  In this paper we explore $pp \to W^\pm (\ell^\pm \nu) \gamma$ to $\mathcal
O(1/\Lambda^4)$ in the SMEFT expansion. Calculations to this order are
necessary to properly capture SMEFT contributions that grow with energy, as the
interference between energy-enhanced SMEFT effects at $\mathcal O(1/\Lambda^2)$
and the Standard Model is suppressed. We find that there are several dimension
eight operators that interfere with the Standard Model and lead to the same
energy growth, $\sim \mathcal O(E^4/\Lambda^4)$, as dimension six squared.
While energy-enhanced SMEFT contributions are a main focus, our calculation
includes the complete set of $\mathcal O(1/\Lambda^4)$ SMEFT effects consistent
with $U(3)^5$ 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 SMEFT
operators, 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 several
distributions to illustrate the shape differences of the different
contributions.
