  A light scalar $X_{0}$ or vector $X_{1}$ particles have been introduced as a
possible explanation for the $(g-2)_{\mu}$ anomaly and dark matter phenomena.
  Using $(8.998\pm 0.039)\times10^9$ $\jpsi $ events collected by the BESIII
detector, we search for a light muon philic scalar $X_{0}$ or vector $X_{1}$ in
the processes $J/\psi\to\mu^+\mu^- X_{0,1}$ with $X_{0,1}$ invisible decays. No
obvious signal is found, and the upper limits on the coupling $g_{0,1}'$
between the muon and the $X_{0,1}$ particles are set to be between
$1.1\times10^{-3}$ and $1.0\times10^{-2}$ for the $X_{0,1}$ mass in the range
of $1<M(X_{0,1})<1000$ MeV$/c^2$ at 90$\%$ confidence level.
