Summations of large logarithms by parton showers

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.

Automated summary

The proposed method aims to examine how a parton shower sums large logarithms, by working with integral transforms and reformulating the shower to obtain the transformed distribution as an exponential. This program was applied to the thrust distribution in electron-positron annihilation, with the approach of computing some perturbative coefficients in the exponent and testing their consistency with next-to-leading-log summation of the thrust logarithms.