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

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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 750 GeV and 2700 GeV at 2 sigma, if the bino mass M₁ is below 1 TeV. Therefore, a detection of a smuon (in conjunction with a sub-TeV bino) at the LHC would directly imply a non-zero muon Yukawa coupling in the MSSM superpotential. Inclusion of slepton flavor mixing could in principle lower the mass of one smuon-like slepton below 750 GeV. However, the experimental bounds on radiative lepton decays instead strengthen the lower mass bound, with larger effects for smaller M₁, 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 non-zero.