Matrix Element Corrections to Parton Shower Simulations of Heavy Quark Decay

TL;DR

This paper tackles the limited phase-space accuracy of parton showers by incorporating matrix-element corrections into heavy-quark decay simulations, specifically t → Wb, within the HERWIG generator. It introduces hard corrections to fill dead zones and soft corrections to adjust the hardest emissions, connecting shower variables to exact matrix-element kinematics and employing a gluon-energy cutoff to manage soft singularities. The results show improved jet observables and good agreement with exact leading-order matrix elements, validating the approach and its practical impact on top-quark decay modeling. The authors also outline extending matrix-element corrections to top production to achieve a more complete description of heavy-quark processes.

Abstract

Parton showers are accurate for soft and/or collinear emission, but for a good description of the whole of phase space they need to be supplemented by matrix element corrections. In this paper, we discuss matrix element corrections to the decay t->Wb and apply our results to the HERWIG Monte Carlo event generator. The phenomenological results show marked improvement relative to previous versions and agree well with the exact first-order matrix-element calculation.

Figures (7)

• Figure 1: Phase space limits on $x_1={{2p_1 \cdot q}\over{m_t^2}}-a$ and $x_3={{2p_3 \cdot q}\over{m_t^2}}$ in the decay $t\to bW\!g$ (solid) and the edge of the region covered by HERWIG (dashed). Also shown, barely visible in the top-left corner, is a 2 GeV cutoff on the gluon energy.
• Figure 2: Differential distribution of invariant opening angle, $\Delta R^2=\Delta\eta^2+\Delta\phi^2$ for three-jet $e^+e^-\to t\bar{t}$ events at $\surd s=360$ GeV, according to HERWIG version 5.9 (dashed), 6.0 (dot-dashed) and the version with matrix element corrections, 6.1 (solid).
• Figure 3: As Fig. \ref{['dr1']} but for the distribution of Durham jet algorithm measure, $y_3=\min_{ij}[\frac{2}{s}\min(E_i^2,E_j^2)(1-\cos\theta_{ij})]$.
• Figure 4: As Fig. \ref{['dr1']} but from HERWIG 6.1 (solid) and the tree-level calculation with $\alpha_s=0.145$ (dashed).
• Figure 5: As Fig. \ref{['y1']} but from HERWIG 6.1 (solid) and the tree-level calculation with $\alpha_s=0.145$ (dashed).