We present the first combination of NLO QCD matrix elements for di-Higgs
production, retaining the full top quark mass dependence, with a parton shower.
Results are provided within both the POWHEG-BOX and MadGraph5_aMC@NLO Monte
Carlo frameworks. We assess in detail the theoretical uncertainties and provide
differential results. We find that, as expected, the shower effects are
relatively large for observables like the transverse momentum of the Higgs
boson pair, which are sensitive to extra radiation. However, these shower
effects are still much smaller than the differences between the Born-improved
HEFT approximation and the full NLO calculation in the tails of the
distributions.Comment: replaced by published version; in addition typos corrected in
definition of pole coefficients below Eq.(2.4
