Matrix-Element Corrections to Parton Shower Algorithms

TL;DR

This work analyzes how to embed exact first-order matrix elements into parton shower algorithms to fix the hard-emission regime while preserving soft/collinear accuracy. It contrasts two strategies—complementary phase-space division and direct corrections to the shower—highlighting self-consistency conditions and double-counting prevention via form-factor and veto techniques. The findings show that phase-space splitting is often important, whereas uniform per-emission corrections require careful implementation, especially for angular-ordered showers, and can be extended to other processes beyond e+e- and DIS. The proposed framework offers practical prescriptions for robust ME-corrected showers and enhances the reliability of predictions in jet and event-shape observables.

Abstract

We discuss two ways in which parton shower algorithms can be supplemented by matrix-element corrections to ensure the correct hard limit: by using complementary phase-space regions, or by modifying the shower itself. In the former case, existing algorithms are self-consistent only if the total correction is small. In the latter case, existing algorithms are never self-consistent, a problem that is particularly severe for angular-ordered parton shower algorithms. We show how to construct self-consistent algorithms in both cases. The postscript file for this paper can also be obtained by anonymous ftp from thep.lu.se in the file pub/Preprints/lu_tp_94_17.ps

Figures (2)

• Figure 1: The phase-space for e^+e^-$\mathrm{e^+e^-}$ divided according to an ordering variable $q^2$ into a matrix-element region, $q^2>Q^2,$ and a parton shower region, $q^2<Q^2$. Recall that the matrix element is divergent at $x_{1,2}=1$.
• Figure 2: Emission of two gluons in which the first (according to the ordering variable of the algorithm) is softer, and at a larger angle, than the second. Both should be described by the first-order matrix element: the second because the recoil from the first is negligible, so it is effectively emitted by the original current; and the first because it represents the coherent sum of emissions from the external lines which, after azimuthal averaging, is equivalent to a single emission from the internal line pretending that the later emission did not happen, i.e. it is also effectively emitted by the original current.