SUSY naturalness without prejudice

Abstract

Unlike the Standard Model (SM), supersymmetric models stabilize the electroweak (EW) scale $v$ at the quantum level and {\it predict} that $v$ is a function of the TeV-valued SUSY parameters ($\gamma_\alpha$) 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 $\delta\chi^2$ (from $\chi^2_{min}$ of a model) automatically encode information about the "traditional" EW fine-tuning measuring this stability, {\it provided that} the EW scale $v\sim m_Z$ is indeed regarded as a function $v=v(\gamma)$. It is known that large EW fine-tuning may signal an incomplete theory of soft terms and can be reduced when relations among $\gamma_\alpha$ 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 $\delta\chi^2$ and the s-standard deviation confidence interval by using $v=v(\gamma)$ 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".