Multivariable evolution in final state parton shower algorithms

TL;DR

This paper explores a novel approach to parton shower algorithms by using multiple scale variables and special treatment of soft emission singularities, aiming to improve the modeling of particle collisions.

Contribution

It introduces a multivariable evolution framework for parton showers, enhancing the traditional single-scale methods with a new treatment of soft singularities.

Findings

Improved modeling of soft emissions without collinear singularities.

Enhanced flexibility in defining evolution surfaces in parton splitting space.

Potential advantages over traditional single-scale shower algorithms.

Abstract

One can use more than one scale variable to specify the family of surfaces in the space of parton splitting parameters that define the evolution of a parton shower. Considering $e^+e^-$ annihilation, we use two variables, with shower evolution following a special path in this two dimensional space. In addition, we treat in a special way the part of the splitting function that has a soft emission singularity but no collinear singularity. This leads to certain advantages compared to the usual shower formulation with only one scale variable.