Search for the radiative decay ${D}_{s}^{+}\to \mathrm{\gamma \rho }{\left(770\right)}^{+}$

Using 7.33 fb −1 of e + e − collision data samples collected with the BESIII detector at center-of-mass energies between 4.128 and 4.226 GeV, we search for the radiative decay ${D}_{s}^{+}\to \mathrm{\gamma \rho }{\left(770\right)}^{+}$ for the first time. A hint of ${D}_{s}^{+}\to \mathrm{\gamma \rho }{\left(770\right)}^{+}$ is observed with a statistical significance of 2.5σ. The branching fraction of ${D}_{s}^{+}\to \mathrm{\gamma \rho }{\left(770\right)}^{+}$ is measured to be (2.2 ± 0.9stat. ± 0.2syst. ) × 10 −4, corresponding to an upper limit of 6.1 × 10 −4 at the 90% confidence level.