Higher order electroweak and QCD corrections in $e^{+}{e}^{-}$μ${}^{+}$μ${}^{-}$ production at LHC

This thesis focuses on improving the theoretical modelling of the process pp → $e^{+}{e}^{-}$μ${}^{+}$μ${}^{-}$ at LHC by including both EW and QCD higher-order perturbative corrections. The EW corrections are studied at NLO fixed order and in a multijetmerged parton-shower simulation. The NLO EW fixed order correction is studied for the $e^{+}{e}^{-}$μ${}^{+}$μ${}^{-}$ final state and, for the first time, for $e^{+}{e}^{-}$μ${}^{+}$μ${}^{-}$ associated with a jet. In the multijet-merged calculation, EW effects are included only via the NLO virtual and NLL Sudakov approximations. To this end, the fixed order calculation is used as a benchmark for these approximations. In both calculations, the resummation of Sudakov logarithms is discussed, especially the matching to the EW NLO fixed order calculation. For what concerns the higher order QCD corrections, this is the NLO QCD of loop-induced $e^{+}{e}^{-}$μ${}^{+}$μ${}^{-}$ production. Specifically, the study conducted in this thesis focuses on loop-induced NLO parton-shower matching. This calculation is compared to the fixed order NLO QCD and the 0+1-jet merged matrix elements at leading order to highlight non-trivial effects due to the NLO parton-shower matching. Due to the slow evaluation of the two-loop virtual matrix elements, I have studied the possibility of improving the evaluation time using a multi-dimensional interpolation method. Both these corrections have been studied and implemented in the MC generator Sherpa.