We present a new approach to coherent parton showers in the decays of coloured resonances, based on the notion of resonance-final (RF) QCD antennae. A full set of mass- and helicity-dependent $2to 3$ antenna functions are defined, with the additional requirement of positivity over the respective branching phase spaces. Their singularity structure is identical to that of initial-final (IF) antennae in $2to N$ hard processes (once mass terms associated with the incoming legs are allowed for), but the phase-space factorisations are different. The consequent radiation patterns respect QCD coherence (at leading colour) and reduce to Dokshitzer-Gribov-Lipatov-Altarelli-Parisi and eikonal kernels in the respective collinear and soft limits. The main novelty in the phase-space factorisation is that branchings in RF antennae impart a collective recoil to the other partons within the same decay system. An explicit implementation of these ideas, based on the Sudakov veto algorithm, is provided in the VINCIA antenna-shower plug-in to the PYTHIA 8 Monte Carlo event generator. We apply our formalism, matched to next-to-leading order accuracy using POWHEG, to top quark production at the LHC, and investigate implications for direct measurement of the top quark mass. Finally, we make recommendations for assessing theoretical uncertainties arising from parton showers in this context.
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