In this work we present the implementation of generators for W and Z bosons in association with two jets interfaced to parton showers using the POWHEG BOX. We incorporate matrix elements from the parton-level Monte Carlo program MCFM in the POWHEG BOX, allowing for a considerable improvement in speed compared to previous implementations. We address certain problems that arise when processes that are singular at the Born level are implemented in a shower framework using either a generation cut or a Born suppression factor to yield weighted events. In such a case, events with very large weights can be generated after the shower through a number of mechanisms. Events with very small transverse momentum at the Born level can develop large transverse momentum either after the hardest emission, after the shower, or after the inclusion of multi-parton interactions. We present a solution to this problem that can be easily implemented in the POWHEG BOX. We also show that a full solution to this problem can only be achieved if the generator maintains physical validity also when the transverse momentum of the emitted partons becomes unresolved. One such scheme is the recently-proposed MiNLO method for the choice of scale and the exponentiation of Sudakov form factors in NLO computations. We present a validation study of our generators, by comparing their output to available LHC data.
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