The Georgi Algorithms of Jet Clustering

TL;DR

This paper establishes a theoretical foundation for Georgi's jet clustering algorithms, generalizes the jet function, and derives constraints ensuring process independence, angular consistency, and Lorentz invariance.

Contribution

It links Georgi's algorithms to parton shower kinematics, introduces a generalized jet function with an index, and derives parameter constraints for consistent jet clustering.

Findings

Derived constraints on jet function parameters for process independence.

Generalized jet function to include more degrees of freedom.

Ensured Lorentz invariance of jet function values.

Abstract

We reveal the direct link between the jet clustering algorithms recently proposed by Howard Georgi and parton shower kinematics, providing firm foundation from the theoretical side. The kinematics of this class of elegant algorithms is explored systematically for partons with arbitrary masses and the jet function is generalized to $J^{(n)}_\beta$ with a jet function index $n$ in order to achieve more degrees of freedom. Based on three basic requirements that, the result of jet clustering is process-independent and hence logically consistent, for softer subjets the inclusion cone is larger to conform with the fact that parton shower tends to emit softer partons at earlier stage with larger opening angle, and that the cone size cannot be too large in order to avoid mixing up neighboring jets, we derive constraints on the jet function parameter $\beta$ and index $n$ which are closely related to cone size cutoff. Finally, we discuss how jet function values can be made invariant under Lorentz boost.