternative measure of the mean quality of fit favors a somewhat lower Higgs mass range; this implies even more optimistic prospects for the CMSSM light Higgs search than with the more conservative Bayesian approach. In conclusion, at the Tevatron either some evidence will be found for the light Higgs boson or, at a high confidence level, the CMSSM will be ruled out.