Muon g−2 and dark matter suggest nonuniversal gaugino masses: SU(5)×A4 case study at the LHC

Abstract

We argue that in order to account for the muon anomalous magnetic moment $g\ensuremath{-}2$, dark matter and LHC data, nonuniversal gaugino masses ${M}_{i}$ at the high scale are required in the framework of the minimal supersymmetric standard model. We also need a right-handed smuon ${\stackrel{\texttildelow{}}{\ensuremath{\mu}}}_{R}$ with a mass around 100 GeV, evading LHC searches due to the proximity of a neutralino ${\stackrel{\texttildelow{}}{\ensuremath{\chi}}}_{1}^{0}$ several GeV lighter which allows successful dark matter. We discuss such a scenario in the framework of an $SU(5)$ grand unified theory (GUT) combined with ${A}_{4}$ family symmetry, where the three $\overline{5}$ representations form a single triplet of ${A}_{4}$ with a unified soft mass ${m}_{F}$, while the three 10 representations are singlets of ${A}_{4}$ with independent soft masses ${m}_{T1},{m}_{T2},{m}_{T3}$. Although ${m}_{T2}$ (and hence ${\stackrel{\texttildelow{}}{\ensuremath{\mu}}}_{R}$) may be light, the muon $g\ensuremath{-}2$ and relic density also requires light ${M}_{1}\ensuremath{\simeq}250\text{ }\text{ }\mathrm{GeV}$, which is incompatible with universal gaugino masses due to LHC constraints on ${M}_{2}$ and ${M}_{3}$ arising from gaugino searches. After showing that universal gaugino masses ${M}_{1/2}$ at the GUT scale are excluded by gluino searches, we provide a series of benchmarks which show that while ${M}_{1}={M}_{2}\ensuremath{\ll}{M}_{3}$ is in tension with 8 and 13 TeV LHC data, ${M}_{1}<{M}_{2}\ensuremath{\ll}{M}_{3}$ is currently allowed. Even this scenario is almost excluded by the tension between the muon $g\ensuremath{-}2$, relic density, dark matter direct detection and LHC data. We focus on a region of parameter space that has not been studied in detail before being characterized by low Higgsino mass $\ensuremath{\mu}\ensuremath{\approx}\ensuremath{-}300\text{ }\text{ }\mathrm{GeV}$, as required by the muon $g\ensuremath{-}2$. The LHC will be able to fully test this scenario with the upgraded luminosity via muon-dominated tri- and dilepton signatures resulting from Higgsino-dominated ${\stackrel{\texttildelow{}}{\ensuremath{\chi}}}_{1}^{\ifmmode\pm\else\textpm\fi{}}{\stackrel{\texttildelow{}}{\ensuremath{\chi}}}_{2}^{0}$ and ${\stackrel{\texttildelow{}}{\ensuremath{\chi}}}_{1}^{+}{\stackrel{\texttildelow{}}{\ensuremath{\chi}}}_{1}^{\ensuremath{-}}$ production.