Summations of large logarithms by parton showers

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.

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

“…The operator Y(µ 2 ; ν) is defined to have two properties. First, it does not change the number of partons or their momenta or flavors [4]. Second,…”

“…The analysis adapts the general formulation of this program in Ref. [4] to the practical analysis of first order parton shower algorithms. Our example is the thrust distribution in electron-positron annihilation.…”

“…We begin with an operator Y(µ 2 ; ν), which is defined in Ref. [4] using the all-order formalism of Ref. [14] for describing parton shower algorithms.…”

“…In this paper, we consider only electron-positron annihilation. Although Y(µ 2 ; ν) does not change the number of partons or their momenta or flavors [4], it can change the parton colors.…”

“…We have presented a general formulation of this program in Ref. [4]. The general formulation applies to hadron-hadron collisions, lepton-hadron collisions, and electron-positron collisions and to a general infrared-safe observable J.…”