NLO corrections to triple vector-boson production in final states with three charged leptons and two jets

Abstract: Tri-boson production together with vector-boson scattering is a privileged channel to study the electroweak structure of the Standard Model. Upcoming LHC running stages will allow to measure these processes at unprecedented accuracy and for all possible final states, which requires to push theory predictions to still unexplored frontiers. In this work we present the first calculation for the process ${\rm p}{\rm p}\to\mu^+\mu^-{\rm e}^+\nu_{\rm e}\,{\rm j}\,{\rm j}$ at the LHC in a tri-boson phase space. We evaluate the three LO contributions, namely the $\mathcal{O}(\alpha^6)$, which contains the genuine tri-boson signature, along with the $\mathcal{O}(\alpha_{\rm s}\alpha^5)$ and $\mathcal{O}(\alpha_{\rm s}^2\alpha^4)$, and the two $\mathcal{O}(\alpha^7)$ and $\mathcal{O}(\alpha_{\rm s}\alpha^6)$ NLO corrections. The calculation is based on full Standard-Model matrix elements, including all resonant and non-resonant terms, complete spin correlations and interference effects. Integrated and differential cross sections are presented for a fiducial region inspired by High Luminosity LHC prospect studies. We find electroweak corrections of $-14\%$ for the fiducial cross section, almost twice as large as for other tri-boson processes.