Double-pole approximation for leading-order semi-leptonic vector-boson scattering at the LHC

A bstract: Measuring vector-boson scattering beyond the fully-leptonic final state is becoming possible at the LHC, which demands to have a solid control on the theory predictions for all final states of this class of processes. In this work we present a full off-shell leading-order calculation for the process pp → ℓ ⁺ ν _ℓ + 4j in two fiducial regions which are particularly relevant for its experimental measurement. In addition to the fully electroweak order, i.e. $$ \mathcal{O}\left({\alpha}^6\right) $$ O α 6 , we complement our results with $$ \mathcal{O}\left({\alpha}_{\textrm{s}}{\alpha}^5\right) $$ O α s α 5 and $$ \mathcal{O}\left({\alpha}_{\textrm{s}}^2{\alpha}^4\right) $$ O α s 2 α 4 for inclusive predictions. At $$ \mathcal{O}\left({\alpha}^6\right) $$ O α 6 we present for the first time a systematic treatment of the process in double-pole approximation and we perform a detailed study of its range of validity by considering inclusive and differential predictions compared to the full off-shell calculation.