QCD Matrix Elements + Parton Showers

TL;DR

The paper tackles the challenge of accurately simulating multi-jet final states in $e^+e^-$ collisions by separating matrix-element calculations and parton showers at a jet-resolution scale $y_{ ext{ini}}$ defined via the $k_T$ algorithm. It combines tree-level matrix elements with Sudakov suppression for the high-$y$ region and employs vetoed, angular-ordered showers to fill the low-$y$ region, achieving cancellation of $y_{ ext{ini}}$ dependence at next-to-leading logarithmic accuracy. Key contributions include explicit NLL jet-rate expressions, a practical procedure to augment matrix-element configurations with Sudakov weights, and a veto-based shower framework implemented approximately in APACIC++, with results showing good agreement for multi-jet observables. The approach merges the strengths of matrix elements and parton showers while reducing double counting, and is extensible to DIS, hadron-hadron collisions, and potential inclusion of NLO corrections and mass effects.

Abstract

We propose a method for combining QCD matrix elements and parton showers in Monte Carlo simulations of hadronic final states in $e^+e^-$ annihilation. The matrix element and parton shower domains are separated at some value $y_{ini}$ of the jet resolution, defined according to the $k_T$-clustering algorithm. The matrix elements are modified by Sudakov form factors and the parton showers are subjected to a veto procedure to cancel dependence on $y_{ini}$ to next-to-leading logarithmic accuracy. The method provides a leading-order description of hard multi-jet configurations together with jet fragmentation, while avoiding the most serious problems of double counting. We present first results of an approximate implementation using the event generator APACIC++.

Figures (11)

• Figure 1: Branching structure of three-jet final state.
• Figure 2: An Abelian four-jet contribution.
• Figure 3: A non-Abelian four-jet contribution.
• Figure 4: Vetoed showers on two-jet contribution.
• Figure 5: Vetoed showers on contribution with two jets at scale $Q_1$ and three at scale $Q_0$.