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

A search is performed for the rare decay W$^\pm\to\pi^\pm\gamma$ in proton-proton collisions at $\sqrt{s} =$ 13 TeV. Data corresponding to an integrated luminosity of 137 fb$^{-1}$ were collected during 2016 to 2018. This novel analysis exploits the W boson production in top quark pair events. The leptonic decay of the W boson from one of the top quarks is used to tag the event, and the b quark jets are used to reduce the background from the hadronization of light-flavor quarks and gluons. The W boson originating from the other top quark is used to search for the W$^\pm\to\pi^\pm\gamma$ decay. Such events are characterized by an isolated track and an isolated photon of large transverse momentum. The W$^\pm\to\pi^\pm\gamma$ decay is not observed. An upper exclusion limit is set to this branching fraction, corresponding to 1.50$\times$ 10$^{-5}$ at 95% confidence level.