Abstract
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 $2\to 3$ 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 $2\to N$ 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.
Highlights
In the reconstruction of resonances produced at the Large Hadron Collider, shower Monte Carlo (MC) event generators play an ongoing critical role
The recoil spectrum for VINCIA where the recoil is shared between the W and the first emission is softer, as would be expected. The discrepancies in both plots can be explained when the differences in how phase space is sampled, that arise from slight differences in the Sudakov factors, is taken into account. These sampling differences may be removed by plotting the average jΔp⃗ Wj as a function of PYTHIA’s evolution variable, pTevol [6]. (We describe how this is calculated for VINCIA in Appendix B.) Since this variable is a good representative for the hardness of the emission, it should correlate well with the amount of recoil required; by averaging, any bias due to different sampling in pTevol is removed
Unlike the dipole-shower formalism where the soft limits are partitioned across two radiators, we can utilise the positive-definiteness of the massive eikonal and construct our antenna functions such that they are positive-definite everywhere
Summary
In the reconstruction of resonances produced at the Large Hadron Collider, shower Monte Carlo (MC) event generators (see [1]) play an ongoing critical role. We consider top quark production as a case study for an application of our formalism This is a well-motivated example, since it was recently noted in [13,14] that the existing approaches of PYTHIA 8.2 [6,15,16,17] and HERWIG 7.1 [18,19,20,21,22] exhibit substantial shape differences in their predictions for the differential distribution of the reconstructed invariant mass of the top, already at the level of the parton shower. This is partially motivated by the presence of an existing interface to POWHEG BOX [13,14]
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