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After the discovery of a Higgs boson in 2012 at the CERN Large HadronCollider (LHC) the detailed study of its properties, and most importantly itscouplings to other particles, has started. This is a very important task to becompleted, in particular to test whether it is indeed the Higgs boson predictedby the Standard Model (SM). The precise study of the Higgs couplings to gaugebosons is of particular importance and requires as much information aspossible. In this view this paper provides the next-to-leading order (NLO) QCDcorrections to the production cross sections and differential distributions ofa SM Higgs boson in association with a pair of weak bosons $W^+W^-$, $W^\pm Z$and $ZZ$, matched with parton shower (PS) in the POWHEG-BOX framework. The NLOQCD corrections are found to be significant and PS effects are sizable at low$p_T$ in the jet differential distributions, as expected, while these effectsare negligible in other distributions. We will also provide a detailed study ofthe theoretical uncertainties affecting the total production rates at the LHCand at the Future Circular Collider in hadron-hadron mode, the potential 100TeV follow-up of the LHC machine: the scale uncertainty calculated by thevariation of the renormalization and factorization scales, the partondistribution function and related $\alpha_s$ errors as well as the parametricuncertainties on the input weak boson masses.

Next-To-Leading Order QCD Corrections to Associated Production of a SM Higgs Boson with a Pair of Weak Bosons in the POWHEG-BOX