Summations by parton showers of large logarithms in electron-positron annihilation

TL;DR

This paper applies a method to sum large logarithms in the thrust distribution of electron-positron annihilation using parton shower algorithms, reformulating calculations via integral transforms to analyze perturbative expansions.

Contribution

It introduces a novel approach to summing large logarithms in parton showers by using integral transforms and exponential reformulation for the thrust distribution.

Findings

Validated the method with several shower algorithms

Provided insights into the perturbative structure of the thrust distribution

Enhanced understanding of logarithm summation in parton showers

Abstract

In a companion publication, we have explored how to examine the summation of large logarithms in a parton shower. Here, we apply this general program to the thrust distribution in electron-positron annihilation, using several shower algorithms. The method is to work with an appropriate integral transform of the distribution for the observable of interest. Then, we reformulate the parton shower calculation so as to obtain the transformed distribution as an exponential for which we can compute the terms in the perturbative expansion of the exponent.