Naturalness implies intra-generational degeneracy for decoupled squarks and sleptons

Abstract

The SUSY flavor, CP, gravitino and proton-decay problems are all solved to varying degrees by a decoupling solution wherein first/second generation matter scalars would exist in the multi-TeV regime. Recent models of natural SUSY presumably allow for a co-existence of naturalness with the decoupling solution. We show that: if sfermions are heavier than $\sim 10$ TeV, then a small first/second generation contribution to electroweak fine-tuning (EWFT) requires a rather high degree of intra-generational degeneracy of either 1. (separately) squarks and sleptons, 2. (separately) left- and right-type sfermions, 3. members of SU(5) multiplets, or 4. all members of a single generation as in SO(10). These (partial) degeneracy patterns required by naturalness hint at the necessity of an organizing principle, and highlight the limitations of models such as the pMSSM in the case of decoupled first/second generation scalars.