New formalism for QCD parton showers

TL;DR

This paper introduces a boost-invariant, angular-ordered QCD parton shower formalism based on a transverse-momentum–driven evolution variable, enabling mass-dependent splitting and improved soft-gluon coherence. It defines specific kinematics and running-coupling scales for final- and initial-state emissions, and treats colour connections across FF, II, IF, and decay topologies to ensure coherent radiation patterns. The approach yields better phase-space coverage, especially in the soft region, and provides systematic matrix-element corrections for hard emissions, all implemented in the HERWIG++ generator. The framework lays groundwork for NLO matching and refined heavy-quark fragmentation, with detailed examples and dead-region management to ensure robust sampling of realistic hadronic final states.

Abstract

We present a new formalism for parton shower simulation of QCD jets, which incorporates the following features: invariance under boosts along jet axes, improved treatment of heavy quark fragmentation, angular-ordered evolution with soft gluon coherence, more accurate soft gluon angular distributions, and better coverage of phase space. It is implemented in the new HERWIG++ event generator.

Figures (12)

• Figure 1: Final-state parton branching. The blob represents the hard subprocess.
• Figure 2: Initial-state parton branching. The blob represents the hard subprocess.
• Figure 3: Phase space for $e^+e^-\to q{\bar{q}} g$ for $m_q=5$ GeV, $Q^2=m_Z^2$, with symmetric definition of quark and antiquark jets.
• Figure 4: Phase space for $e^+e^-\to q{\bar{q}} g$ for $m_q=5$ GeV, $Q^2=m_Z^2$, with maximal region for the quark jet.
• Figure 5: The function $f(\tilde{\kappa})$ giving the gluon angular distribution in the soft limit, for $m=5$ GeV, $Q^2=m_Z^2$. The exact result eq. (\ref{['eq_dPVsoft']}), solid curve, and shower approximation (\ref{['eq_dPsoft']}), dashed, are not distinguishable on this scale.