Radiative natural supersymmetry: Reconciling electroweak fine-tuning and the Higgs boson mass

Abstract

Models of natural supersymmetry seek to solve the little hierarchy problem by positing a spectrum of light Higgsinos $\ensuremath{\lesssim}200--300\text{ }\text{ }\mathrm{GeV}$ and light top squarks $\ensuremath{\lesssim}600\text{ }\text{ }\mathrm{GeV}$ along with very heavy squarks and TeV-scale gluinos. Such models have low electroweak fine-tuning and satisfy the LHC constraints. However, in the context of the minimal supersymmetric standard model, they predict too low a value of ${m}_{h}$, are frequently in conflict with the measured $b\ensuremath{\rightarrow}s\ensuremath{\gamma}$ branching fraction, and the relic density of thermally produced Higgsino-like weakly interacting massive particles (WIMPs) falls well below dark matter measurements. We propose a framework dubbed radiative natural supersymmetry (RNS), which can be realized within the minimal supersymmetric standard model (avoiding the addition of extra exotic matter) and which maintains features such as gauge coupling unification and radiative electroweak symmetry breaking. The RNS model can be generated from supersymmetry (SUSY) grand unified theory type models with nonuniversal Higgs masses. Allowing for high-scale soft SUSY breaking Higgs mass ${m}_{{H}_{u}}>{m}_{0}$ leads to automatic cancellations during renormalization group running and to radiatively-induced low fine-tuning at the electroweak scale. Coupled with large mixing in the top-squark sector, RNS allows for fine-tuning at the 3%--10% level with TeV-scale top squarks and a 125 GeV light Higgs scalar $h$. The model allows for at least a partial solution to the SUSY flavor, $CP$, and gravitino problems since first-/second-generation scalars (and the gravitino) may exist in the 10--30 TeV regime. We outline some possible signatures for RNS at the LHC, such as the appearance of low invariant mass opposite-sign isolated dileptons from gluino cascade decays. The smoking gun signature for RNS is the appearance of light Higgsinos at a linear ${e}^{+}{e}^{\ensuremath{-}}$ collider. If the strong $CP$ problem is solved by the Peccei-Quinn mechanism, then RNS naturally accommodates mixed axion-Higgsino cold dark matter, where the light Higgsino-like WIMPs---which in this case make up only a fraction of the measured relic abundance---should be detectable at upcoming WIMP detectors.