Quantifying the tension between the Higgs mass and (g-2)μ in the constrained MSSM

Supersymmetry has often been invoked as the new physics that might reconcile the experimental muon magnetic anomaly, aμ, with the theoretical prediction (basing the computation of the hadronic contribution on e+e- data). However, in the context of the constrained minimal supersymmetric standard model (CMSSM), the required supersymmetric contributions (which grow with decreasing supersymmetric masses) are in potential tension with a possibly large Higgs mass (which requires large stop masses). In the limit of very large mh supersymmetry gets decoupled, and the CMSSM must show the same discrepancy as the standard model with a μ. But it is much less clear for which size of mh does the tension start to be unbearable. In this paper, we quantify this tension with the help of Bayesian techniques. We find that for mh≥125GeV the maximum level of discrepancy given the current data (∼3.2σ) is already achieved. Requiring less than 3σ discrepancy, implies m h120GeV. For a larger Higgs mass we should give up either the CMSSM model or the computation of aμ based on e+e -; or accept living with such an inconsistency. © 2011 American Physical Society.