Multi-Emission Kernels for Parton Branching Algorithms

TL;DR

This paper develops a comprehensive framework for multi-emission kernels in parton branching algorithms, enabling more accurate modeling of soft and collinear radiation at the amplitude level with potential applications in subtraction methods.

Contribution

It introduces a novel method to construct multi-emission kernels that incorporate unresolved emissions and connects kinematic schemes to power counting, advancing parton shower modeling.

Findings

Framework for multi-emission kernels at amplitude level

Partitioning of soft radiation beyond single-emission models

Potential applications in subtraction and probabilistic algorithms

Abstract

We introduce a general framework to construct multi-emission kernels for parton branching algorithms at the amplitude level and across different soft and collinear limits. We highlight the connection of kinematic parameterizations and recoil schemes to the underlying power counting, and discuss in detail how soft radiation can be partitioned in between different collinear configurations beyond the single-emission picture underpinning the traditional dipole and angular ordering approaches. Our work is a vital cornerstone to build parton branching algorithms which include multiply-unresolved emissions in a fully differential way, and our construction can also be used to obtain splitting functions for probabilistic algorithms or other cross-section level objects such as subtraction terms.