Search for the rare exclusive hadronic decay of a W boson into a pion and a photon in proton-proton collisions at $13 \, \mathrm{TeV}$

A search is performed for the rare exclusive hadronic decay $\mathrm{W}\to\pi\gamma$ in pp collisions at $\sqrt{s} = 13$ TeV. Data collected by the CMS experiment at the LHC during the $2016$, $2017$ and $2018$ data-taking periods, which correspond to an integrated luminosity of $137 \,\mathrm{fb^{-1}}$, are analyzed. The analysis exploits the W boson production from $\mathrm{t\bar{t}}$ events. The leptonic decay of the W boson from one of the top quarks is used to tag the event, and the b-jets are exploited to reduce the QCD background from the hadronization of light quarks. The W boson originating from the other top quark is used to search for the $\mathrm{W}\to\pi\gamma$ decay. The rare decay is characterized by a high-transverse momentum, isolated track and a high-energy, isolated photon. The $\mathrm{W}\to\pi\gamma$ decay is not observed, and an upper limit is set to its branching fraction, corresponding to $1.51\times 10^{-5}$ at $95\%$ confidence level.