Merging H/W/Z + 0 and 1 jet at NLO with no merging scale: a path to parton shower + NNLO matching

We consider the POWHEG generator for a H/W/Z boson plus one jet, augmented with the recently proposed MiNLO method for the choice of scales and the inclusion of Sudakov form factors. Within this framework, the generator covers all the transverse-momentum region of the H/W/Z boson, i.e. no generation cuts are needed to obtain a finite result. By construction, the generator achieves NLO accuracy for distributions involving a finite (and relatively large) transverse momentum of the boson. We examine the conditions under which also the totally inclusive distributions (e.g. the boson rapidity distribution) achieve NLO accuracy. We find that a minimal modification of the MiNLO prescription is sufficient to achieve such accuracy. We thus construct a NLO generator for H/W/Z boson plus one jet production such that it smoothly merges into a NLO single boson production in the small transverse-momentum region. We notice that, by simply reweighting the boson rapidity distribution to NNLO predictions, we achieve a NNLO accurate generator matched to a shower. The approach applies to all production processes involving a colorless massive system plus one jet. We discuss how it may be extended to general processes.