Probing new physics scenarios of muon $g-2$ via $J/\psi$ decay at BESIII

The disagreement between the standard model prediction and the experimental measurement of muon anomalous magnetic moment can be alleviated by invoking an additional particle which is either a vector boson ($X_1$) or a scalar ($X_0$). This new particle, with the mass $m_X \lesssim 2 m_\mu$, can be searched for in the decay $J/\psi \to \mu^- \mu^+ X$, where $X$ is missing. Our numerical study shows that the search is quite feasible at the BESIII experiment in the parameter space allowed by muon $g-2$ measurements.