Search for a muonphilic scalar $X_0$ or vector $X_1$ via $J\mathrm{/}\psi \to {\mu }^{+}{\mu }^{-}+\mathrm{i}\mathrm{n}\mathrm{v}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{b}\mathrm{l}\mathrm{e}$ decays at BESII

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 $(8.998\pm 0.039)\times {10}^9$ $\text{jpsi}$ events collected by the BESIII detector, we search for a light muon philic scalar $X_0$ or vector $X_1$ in the processes $J\mathrm{/}\psi \to {\mu }^{+}{\mu }^{-}{X}_{0,1}$ with $X_{0,1}$ invisible decays. No obvious signal is found, and the upper limits on the coupling $g_{0,1}^{\mathrm{\prime }}$ between the muon and the $X_{0,1}$ particles are set to be between $1.1\times {10}^{-3}$ and $1.0\times {10}^{-2}$ for the $X_{0,1}$ mass in the range of $1<M(X_{0,1})<1000$ MeV$\mathrm{/}{c}^2$ at 90$\mathrm{\%}$ confidence level.