Search for the radiative transitions $\psi (3770)\to \gamma {\eta }_c$ and $\gamma {\eta }_c(2S)$

By using a 2.92 fb${}^{-1}$ data sample taken at $\sqrt{s}=3.773$ GeV with the BESIII detector operating at the BEPCII collider, we search for the radiative transitions $\psi (3770)\to \gamma {\eta }_c$ and $\gamma {\eta }_c(2S)$ through the hadronic decays ${\eta }_c({\eta }_c(2S))\to K_S^0{K}^{\pm }{\pi }^{\mp }$. No significant excess of signal events above background is observed. We set upper limits at a 90% confidence level for the product branching fractions to be $$\mathcal{B}$(\psi(3770)\to\gamma\eta_c)\times $\mathcal{B}$(\eta_c\to K^0_SK^\pm\pi^\mp) < 1.6\times10^{-5}$and$$\mathcal{B}$(\psi(3770)\to\gamma\eta_c(2S))\times $\mathcal{B}$(\eta_c(2S)\to K^0_SK^\pm\pi^\mp) < 5.6\times10^{-6}$. Combining our result with world-average values of $\mathcal{B}({\eta }_c({\eta }_c(2S))\to K_S^0{K}^{\pm }{\pi }^{\mp })$, we find the branching fractions $\mathcal{B}(\psi (3770)\to \gamma {\eta }_c)<6.8\times {10}^{-4}$ and $\mathcal{B}(\psi (3770)\to \gamma {\eta }_c(2S))<2.0\times {10}^{-3}$ at a 90% confidence level.