Summations of large logarithms by parton showers

TL;DR

This paper introduces a method to analyze how parton showers sum large logarithms by transforming distributions and computing perturbative coefficients, applied specifically to the thrust distribution in electron-positron annihilation.

Contribution

It presents a novel integral transform approach to examine the summation of large logarithms in parton showers, enabling direct computation of perturbative coefficients.

Findings

The method successfully computes perturbative coefficients in the exponent.

Numerical tests show consistency with next-to-leading-logarithm summation.

Applicable to various shower algorithms for analyzing large logarithm summation.

Abstract

We propose a method to examine how a parton shower sums large logarithms. In this method, one works with an appropriate integral transform of the distribution for the observable of interest. Then, one reformulates the parton shower so as to obtain the transformed distribution as an exponential for which one can compute the terms in the perturbative expansion of the exponent. We apply this general program to the thrust distribution in electron-positron annihilation, using several shower algorithms. Of the approaches that we use, the most generally applicable is to compute some of the perturbative coefficients in the exponent by numerical integration and to test whether they are consistent with next-to-leading-log summation of the thrust logarithms.