A natural Little Hierarchy for SUSY from radiative breaking of PQ symmetry

Abstract

While LHC8 Higgs mass and sparticle search constraints favor a multi-TeV value of gravitino mass m_{3/2}, electroweak naturalness favors a superpotential higgsino mass \mu ~100-200 GeV: the mis-match results in an apparent Little Hierarchy characterized by \mu << m_{3/2}. It has been suggested that the Little Hierarchy arises from a mis-match between Peccei-Quinn (PQ) and hidden sector intermediate scales v_{PQ}<< m_{\rm hidden}. We examine the Murayama-Suzuki-Yanagida (MSY) 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 ~100-200 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 WIMP 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({\rm higgsino}).