A REVIEW OF NATURALNESS AND DARK MATTER PREDICTION FOR THE HIGGS MASS IN MSSM AND BEYOND

Within a two-loop leading-log approximation, we review the prediction for the lightest Higgs mass (m(h)) in the framework of constrained MSSM (CMSSM), derived from the naturalness requirement of minimal fine-timing (Delta) of the electroweak scale, and dark matter consistency. As a result, the IIiggs mass is predicted to be just above the LEP2 bound, m(h) = 115.9 +/- 2 GeV, corresponding to a minimal Delta = 178, the value obtained from consistency with electroweak and WMAP (3 sigma) constraints, but without the LEP2 bound. Due to quantum corrections (largely QCD ones for m(h) above LEP2 bound), Delta grows approximate to exponentially on either side of the above value of m(h), which stresses the relevance of this prediction. A value m(h) > 121 (126) GeV cannot be accommodated within the CMSSM unless one accepts a fine-tuning cost worse than Delta > 100 (1000), respectively. We review how the above prediction for m(h) and Delta 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 m(h) as large as 130 GeV with an acceptable Delta < 10. The size of the supersymmetric correction that each individual operator of d = 6 brings to the value of m(h) for points with Delta < 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.