A 119-125 GeV Higgs from a string derived slice of the CMSSM

The recent experimental hints for a relatively heavy Higgs with a mass in the range 119-125 GeV favour supersymmetric scenarios with a large mixing in the stop mass matrix. It has been shown that this is possible in the constrained Minimal Supersymmetric Standard Model (CMSSM), but only for a very specific relation between the trilinear parameter and the soft scalar mass, favouring A approximate to -2m for a relatively light spectrum, and sizable values of tan beta. We describe here a string-derived scheme in which the first condition is automatic and the second arises as a consequence of imposing radiative EW symmetry breaking and viable neutralino dark matter in agreement with WMAP constraints. More specifically, we consider modulus dominated SUSY-breaking in Type II string compactifications and show that it leads to a very predictive CMSSM-like scheme, with small departures due to background fluxes. Imposing the above constraints leaves only one free parameter, which corresponds to an overall scale. We show that in this construction A = -3/root 2m similar or equal to -2m and in the allowed parameter space tan beta similar or equal to 38 - 41, leading to 119GeV < m(h) < 125 GeV. The recent LHCb results on BR(B-s -> mu(+)mu(-)) further constrain this range, leaving only the region with m(h) similar to 125. GeV. We determine the detectability of this model and show that it could start being probed by the LHC at 7(8) TeV with a luminosity of 5(2) fb(-1), and the whole parameter space would be accessible for 14TeV and 25 fb(-1). Furthermore, this scenario can host a long-lived stau with the right properties to lead to catalyzed BBN. We finally argue that anthropic arguments could favour the highest value for the Higgs mass that is compatible with neutralino dark matter, i.e., m(h) similar to 125GeV.