Natural little hierarchy for SUSY from radiative breaking of the Peccei-Quinn symmetry

Abstract

While LHC8 Higgs mass and sparticle search constraints favor a multi-TeV value of soft SUSY breaking terms, electroweak naturalness favors a superpotential Higgsino mass $\ensuremath{\mu}\ensuremath{\sim}100--200\text{ }\text{ }\mathrm{GeV}$: the mismatch results in an apparent little hierarchy characterized by $\ensuremath{\mu}\ensuremath{\ll}{m}_{\text{soft}}$ (with ${m}_{\text{soft}}\ensuremath{\sim}{m}_{3/2}$ in gravity mediation). It has been suggested that the little hierarchy arises from a mismatch between Peccei-Quinn (PQ) and hidden sector intermediate scales ${v}_{\mathrm{PQ}}\ensuremath{\ll}{m}_{\text{hidden}}$. We examine the Murayama-Suzuki-Yanagida model of radiatively driven PQ symmetry breaking which not only generates a weak scale value of $\ensuremath{\mu}$ but also produces intermediate scale Majorana masses for right-hand neutrinos. For this model, we show ranges of parameter choices with multi-TeV values of ${m}_{3/2}$ which can easily generate values of $\ensuremath{\mu}\ensuremath{\sim}100--200\text{ }\text{ }\mathrm{GeV}$ so that the apparent little hierarchy suggested from data emerges quite naturally. In such a scenario, dark matter would be comprised of an axion plus a Higgsino-like weakly-interacting massive particle admixture where the axion mass and Higgsino masses are linked by the value of the PQ scale. The required light Higgsinos should ultimately be detected at a linear ${e}^{+}{e}^{\ensuremath{-}}$ collider with $\sqrt{s}>2m(\text{Higgsino})$.