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We present predictions for production (with exact decays) that are next-to-next-to-leading order (NNLO) accurate and consistently matched to a parton shower. The matching is achieved by upgrading, with MiNLO, the NLO calculation of jet production, in such a way that NLO accuracy is guaranteed for inclusive observables, and by performing subsequently a reweighting of the WWJ-MiNLO events, differential in the Born variables, to the NNLO results obtained with MATRIX.

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