Next-to-leading order QCD corrections to associated production of a SM Higgs boson with a pair of weak bosons in the POWHEG-BOX

After the discovery of a Higgs boson in 2012 at the CERN Large Hadron Collider (LHC) the detailed study of its properties, and most importantly its couplings to other particles, has started. This is a very important task to be completed, in particular to test whether it is indeed the Higgs boson predicted by the Standard Model (SM). The precise study of the Higgs couplings to gauge bosons is of particular importance and requires as much information as possible. In this view this paper provides the next-to-leading order (NLO) QCD corrections to the production cross sections and differential distributions of a SM Higgs boson in association with a pair of weak bosons W+W-, W(+/-)Z and ZZ, matched with parton shower (PS) in the POWHEG-BOX framework. The NLO QCD corrections are found to be significant and PS effects are sizable at low p(T) in the jet differential distributions, as expected, while these effects are negligible in other distributions. We will also provide a detailed study of the theoretical uncertainties affecting the total production rates at the LHC and at the Future Circular Collider in hadron-hadron mode, the potential 100 TeV follow-up of the LHC machine: the scale uncertainty calculated by the variation of the renormalization and factorization scales, the parton distribution function and related as errors as well as the parametric uncertainties on the input weak boson masses.