Logarithmic accuracy of parton showers: a fixed-order study

TL;DR

This paper develops a framework to evaluate the logarithmic accuracy of parton-shower algorithms by analyzing their ability to replicate singularity structures and resummation results, with a focus on transverse momentum ordered showers.

Contribution

It introduces a fundamental approach for assessing parton-shower accuracy based on singularity and resummation criteria, applied to second-order properties of transverse momentum ordered showers.

Findings

Identifies regions where showers fail to reproduce singular limits.

Links shower characteristics to logarithmic resummation accuracy.

Analyzes effects at second order in strong coupling.

Abstract

We formulate some first fundamental elements of an approach for assessing the logarithmic accuracy of parton-shower algorithms based on two broad criteria: their ability to reproduce the singularity structure of multi-parton matrix elements, and their ability to reproduce logarithmic resummation results. We illustrate our approach by considering properties of two transverse momentum ordered final-state showers, examining features up to second order in the strong coupling. In particular we identify regions where they fail to reproduce the known singular limits of matrix elements. The characteristics of the shower that are responsible for this also affect the logarithmic resummation accuracies of the shower, both in terms of leading (double) logarithms at subleading $N_C$ and next-to-leading (single) logarithms at leading $N_C$.