Where to look for natural supersymmetry

Understand

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.