Multi-Collinear Splitting Kernels for Track Function Evolution

TL;DR

This paper calculates the next-to-leading order evolution of track functions, which describe charged hadron fragmentation in jets, improving the precision of track-based predictions at the LHC.

Contribution

It introduces the NLO evolution equations for track functions, including the full 1→3 splitting kernel, and demonstrates their implementation and significance for jet substructure analysis.

Findings

Computed NLO evolution of track functions with full 1→3 splitting kernel

Implemented numerical solution of the evolution equations

Showed NLO corrections significantly impact predictions

Abstract

Jets and their substructure play a central role in many analyses at the Large Hadron Collider (LHC). To improve the precision of measurements, as well as to enable measurement of jet substructure at increasingly small angular scales, tracking information is often used due to its superior angular resolution and robustness to pile-up. Calculations of track-based observables involve non-perturbative track functions, that absorb infrared divergences in perturbative calculations and describe the transition to charged hadrons. The infrared divergences are directly related to the renormalization group evolution (RGE), and can be systematically computed in perturbation theory. Unlike the standard DGLAP evolution, the RGE of the track functions is non-linear, encoding correlations in the fragmentation process. We compute the next-to-leading order (NLO) evolution of the track functions, which involves in its kernel the full $1\rightarrow3$ splitting function. We discuss in detail how how we implement the evolution equation numerically, and illustrate the size of the NLO corrections. We also show that our equation can be viewed as a master equation for collinear evolution at NLO, by illustrating that by integrating out specific terms, one can derive the evolution for any $N$-hadron fragmentation function. Our results provide a crucial ingredient for obtaining track-based predictions for generic measurements at the LHC, and for improving the description of the collinear dynamics of jets.