Gaining analytic control of parton showers

TL;DR

This paper develops a modified parton shower algorithm that conserves four-momentum at each vertex while maintaining an analytically known probability distribution, enabling better theoretical control and matching with matrix element calculations.

Contribution

It introduces a new algorithm for parton showers that preserves four-momentum conservation without losing analytic control of the probability distribution.

Findings

The modified shower algorithm maintains four-momentum conservation.

Analytic form of the probability distribution is derived for the new algorithm.

Facilitates improved matching with matrix element calculations.

Abstract

Parton showers are widely used to generate fully exclusive final states needed to compare theoretical models to experimental observations. While, in general, parton showers give a good description of the experimental data, the precise functional form of the probability distribution underlying the event generation is generally not known. The reason is that realistic parton showers are required to conserve four-momentum at each vertex. In this paper we investigate in detail how four-momentum conservation is enforced in a standard parton shower and why this destroys the analytic control of the probability distribution. We show how to modify a parton shower algorithm such that it conserves four-momentum at each vertex, but for which the full analytic form of the probability distribution is known. We then comment how this analytic control can be used to match matrix element calculations with parton showers, and to estimate effects of power corrections and other uncertainties in parton showers.