Track functions describe the collective effect of the fragmentation of quarks and gluons into charged hadrons, making them a key ingredient for jet substructure measurements at hadron colliders where track-based measurements offer superior angular resolution.
Unlike DGLAP, the evolution of track functions incorporates correlations between final-state hadrons, and is hence non-linear. Following our study on the track function evolution in Mellin space and its application to correlations of charged energy flows, we derive the NLO renormalization of the track functions in momentum space in both N=4 SYM and QCD, which are the first example of evolution equations involving the full 1-to-3 splitting functions.
We clarify how our evolution equations can be reduced to those for the single- and multi-hadron fragmentation functions, and can hence be viewed as the most general collinear evolution equations at NLO.
The equations have been solved numerically, and the energy fraction in charged hadrons in e+e- annihilation up to NNLO has been computed. 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 advancement of modern parton showers.
