Observation of the electroweak production of W$\gamma$ in association with two jets in proton-proton collisions at $\sqrt{s}=13~\mathrm{TeV}$

A measurement of the electroweak (EW) production of a W boson and a photon in association with two jets in proton-proton collisions, where the W boson decays leptonically, is presented. Events are selected by requiring one identified electron or muon, missing transverse momentum, one photon, and two jets with a large dijet mass and a large rapidity separation. The measurement is based on data collected with the CMS detector in 2016 at a center-of-mass energy of $13~\mathrm{TeV}$, corresponding to an integrated luminosity of $35.9~\mathrm{fb}^{-1}$. The observed (expected) significance for this process is 4.9 (4.6) standard deviations. After combining with previously reported CMS results based on $8~\mathrm{TeV}$ data, the observed (expected) significance is 5.3 (4.8) standard deviations. This constitutes the first observation of EW W$\gamma$ production in pp collisions. The cross section measured in the fiducial region is $20.4\pm 4.5~\mathrm{fb}$ and the total cross section for EW + QCD W$\gamma$ production in association with 2 jets in the same fiducial region is measured to be $108\pm 16~\mathrm{fb}$. All measurements are in good agreement with recent theory predictions. We set the most stringent limits to date on the anomalous quartic gauge coupling parameters $F_\mathrm{M,2-5}$ and $F_\mathrm{T,6-7}$.