We consider W±Z production in hadronic collisions and present high-precision predictions in QCD and electroweak (EW) perturbation theory matched to parton showers. To this end, we match next-to-next-to-leading order QCD corrections to parton showers using the MiNNLOPS method and consistently combine them with next-to-leading order EW corrections matched to parton showers. This is the first time such accuracy in the event generation is achieved for any collider process, and we study in detail the impact of different choices in the combination of QCD and EW corrections as well as QCD and QED showers. Spin correlations, interferences and off-shell effects are retained by considering the full leptonic processes $$ pp\to {\ell}^{+}{\ell}^{-}{\ell}^{\prime \pm }{\nu}_{\ell}^{\prime } $$ pp → ℓ + ℓ − ℓ ′ ± ν ℓ ′ with ℓ′ ≠ ℓ and ℓ′ = ℓ without approximations, and the matching to QED radiation is performed preserving the resonance structure of the process. We find that NNLO QCD predictions including QCD and QED shower effects provide a very good approximation in the bulk-region of the phase space, while EW effects become increasingly important in the high-energy tails of kinematic distributions. Our default predictions are in excellent agreement with recent ATLAS data.

We consider the Higgsstrahlung process in hadronic collisions and present the computation of next-to-next-to-leading order predictions matched to parton showers for both production and H → $$ b\overline{b} $$ b b ¯ decay employing the MiNNLOPS method. We present predictions for ZH and W±H production including spin correlations and off-shell effects by calculating the full processes pp → ℓ+ℓ−H → ℓ+ℓ−$$ b\overline{b} $$ b b ¯ , pp → $$ {\nu}_{\ell }{\overline{\nu}}_{\ell }H $$ ν ℓ ν ¯ ℓ H → $$ {\nu}_{\ell }{\overline{\nu}}_{\ell }b\overline{b} $$ ν ℓ ν ¯ ℓ b b ¯ and pp → ℓ±νℓH → $$ {\ell}^{\pm }{\overline{\nu}}_{\ell }b\overline{b} $$ ℓ ± ν ¯ ℓ b b ¯ in the narrow-width approximation for the Higgs boson. For the W±H process, NNLO+PS accuracy in production and decay is achieved for the first time. Our calculations are validated against earlier simulations in the NNLOPS approach that includes NNLO corrections via multi-differential reweighting. The new MiNNLOPS generators for these processes, which evaluate NNLO corrections on-the-fly in the event generation, will supersede those earlier calculations. Our predictions are in good agreement with recent measurements of the Higgsstrahlung cross sections.

We consider associated Zh production with Z → ℓ+ℓ− and $$ h\to b\overline{b} $$ h → b b ¯ decays in hadronic collisions. In the framework of the Standard Model effective field theory (SMEFT) we calculate the QCD corrections to this process and achieve next-to-next-to-leading order plus parton shower (NNLO+PS) accuracy using the MiNNLOPS method. This precision is obtained for a subset of six SMEFT operators, including the corrections from effective Yukawa- and chromomagnetic dipole-type interactions. Missing higher-order QCD effects associated with the considered dimension-six operators are estimated to have a relative numerical impact of less than a percent on the total rate once existing experimental limits on the relevant Wilson coefficients are taken into account. We provide a dedicated Monte Carlo (MC) code that evaluates the NNLO SMEFT corrections on-the-fly in the event generation. This MC generator is used to study the numerical impact of NNLO+PS corrections on the kinematic distributions in $$ pp\to Zh\to {\mathrm{\ell}}^{+}{\mathrm{\ell}}^{-}b\overline{b} $$ pp → Zh → ℓ + ℓ − b b ¯ production employing simple SMEFT benchmark scenarios. We identify the invariant mass $$ {m}_{b\overline{b}} $$ m b b ¯ of the two b-tagged jets as well as the three-invariant jet mass $$ {m}_{b\overline{b}j} $$ m b b ¯ j as particularly interesting observables to study SMEFT effects. These distributions receive contributions that change both their normalisation and shape with the latter modifications depending on the exact jet definition. To our knowledge SMEFT effects of this type have so far not been discussed in the literature. The presented MC generator can also serve as a starting point to obtain NNLO+PS accuracy for a suitable enlarged set of effective operators in the future.

One of the few exact results for the description of the time-evolution of an inhomogeneous, interacting many-particle system is given by the Harmonic Potential Theorem (HPT) [1]. The relevance of this theorem is that it sets a tight constraint on time-dependent many-body approximations. In this contribution, we show that the original formulation of the HPT is valid also for the case of spin-, velocity-and density-dependent interactions. This result is completely general and relevant, among the rest, for nuclear structure theory both in the case of ab initio and of more phenomenological approaches. As an example, we report on a numerical implementation by testing the small-amplitude limit of the time-dependent Hartree-Fock -also known as Random Phase Approximation (RPA)for the translational frequencies of a neutron system trapped in a harmonic potential.