Understand
We argue that in order to account for the muon anomalous magnetic moment $g-2$, dark matter and LHC data, non-universal gaugino masses $M_i$ at the high scale are required in the framework of the Minimal Supersymmetric Standard Model (MSSM).
- We also need a right-handed smuon $\tilde\mu_R$ with a mass around 100 GeV, evading LHC searches due to the proximity of a neutralino $\tilde{\chi}^0_1$ 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 $\tilde\mu_R$) may be light, the muon $g-2$ and relic density also requires light $M_1\simeq 250$ GeV, which is incompatible with universal gaugino masses due to LHC constraints on $M_2$ and $M_3$ arising from gaugino searches.