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. $$ \mathcal{O}\left({\alpha}^6\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mfenced> <mml:msup> <mml:mi>α</mml:mi> <mml:mn>6</mml:mn> </mml:msup> </mml:mfenced> </mml:math> , we complement our results with $$ \mathcal{O}\left({\alpha}_{\textrm{s}}{\alpha}^5\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mfenced> <mml:mrow> <mml:msub> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:msup> <mml:mi>α</mml:mi> <mml:mn>5</mml:mn> </mml:msup> </mml:mrow> </mml:mfenced> </mml:math> and $$ \mathcal{O}\left({\alpha}_{\textrm{s}}^2{\alpha}^4\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mfenced> <mml:mrow> <mml:msubsup> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:msup> <mml:mi>α</mml:mi> <mml:mn>4</mml:mn> </mml:msup> </mml:mrow> </mml:mfenced> </mml:math> for inclusive predictions. At $$ \mathcal{O}\left({\alpha}^6\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mfenced> <mml:msup> <mml:mi>α</mml:mi> <mml:mn>6</mml:mn> </mml:msup> </mml:mfenced> </mml:math> 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.