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A search is performed for the rare decay W$^\pm\to\pi^\pm\gamma$ inproton-proton collisions at $\sqrt{s} =$ 13 TeV. Data corresponding to an on Wintegrated luminosity of 137 fb$^{-1}$ were collected during 2016 to 2018 withthe CMS detector. This analysis exploits a novel search strategy based on Wboson production in top quark pair events. An inclusive search for theW$^\pm\to\pi^\pm\gamma$ decay is not optimal at the LHC because of the hightrigger thresholds. Instead, a trigger selection is exploited in which the Wboson originating from one of the top quarks is used to tag the event in aleptonic decay. The W boson emerging from the other top quark is used to searchfor the W$^\pm\to\pi^\pm\gamma$ signature. Such decays are characterized by anisolated track pointing to a large energy deposit, and by an isolated photon oflarge transverse momentum. The presence of b quark jets reduces the backgroundfrom the hadronization of light-flavor quarks and gluons. TheW$^\pm\to\pi^\pm\gamma$ decay is not observed. An upper exclusion limit is setto this branching fraction, corresponding to 1.50 $\times$ 10$^{-5}$ at 95%confidence level, whereas the expected upper limit exclusion limit is 0.85$^{+0.52}_{-0.29}$ $\times$ 10$^{-5}$.

Search for the rare decay of the W boson into a pion and a photon in proton-proton collisions at $\sqrt{s} = $ 13 TeV