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 $\mu \sim 100–200\mathrm{GeV}$: the mismatch results in an apparent little hierarchy characterized by $\mu \ll m_{\text{soft}}$ (with $m_{\text{soft}}\sim m_{3/2}$ in gravity mediation). It has been suggested that the little hierarchy arises from a mismatch between Peccei-Quinn (PQ) and hidden sector intermediate scales $v_{\mathrm{PQ}}\ll m_{\text{hidden}}$. We examine the Murayama-Suzuki-Yanagida model of radiatively driven PQ symmetry breaking which not only generates a weak scale value of $\mu$ 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 $\mu \sim 100–200\mathrm{GeV}$ 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 $e^{+}{e}^{-}$ collider with $\sqrt{s}>2m(\text{Higgsino})$.

• Received 4 November 2014

DOI:https://doi.org/10.1103/PhysRevD.91.015003