Search for new light vector boson using $J\mathrm{/}\mathrm{\Psi }$ at BESIII and Belle II

We investigate various search strategies for light vector boson $X$ in $\mathcal{O}(10)\mathrm{M}\mathrm{e}\mathrm{V}$ mass range using $J\mathrm{/}\mathrm{\Psi }$ associated channels at BESIII and Belle II: (i) $J\mathrm{/}\mathrm{\Psi }\to {\eta }_{c}X$ with ${10}^{10}J\mathrm{/}\mathrm{\Psi }$s at BESIII, (ii) $J\mathrm{/}\mathrm{\Psi }({\eta }_c+X)+\mathrm{\ell }\bar{\mathrm{\ell }}$ production at Belle~II, and (iii) $J\mathrm{/}\mathrm{\Psi }+X$ with the displaced vertex in $X\to e^{+}{e}^{-}$ decay are analyzed and the future sensitivities at Belle II with 50 ${\mathrm{a}\mathrm{b}}^{-1}$ luminosity are comprehensively studied. By requiring the displaced vertex to be within the beam pipe, the third method results in nearly background-free analysis, and the vector boson-electron coupling and the vector boson mass can be probed in the unprecedented range, ${10}^{-4}\le \mathrm{\mid }{\epsilon }_e\mathrm{\mid }\le {10}^{-3}$ and $9~{\rm MeV}\leq m_X\leq 100 {\rm MeV}$with50${\rm ab}^{-1}$ at Belle II. This covers the favored signal region of ${}^8{\mathrm{B}\mathrm{e}}^{\ast }$ anomaly recently reported by Atomki experiment with $m_X\simeq 17\mathrm{M}\mathrm{e}\mathrm{V}$.