SMEFT at NNLO$+$PS: $Vh$ production

In the context of the Standard Model effective field theory (SMEFT) the next-to-next-to-leading (NNLO) QCD corrections to the Higgsstrahlungs ($Vh$) processes in hadronic collisions are calculated and matched to a parton shower (PS). NNLO+PS precision is achieved for the complete sets of SMEFT operators that describe the interactions between the Higgs and two vector bosons and the couplings of the Higgs, a $W$ or a $Z$ boson, and light fermions. A POWHEG-BOX implementation of the computed NNLO SMEFT corrections is provided that allows for a realistic exclusive description of $Vh$ production at the level of hadronic events. This feature makes it an essential tool for future Higgs characterisation studies by the ATLAS and CMS collaborations. Utilising our new Monte Carlo code the numerical impact of NNLO+PS corrections on the kinematic distributions in $pp \to Zh \to \ell^+ \ell^- h$ production is explored, employing well-motivated SMEFT benchmark scenarios.