Search for the exclusive $W$ boson hadronic decays $W^{\pm }\to {\pi }^{\pm }\gamma$, $W^{\pm }\to K^{\pm }\gamma$ and $W^{\pm }\to {\rho }^{\pm }\gamma$ with the ATLAS detector

A search for the exclusive hadronic decays $W^{\pm }\to {\pi }^{\pm }\gamma$, $W^{\pm }\to K^{\pm }\gamma$ and $W^{\pm }\to {\rho }^{\pm }\gamma$ is performed using up to $140{\text{fb}}^{-1}$ of proton-proton collisions recorded with the ATLAS detector at a center-of-mass energy of $\sqrt{s}=13\text{TeV}$. These rare processes provide a test bench for the quantum chromodynamics factorization formalism used to calculate cross sections at colliders, as well as a probe of $W$ boson coupling to quarks and a new way to measure the $W$ boson mass through fully reconstructed decay products. The search results in the most stringent upper limit to date on the branching fractions $\mathcal{B}(W^{\pm }\to {\pi }^{\pm }\gamma )<1.9\times {10}^{-6}$, $\mathcal{B}(W^{\pm }\to K^{\pm }\gamma )<1.7\times {10}^{-6}$, $\mathcal{B}(W^{\pm }\to {\rho }^{\pm }\gamma )<5.2\times {10}^{-6}$ at 95% confidence level.