Yukawa coupling and anomalous magnetic moment of the muon: An update for the LHC era

We study the interplay between a soft muon Yukawa coupling generated radiatively with the trilinear $A$-terms of the minimal supersymmetric standard model (MSSM) and the anomalous magnetic moment of the muon. In the absence of a tree-level muon Yukawa coupling the lightest smuon mass is predicted to be in the range between 600 GeV and 2200 GeV at $2\ensuremath{\sigma}$, if the bino mass ${M}_{1}$ is below 1 TeV. Therefore, a detection of a smuon (in conjunction with a sub-TeV bino) at the LHC would directly imply a nonzero muon Yukawa coupling in the MSSM superpotential. Inclusion of slepton flavor mixing could in principle lower the mass of one smuonlike slepton below 600 GeV. However, the experimental bounds on radiative lepton decays instead strengthen the lower mass bound, with larger effects for smaller ${M}_{1}$, We also extend the analysis to the electron case and find that a light selectron close to the current experimental search limit may prove the MSSM electron Yukawa coupling to be nonzero.