Yukawa Unification and the Superpartner Mass Scale

Naturalness in supersymmetry (SUSY) is under siege by increasingly stringent LHC constraints, but natural electroweak symmetry breaking still remains the most powerful motivation for superpartner masses within experimental reach. If naturalness is the wrong criterion then what determines the mass scale of the superpartners? We motivate su-persymmetry by (1) gauge coupling unification, (2) dark matter, and (3) precision b − τ Yukawa unification. We show that for an LSP that is a bino-Higgsino admixture, these three requirements lead to an upper-bound on the stop and sbottom masses in the several TeV regime because the threshold correction to the bottom mass at the superpartner scale is required to have a particular size. For tanβ ≈ 50, which is needed for t−b−τ unification, the stops must be lighter than 2.8 TeV when At has the opposite sign of the gluino mass, as is favored by renormalization group scaling. For lower values of tanβ, the top and bottom squarks must be even lighter. Yukawa unification plus dark matter implies that superpart-ners are likely in reach of the LHC, after the upgrade to 14 (or 13) TeV, independent of any considerations of naturalness. We present a model-independent, bottom-up analysis of the SUSY parameter space that is simultaneously consistent with Yukawa unification and the hint for mh = 125 GeV. We study the flavor and dark matter phenomenology that accompanies this Yukawa unification. A large portion of the parameter space predicts that the branching fraction for Bs → µ+µ − will be observed to be significantly lower than the SM value. ar X i