On the quarkonium-in-jet collinear fragmentation at moderate-to-large transverse momentum

We report progress on the Heavy-Flavor Non-Relativistic Evolution (HF-NRevo) setup, a novel methodology to address quarkonium formation within the fragmentation approximation. Our study sheds light on the moderate to large transverse-momentum sector, where the leading-twist collinear fragmentation of a single parton prevails over the higher-twist fragmentation from a constituent heavy-quark pair produced in the hard scattering. As for the initial energy-scale inputs, we rely on nonrelativistic next-to-leading calculations for all the parton-to-quarkonia fragmentation channels. Preliminary sets of variable-flavor number-scheme (VFNS) fragmentation functions, named NRFF1.0, are built via an evolution-threshold enhanced DGLAP scheme. Taking NRFF1.0 as a starting point, we use HF-NRevo to address the collinear fragmentation of quarkonia inside jets.