Multi-collinear splitting kernels for track function evolution

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