Momentum conservation and unitarity in parton showers and NLL resummation

TL;DR

This paper systematically compares NLL resummation and parton showers, developing a momentum-conserving shower algorithm and analyzing differences with modern dipole-based showers in electron-positron annihilation.

Contribution

It introduces a Markovian Monte Carlo algorithm for additive observables, removing approximations to align NLL resummation with momentum and probability conserving parton showers.

Findings

Identifies differences between NLL resummation and parton showers.

Develops a traditional, momentum-conserving parton shower based on coherent branching.

Analyzes the impact of various approximations and compares with dipole-based algorithms.

Abstract

We present a systematic study of differences between NLL resummation and parton showers. We first construct a Markovian Monte-Carlo algorithm for resummation of additive observables in electron-positron annihilation. Approximations intrinsic to the pure NLL result are then removed, in order to obtain a traditional, momentum and probability conserving parton shower based on the coherent branching formalism. The impact of each approximation is studied, and an overall comparison is made between the parton shower and pure NLL resummation. Differences compared to modern parton-shower algorithms formulated in terms of color dipoles are analyzed.