# Joint Track Functions: Expanding the Space of Calculable Correlations at Colliders

**Authors:** Kyle Lee, Ian Moult  
**arXiv:** [2308.01332](https://arxiv.org/abs/2308.01332)  
**Date:** 2023-08-02  
**Summary page:** https://www.summarizepaper.com/en/paper/2308.01332v1/

## Key points

- Collider experiments rely on factorization theorems for theoretical description
- Progress in extending factorization theorems to differential jet substructure observables
- Focus mainly on infrared safe observables capturing energy correlations in final state hadrons
- Valuable information encoded in energy correlations between hadrons with different quantum numbers
- Authors derive factorization theorems for correlations involving energy flux carried by hadrons with specific quantum numbers
- Joint track functions extend track function formalism and describe fraction of energy carried by hadrons with multiple quantum numbers resulting from quark or gluon fragmentation
- Authors study general properties of joint track functions and apply them to correlations involving positive and negative electromagnetic charges
- Correlations in electromagnetically charged energy flux calculated using parton shower Monte Carlo programs
- Proposal and study of a C-odd $\mathcal{E}_{\mathcal{Q}}$ detector exhibiting distinct scaling behavior compared to standard energy correlators
- Formalism expands class of computable observables at hadron colliders with wide-ranging applications in particle physics and nuclear physics.

## Summary

In collider experiments, the theoretical description of observables relies on factorization theorems that separate perturbative dynamics from universal non-perturbative matrix elements. While there has been significant progress in extending these factorization theorems to differential jet substructure observables, the focus has mainly been on infrared safe observables that only capture correlations in the energy of final state hadrons. However, valuable information about the underlying collision dynamics is encoded in how energy is correlated between hadrons with different quantum numbers. In this paper, authors Kyle Lee and Ian Moult expand the class of calculable correlations by deriving factorization theorems for a broad range of correlations involving the energy flux carried by hadrons specified by quantum numbers. These functions extend the track function formalism and describe the fraction of energy carried by hadrons with multiple quantum numbers resulting from quark or gluon fragmentation. The authors study the general properties of these joint track functions and specifically apply them to correlations involving positive and negative electromagnetic charges. To calculate correlations in electromagnetically charged energy flux, they extract these joint track functions from parton shower Monte Carlo programs. Additionally, they propose and study a C-odd $\mathcal{E}_{\mathcal{Q}}$ detector which exhibits qualitatively distinct scaling behavior compared to standard energy correlators. The formalism presented in this paper significantly expands the class of observables that can be computed at hadron colliders and has wide-ranging applications from particle physics to nuclear physics. The authors provide 25 pages of detailed analysis along with nine figures illustrating their findings.