Charting generalized supersoft supersymmetry

Without any shred of evidence for new physics from LHC, the last hiding spots of natural electroweak supersymmetry seem to lie either in compressed spectra or in spectra where scalars are suppressed with respect to the gauginos. While in the MSSM (or in any theory where supersymmetry is broken by the $F$-vev of a chiral spurion), a hierarchy between scalar and gaugino masses requires special constructions, it is automatic in scenarios where supersymmetry is broken by $D$-vev of a real spurion. In the latter framework, gaugino mediated contributions to scalar soft masses are finite (loop suppressed but not $\log$-enhanced), a feature often referred to as "supersoftness". Though phenomenologically attractive, pure supersoft models suffer from the $\mu$-problem, potential color-breaking minima, large $T$-parameter, etc. These problems can be overcome without sacrificing the model's virtues by departing from pure supersoftness and including $\mu$-type operators that use the same $D$-vev, a framework known as generalized supersoft supersymmetry. The main purpose of this paper is to point out that the new operators also solve the last remaining issue associated with supersoft spectra, namely that a right handed (RH) slepton is predicted to be the lightest superpartner, rendering the setup cosmologically unfeasible. In particular, we show that the $\mu$-operators in generalized supersoft generate a new source for scalar masses, which can raise the RH-slepton mass above bino due to corrections from renormalisation group evolutions (RGEs). In fact, a mild tuning can open up the bino--RH slepton coannihilation regime for a thermal dark matter. We derive the full set of RGEs required to determine the spectrum at low energies. Beginning with input conditions at a high scale, we show that completely viable spectra can be achieved.