Collinear parton dynamics beyond Dokshitzer-Gribov-Lipatov-Altarelli-Parisi framework

Renormalization group evolution equations describing the scale dependence of quantities in quantum chromodynamics 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 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 paper 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, where it involves the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mn>1</a:mn><a:mo stretchy="false">→</a:mo><a:mn>3</a:mn></a:mrow></a:math> 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 multihadron 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 <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:msup><d:mi>e</d:mi><d:mo>+</d:mo></d:msup><d:msup><d:mi>e</d:mi><d:mo>−</d:mo></d:msup><d:mo stretchy="false">→</d:mo></d:math> hadrons at next-to-next-to-leading order. Our results are an important step toward improving the understanding of the collinear dynamics of jets, with broad applications in jet substructure, ranging from the study of multihadron correlations, to the description of inclusive (sub)jet production, and the advancement of modern parton showers.