Search for the radiative transitions $ψ(3770)\toγη_c$ and $γη_c(2S)$

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 $ψ(3770)\toγη_c$ and $γη_c(2S)$ through the hadronic decays $η_c(η_c(2S))\to K^0_SK^\pmπ^\mp$. 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 $\mathcal{B}(ψ(3770)\toγη_c)\times \mathcal{B}(η_c\to K^0_SK^\pmπ^\mp) < 1.6\times10^{-5}$ and $\mathcal{B}(ψ(3770)\toγη_c(2S))\times \mathcal{B}(η_c(2S)\to K^0_SK^\pmπ^\mp) < 5.6\times10^{-6}$. Combining our result with world-average values of $\mathcal{B}(η_c(η_c(2S))\to K^0_SK^\pmπ^\mp)$, we find the branching fractions $\mathcal{B}(ψ(3770)\toγη_c) < 6.8\times10^{-4}$ and $\mathcal{B}(ψ(3770)\toγη_c(2S)) < 2.0\times10^{-3}$ at a 90% confidence level.

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