Alternative Tests of Quarkonium Production Theory Using Jets

In this talk I discuss an alternative approach for investigating quarkonium production in hadron colliders. I present a complete framework for developing observables for studies of charmonium states produced within a jet. This approach is based on the use of effective field theories of quantum chromodynamics that allow for the approximate factorization of jet cross sections in perturbative calculable terms and universal non-perturbative functions that are extracted from data. Particularly, I explore the factorization approach of non-relativistic quantum chromodynamics (NRQCD) and soft-collinear effective theory (SCET). The fragmenting jet functions play central role in factorization theorems for cross sections for identified hadrons within jets. These cross sections can depend on the hadron-jet energy ratio and possibly on other jet observables. We expand this concept to jet-shape observables known as angularities and introduce the transverse momentum dependent fragmenting jet functions. Applications of these advanced methods to $J/\psi$ production from gluon fragmentation in electron-positron annihilation are presented. Additionally, we compare predictions for $J/\psi$ production in jets, based on the framework of fragmenting jet functions, against experimental data from the LHCb collaboration.