\begin{document}$W^{+} \rightarrow D_s^{+} \gamma$\end{document} and \begin{document}$Z \rightarrow D^0 \gamma$\end{document} is performed using proton-proton collision data collected by the LHCb experiment at a centre-of-mass energy of 13\begin{document}$\mathrm{TeV}$\end{document}, corresponding to an integrated luminosity of 2.0\begin{document}$\mathrm{fb}^{-1}$\end{document}. No significant signal is observed for either decay mode and upper limits on their branching fractions are set using \begin{document}$W^{+} \rightarrow \mu^{+} \nu$\end{document} and \begin{document}$Z \rightarrow \mu^{+} \mu^{-}$\end{document} decays as normalization channels. The upper limits are \begin{document}${{{6.5\times 10^{-4}}}}$\end{document} and \begin{document}${{{2.1\times 10^{-3}}}}$\end{document} at 95% confidence level for the \begin{document}$W^{+} \rightarrow D_s^{+} \gamma$\end{document} and \begin{document}$Z \rightarrow D^0 \gamma$\end{document} decay modes, respectively. This is the first reported search for the \begin{document}$Z \rightarrow D^0 \gamma$\end{document} decay, while the upper limit on the \begin{document}$W^{+} \rightarrow D_s^{+} \gamma$\end{document} branching fraction improves upon the previous best limit."> Search for the rare decays <inline-formula><tex-math id="M1">\begin{document}${\boldsymbol W^{+} \rightarrow \boldsymbol D_s^{+} \gamma}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/28a6cf5d-3a44-473e-96df-fdff14755014/CPC-2022-0603_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/28a6cf5d-3a44-473e-96df-fdff14755014/CPC-2022-0603_M1.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M2">\begin{document}${\boldsymbol Z \rightarrow \boldsymbol D^0 \gamma}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/28a6cf5d-3a44-473e-96df-fdff14755014/CPC-2022-0603_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/28a6cf5d-3a44-473e-96df-fdff14755014/CPC-2022-0603_M2.png"/></alternatives></inline-formula> at LHCb -
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