Higher-order EW corrections in ZZ and ZZj production at the LHC

We consider the production of a pair of $Z$ bosons at the LHC and study the inclusion of EW corrections in theoretical predictions at fixed order and based on multijet-merged parton-shower simulations. To this end we present exact NLO EW results for $pp\to e^+e^-\mu^+\mu^-$, and, for the first time, for $pp\to e^+e^-\mu^+\mu^-j$, and compare them to the EW virtual and NLL Sudakov approximation. We then match the exact NLO EW result to the resummed Sudakov logarithms to achieve an improved NLO EW + NLL $\text{EW}_\text{sud}^\text{exp}$ result. Further, we discuss the inclusion of the above EW corrections in MEPS@NLO event simulations in the framework of the Sherpa event generator. We present detailed phenomenological predictions for inclusive $ZZ$ and $ZZj$ production taking into account the dominant EW corrections through the EW virtual approximation, as well as through (exponentiated) EW Sudakov logarithms.