Alternative Tests of Quarkonium Production Theory Using Jets

In this thesis 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. My work 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 in this thesis I explore the factorization approach of non-relativistic quantum chromodynamics and soft-collinear effective theory. The fragmenting jet functions play central role in factorization theorems for cross sections for identified hadrons within jets. This cross sections can depend on the hadron-jet energy ratio and possibly on other jet observables. I 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/ψ production from gluon fragmentation in electron-positron annihilation are presented and I develop the tools for expanding this work in hadron colliders. Additionally, I compare predictions for J/ψ production in jets, based on the framework of fragmenting jet functions, against recent experimental data from the LHCb collaboration.