SUSY naturalness without prejudice


Unlike the Standard Model (SM), supersymmetric models stabilize the electroweak (EW) scale vv at the quantum level and {\it predict} that vv is a function of the TeV-valued SUSY parameters (γα\gamma_\alpha) of the UV Lagrangian. We show that the (inverse of the) covariance matrix of the model in the basis of these parameters and the usual deviation δχ2\delta\chi^2 (from χmin2\chi^2_{min} of a model) automatically encode information about the "traditional" EW fine-tuning measuring this stability, {\it provided that} the EW scale vmZv\sim m_Z is indeed regarded as a function v=v(γ)v=v(\gamma). It is known that large EW fine-tuning may signal an incomplete theory of soft terms and can be reduced when relations among γα\gamma_\alpha exist (due to GUT symmetries, etc). The global correlation coefficient of this matrix can help one investigate if such relations are present. An upper bound on the usual EW fine-tuning measure ("in quadrature") emerges from the analysis of the δχ2\delta\chi^2 and the s-standard deviation confidence interval by using v=v(γ)v=v(\gamma) and the theoretical approximation (loop order) considered for the calculation of the observables. This upper bound avoids subjective criteria for the "acceptable" level of EW fine-tuning for which the model is still "natural".Comment: 13 pages. LaTeX, (v4: minor corrections

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