QCD event generators with next-to-leading order matrix-elements and parton showers

TL;DR

The paper tackles the challenge of building QCD event generators that combine next-to-leading order matrix elements with leading-log parton showers without double counting. It introduces an LL-subtraction method and an x-deterministic parton shower, implemented with automatic GRACE-generated matrix elements (including loops), and demonstrates its validity through a Drell–Yan example at Tevatron energy. The approach yields IR-safe results, preserves factorization-scale independence, and produces smooth distributions by effectively matching exact matrix elements with LL resummation. This work offers a practical framework for NLO event generation in hadron colliders and showcases automatic, scalable computation suitable for complex final states.

Abstract

A new method to construct event-generators based on next-to-leading order QCD matrix-elements and leading-logarithmic parton showers is proposed. Matrix elements of loop diagram as well as those of a tree level can be generated using an automatic system. A soft/collinear singularity is treated using a leading-log subtraction method. Higher order re-summation of the soft/collinear correction by the parton shower method is combined with the NLO matrix-element without any double-counting in this method. An example of the event generator for Drell-Yan process is given for demonstrating a validity of this method.

Figures (6)

• Figure 1: Dalitz plot of (N+1)-body phase space. $Q^2_i$ is defined in Eq.(\ref{['Ocoll']}) and $Q^2_c$ is a threshold value to separate the visible- and collinear-region.
• Figure 2: Momentum fraction distributions from an x-deterministic parton shower and Cteq5L parton distribution functions. The distributions of $u$-quarks (left), ${\bar{u}}$-quarks (center), and gluons (right) are shown.
• Figure 3: Transverse momentum distribution of gluons. The distributions from the PS applied to the Born process are shown by $*$ commonly in three histograms. Those distributions from $\sigma_{exact}$ (left), $\sigma_{exact}$ with double-count rejection (middle), and $\sigma_{exact}$ with double-count rejection and the $k_T^2$ restriction are compared with the PS.
• Figure 4: Energy and transverse momentum distributions of gluons. The $*$ shows the distributions from the PS on the Born process, solid histograms from $\sigma_{exact}$ with double-count rejection, and circles from ${\tilde{\sigma}}_{LLsub}$ combined with those from the PS on the Born process.
• Figure 5: Feynman diagram of the Drell-Yan process, $q {\bar{q}} \rightarrow {\mu}^- {\mu}^+$ and its radiative processes.