Sensitivity to longitudinal vector boson scattering in semi-leptonic final states at the HL-LHC

Longitudinal vector boson scattering provides an important probe of electroweak symmetry breaking, bringing sensitivity to physics beyond the Standard Model as well as constraining properties of the Higgs boson. It is a difficult process to study due to the small production cross section and challenging separation of the different polarization states. We study the sensitivity to longitudinal $WV$ vector boson scattering at the High-Luminosity Large Hadron Collider in semi-leptonic final states. While these are characterized by larger background contributions compared to fully leptonic final states, they benefit from a higher signal cross section due to the enhanced branching fraction. We determine the polarization through full reconstruction of the event kinematics using the $W$ boson mass constraint and through the use of jet substructure. We show that with these techniques sensitivities around three standard deviations at the HL-LHC are achievable, which makes this channel competitive with its fully leptonic counterparts.