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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 usingup to $140\, \text{fb}^{-1}$ of proton-proton collisions recorded with theATLAS detector at a center-of-mass energy of $\sqrt{s}=13\,\text{TeV}$. Theserare processes provide a test bench for the quantum chromodynamicsfactorization formalism used to calculate cross sections at colliders, as wellas 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 inthe most stringent upper limit to date on the branching fractions$\mathcal{B}(W^{\pm}\to \pi^{\pm}\gamma) < 1.9\times10^{-6}$,$\mathcal{B}(W^{\pm}\to K^{\pm}\gamma) < 1.7\times10^{-6}$,$\mathcal{B}(W^{\pm}\to \rho^{\pm}\gamma) < 5.2\times10^{-6}$ at 95% confidencelevel.

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