Probing invisible decay of dark photon at BESIII and future STCF via monophoton searches

We propose to search the monophoton events at the BESIII detector and future Super Tau Charm Factory to probe the sub-GeV dark photon decay into lighter dark matter. We compute the cross section due to the dark photon associated a standard model photon production, and study the corresponding standard model irreducible/reducible backgrounds. By using the data about 17 fb$^{-1}$ collected at the BESIII detector since 2011, we derive new leading limits of the mixing strength $\varepsilon$, $\varepsilon\lesssim(1.1-1.6)\times 10^{-4}$, in the mass range of 0.04 GeV $\lesssim m_{A^\prime} \lesssim$ 3 GeV. With 30 ab$^{-1}$ data, STCF running at $\sqrt{s} = 2$ GeV, can probe $\varepsilon$ down to 5.1$\times 10^{-6}$ when $m_{A^\prime}=1$ GeV. For models of scalar and fermionic light thermal dark matter production via dark photon, we present the constrains on the dimensionless dark matter parameter $y=\varepsilon^2\alpha_D(m_\chi/m_{A^\prime})^4$ as function of the DM mass $m_{\chi}$ at BESIII and future STCF, conventionally assuming the dark coupling constant $\alpha_D=0.5$ and $m_{A^\prime}=3 m_{\chi}$. We find that BESIII can exclude model of scalar, Majorana, and pseudo-Dirac (with a small splitting) DM for the mass region 0.03$\sim$1 GeV, 0.04$\sim$1 GeV and 0.4$\sim$1 GeV respectively. For values $\alpha_D\lesssim 0.005$, combining the results from 2 GeV STCF with 30 ab$^{-1}$ data and BaBar, one can exclude the above three DM models in the mass region 0.001 GeV $\lesssim m_{\chi} \lesssim$ 1 GeV.