We explored the sparticle mass spectrum in light of the muon $g-2$ anomaly and the little hierarchy problem in a class of the gauge mediated supersymmetry breaking model. Here, the messenger fields transform in the adjoint representation of the Standard Model gauge symmetry. To avoid unacceptably light right-handed slepton masses, the Standard Model is supplemented by the additional $U(1{)}_{B-L}$ gauge symmetry. A nonzero $U(1{)}_{B-L}$ $D$ term makes the right-handed slepton masses compatible with the current experimental bounds. We show that in the framework of ${\mathrm{\Lambda }}_3<0$ and $\mu <0$ the muon $g-2$ anomaly and the observed 125 GeV Higgs boson mass can be simultaneously accommodated. The slepton masses in this case are predicted to lie in the few hundred GeV range, which can be tested at the LHC. Despite the heavy colored sparticle spectrum, the little hierarchy problem in this model can be ameliorated, and the electroweak fine-tuning parameter can be as low as 10 or so.

• Received 14 December 2016

DOI:https://doi.org/10.1103/PhysRevD.95.035028