X(16.7) Production in Electron-Position Collision

The anomaly found in the excited $^8\text{Be}$ nuclear transition to its ground state is attributed to a spin-1 gauge boson $X(16.7)$. To hunt for this boson, we propose two traps: $e^+e^-\to X\gamma$ and $J/\psi\to X\gamma$, both following with $X\to e^+e^-$ decay. We adopt the "vector minus axial-vector" interaction hypothesis. Analysis on the $X(16.7)$ decay length, production rates, differential distribution with respect to the $e^+e^-$ invariant-mass spectrum, and the signal-to-noise ratios (SNR) after the smearing at BESIII detector are discussed in detail. Given the coupling strength of $X$ to vector/axial-vector currents $g_f^{v/a}\sim10^{-3}$ at BESIII: (1) there would be about $6000$ $X$ measurable events per year in electron-positron collision, yet with a large background after smearing, (2) while in $J/\psi$ decays, we find that the axial-vector current may come into play, though merely 52 events may appear, the SNR are inspiring even after smearing.