Upper bounds on sparticle masses from naturalness or how to disprove weak scale supersymmetry

Abstract

While it is often stated that the notion of electroweak (EW) naturalness in supersymmetric models is subjective, fuzzy and model-dependent, here we argue the contrary: electroweak naturalness can be elevated to a {\it principle} which is both objective and predictive. We demonstrate visually when too much fine-tuning sets in at the electroweak scale which corresponds numerically to the measure \Delta_{BG}~\Delta_{EW}> 30. While many constrained SUSY models are already excluded by this value, we derive updated upper bounds on sparticle masses within the two-extra parameter non-universal Higgs model (NUHM2). We confirm the classic Barbieri-Giudice (BG) result that \Delta_{BG}<30 implies mu <350 GeV. However, by combining dependent soft terms which appear as multiples of m_{3/2} in supergravity models, then we obtain m(gluino)< 4 TeV as opposed to the BG result that m(gluino)<350 GeV. We compare the NUHM2 results to a similar scan in the pMSSM with 19 weak scale parameters. In the pMSSM with complete one-loop scalar potential plus dominant two-loop terms, then a m(gluino)<7 TeV bound is found. Our tabulation of upper bounds provides a target for experimenters seeking to discover or else falsify the existence of weak scale supersymmetry. In an Appendix, we show contributions to the naturalness measure from one-loop contributions to the weak scale scalar potential.