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Electroweak (EW) triboson production processes with at least one heavy gaugeboson are of increasing interest at the Large Hadron Collider (LHC) as directprecision probes of one of the least-tested sectors of the Standard Model (SM),the quartic couplings of the EW gauge bosons. These processes therefore offerpromising opportunities for searches for indirect signals of Beyond-the-SM(BSM) physics. In this paper, we present results for fiducial cross sections atnext-to-leading-order (NLO) EW and NLO QCD to $p\;p\toe^{+}\;\nu_{e}\;\mu^{+}\;\mu^{-}\;\gamma$ at the 13 TeV LHC. This signatureincludes the triboson production process $p\;p \to W^{+}\;Z\;\gamma$ withleptonic decays, $W^{+} \to e^{+}\;\nu_{e}$ and $Z \to \mu^{+}\;\mu^{-}$. Thecomputation is based on the complete set of leading-order (LO) contributions of$\mathcal{O}(\alpha^5)$ and on NLO EW and NLO QCD cross sections of$\mathcal{O}(\alpha^6)$ and $\mathcal{O}(\alpha^5 \alpha_\text{s})$,respectively, and thus off-shell effects, spin correlations and non-resonancecontributions are fully taken into account. We construct a Monte Carloframework which provides total and differential cross sections for a chosen setof basic analysis cuts. We find that while NLO EW corrections enhance thefiducial LO total cross section by only $1\%$, they can significantly changesome distributions in certain kinematic regions. For example, the relative NLOEW corrections to the muon transverse momentum distribution at 500 GeV amountsto $-20\%$. To illustrate how missing NLO EW corrections could masquerade asBSM physics, we show examples for the impact of dimension-8 operators in the SMEffective Field Theory framework on selected kinematic distributions.

NLO electroweak and QCD corrections to the production of a photon with three charged lepton plus missing energy at the LHC