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 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 ∆ BG ∼ ∆ 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 ∆ BG < 30 implies µ < 350 GeV. However, by combining dependent soft terms which appear as multiples of m 3/2 in supergravity models, then we obtain mg < ∼ 4 TeV as opposed to the BG result that mg < ∼ 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 mg < 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. *

Gluino reach and mass extraction at the LHC in radiatively-driven natural SUSY

“…The largest of these typically arise from the top squarks and require for EW < 30 that mt 1 3 TeV, a factor 10 higher than the aforementioned BG/DG bounds. Gluinos contribute to u u at two-loop order [35] and in models with gaugino mass unification, then mg 4 TeV [30,41,46]. We see that SUSY models with electroweak naturalness can easily respect LHC sparticle mass bounds and are in accord with the measured value of m h , which requires large mixing among top squarks [47].…”

“…The gluino signal then consists of events with ≥4 hard jets, two or three of which are tagged as b-jets together with very large E T . We expect that our results are only weakly sensitive to our choice of higgsino mass as long as the electroweak fine-tuning parameter EW 30.…”

Sbottoms of natural NMSSM at the LHC

“…Combining analyses for the sbottom and stop to find an optimal sensitivity to a given region in the parameter space parameter has recently been advocated in reference [15]. 1 It may, however, be noted that presence of relatively heavy stops (and/or a gluino) may not be an immediate threat to naturalness as revealed by certain recent parameterizations in the MSSM context that refer only to weak scale values of the parameters as long as |µ| (|µ eff |, in NMSSM) is small enough which is essential to the scenario presented in this work [22][23][24][25].…”

Natural NMSSM with a light Singlet Higgs and Singlino LSP

“…While agreement is not universal on which F max values characterize low fine tuning [19], studies have considered F max of order O(10 2 ) to be typical for the NMSSM [44] and O(10 1 ) to be low fine tuning [22][23][24]45]. A recent study seeking to establish naturalness as objective, model-independent and predictive concludes that a SUSY model with F max < 30 is natural, while one with F max < 10 is stringently natural [46].…”