Full and approximated NLO predictions for like-sign W-boson scattering at the LHC

We report on a recent calculation of next-to-leading-order (NLO) QCD and electroweak corrections to like-sign W-boson scattering at the Large Hadron Collider, including all partonic channels and W-boson decays in the process $pp \to e^+ \nu_e \mu^+ \nu_\mu jj + X$. The calculation is implemented in the Monte Carlo integrator Bonsay and comprises the full tower of NLO contributions of the orders $\alpha_s^3\alpha^4$, $\alpha_s^2\alpha^5$, $\alpha_s\alpha^6$, and $\alpha^7$. Our numerical results confirm and extend previous results, in particular the occurrence of large purely electroweak corrections of the order of $\sim-12\%$ for integrated cross sections, which get even larger in distributions. We construct a "VBS approximation'' for the NLO prediction based on partonic channels and gauge-invariant (sub)matrix elements potentially containing the vector-boson scattering (VBS) subprocess and on resonance expansions of the W decays. The VBS approximation reproduces the full NLO predictions within $\sim1.5\%$ in the most important regions of phase space. Moreover, we discuss results from different versions of "effective vector-boson approximations'' at leading order, based on the collinear emission of W bosons of incoming (anti)quarks. However, owing to the only mild collinear enhancement and the design of VBS analysis cuts, the quality of this approximation turns out to be only qualitative at the LHC.