Collinear Parton Dynamics Beyond DGLAP

TL;DR

This paper derives a comprehensive renormalization group equation for collinear parton dynamics that includes correlations beyond DGLAP, computes its NLO kernel, and applies it to energy flow in jets, enhancing jet substructure understanding.

Contribution

It introduces a general evolution equation for correlated collinear dynamics that unifies DGLAP and multi-hadron fragmentation evolution, with NLO calculations and numerical solutions.

Findings

Derived a new RG evolution equation for correlated collinear dynamics.

Computed the NLO kernel involving 1→3 splitting functions.

Applied the framework to NNLO energy flow in e+e- collisions.

Abstract

Renormalization group evolution equations describing the scale dependence of quantities in quantum chromodynamics (QCD) play a central role in the interpretation of experimental data. Arguably the most important evolution equations for collider physics applications are the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) equations, which describe the evolution of a quark or gluon fragmenting into hadrons, with only a single hadron identified at a time. In recent years, the study of the correlations of energy flow within jets has come to play a central role at collider experiments, necessitating an understanding of correlations, going beyond the standard DGLAP paradigm. In this Letter we derive a general renormalization group equation describing the collinear dynamics that account for correlations in the fragmentation. We compute the kernel of this evolution equation at next-to-leading order (NLO), where it involves the $1\to 3$ splitting functions, and develop techniques to solve it numerically. We show that our equation encompasses all previously-known collinear evolution equations, namely DGLAP and the evolution of multi-hadron fragmentation functions. As an application of our results, we consider the phenomenologically-relevant example of energy flow on charged particles, computing the energy fraction in charged particles in $e^+e^- \to$ hadrons at NNLO. Our results are an important step towards improving the understanding of the collinear dynamics of jets, with broad applications in jet substructure, ranging from the study of multi-hadron correlations, to the description of inclusive (sub)jet production, and the advancement of modern parton showers.