Fitting the Higgs to natural SUSY

We present a fit to the 2012 LHC Higgs data in different supersymmetric frameworks using naturalness as a guiding principle. We consider the MSSM and its D-term and F -term extensions that can raise the tree-level Higgs mass. When adding an extra chiral superfield to the MSSM, three parameters are needed determine the tree-level couplings of the lightest Higgs. Two more parameters cover the most relevant loop corrections, that affect the hγγ and hgg vertexes. Motivated by this consideration, we present the results of a five parameters fit encompassing a vast class of complete supersymmetric theories. We find meaningful bounds on singlet mixing and on the mass of the pseudoscalar Higgs m_A as a function of tan β in the MSSM. We show that in the (m_A, tan β) plane, Higgs couplings measurements are probing areas of parameter space currently inaccessible to direct searches. We also consider separately the two cases in which only loop effects or only tree-level effects are sizable. In the former case we study in detail stops' and charginos' contributions to Higgs couplings, while in the latter we show that the data point to the decoupling limit of the Higgs sector. In a particular realization of the decoupling limit, with an approximate PQ symmetry, we obtain constraints on the heavy scalar Higgs mass in a general type-II Two Higgs Doublet Model.