Within a two-loop leading-log approximation, we review the prediction for the lightest Higgs mass (mh) in the framework of constrained MSSM (CMSSM), derived from the naturalness requirement of minimal fine-tuning (Δ) of the electroweak scale, and dark matter consistency. As a result, the Higgs mass is predicted to be just above the LEP2 bound, mh = 115.9±2 GeV , corresponding to a minimal Δ = 17.8, the value obtained from consistency with electroweak and WMAP (3σ) constraints, but without the LEP2 bound. Due to quantum corrections (largely QCD ones for mh above LEP2 bound), Δ grows ≈ exponentially on either side of the above value of mh, which stresses the relevance of this prediction. A value mh>121 (126) GeV cannot be accommodated within the CMSSM unless one accepts a fine-tuning cost worse than Δ>100 (1000), respectively. We review how the above prediction for mh and Δ changes under the addition of new physics beyond the MSSM Higgs sector, parametrized by effective operators of dimensions d = 5 and d = 6. For d = 5 operators, one can obtain values mh as large as 130 GeV with an acceptable Δ<10. The size of the supersymmetric correction that each individual operator of d = 6 brings to the value of mh for points with Δ<100 (<200), is found to be small, of few ≤4 GeV (≤6 GeV) respectively, for M = 8 TeV where M is the scale of new physics. This value decreases (increases) by approximately 1 GeV for a 1 TeV increase (decrease) of the scale M. The relation of these results to the Atlas/CMS supersymmetry exclusion limits is presented together with their impact for the CMSSM regions of lowest fine-tuning.
On the evaporation of solar dark matter: spin-independent effective operators
