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In this paper we explore $pp \to W^\pm (\ell^\pm \nu) \gamma$ to $\mathcalO(1/\Lambda^4)$ in the SMEFT expansion. Calculations to this order arenecessary to properly capture SMEFT contributions that grow with energy, as theinterference between energy-enhanced SMEFT effects at $\mathcal O(1/\Lambda^2)$and the Standard Model is suppressed. We find that there are several dimensioneight operators that interfere with the Standard Model and lead to the sameenergy growth, $\sim \mathcal O(E^4/\Lambda^4)$, as dimension six squared.While energy-enhanced SMEFT contributions are a main focus, our calculationincludes the complete set of $\mathcal O(1/\Lambda^4)$ SMEFT effects consistentwith $U(3)^5$ flavor symmetry. Additionally, we include the decay of the $W^\pm\to \ell^\pm\nu$, making the calculation actually $\bar q q' \to \ell^\pm \nu\gamma$. As such, we are able to study the impact of non-resonant SMEFToperators, such as $(L^\dag\bar\sigma^\mu \tau^I\, L) (Q^\dag\bar\sigma^\nu\tau^I\, Q)\, B_{\mu\nu}$, which contribute to $\bar q q' \to \ell^\pm \nu\gamma$ directly and not to $\bar q q' \to W^\pm \gamma$. We show severaldistributions to illustrate the shape differences of the differentcontributions.

A case study of SMEFT $\mathcal O(1/\Lambda^4)$ effects in diboson processes: $pp \to W^\pm(\ell^\pm \nu) \gamma$