Where to look for natural supersymmetry

Abstract

Why is natural supersymmetry neither detected nor ruled-out to date? To answer this question we use the Bayesian approach where the emphasis on finding prior-independent features within broader and minimally biased frames is taken as the guiding principle. The 20-parameter minimal supersymmetric standard model (MSSM) fits to subjective naturalness indicate the existence of a prior-independent upper bound on the pseudoscalar Higgs boson mass $m_A$ as a function of $\tan \beta$, the ratio of the vacuum expectation values of the MSSM Higgs doublets. For a 30-parameter MSSM this implies that $m_A\lesssim 3$ TeV and $\tan \beta \lesssim 25$ at 95\% Bayesian confidence. Removing the contradictory subjectiveness within the electroweak fine-tuning measure leads to finding the naturalness line, $m_A\sim \frac{1}{\sqrt{2}}{m}_Z\tan \beta ,$ that reduces by one the number of MSSM Higgs sector free parameters.

Comments: v3: minor changes, published in PRD