Probing Quarkonium Production in Jets Using Effective Field Theories

While bound states of heavy quarks $Q\bar{Q}$ called quarkonia have been studied for nearly a half-century, their production is still not well understood. We examine how techniques from Effective Field Theories (EFTs) of the strong force can be used to probe the production of the $J/\psi(c\bar{c})$. The focus will be to study how quarkonia are produced in jets, highly-collimated sprays of hadrons ubiquitous at particle colliders. We review the study of quarkonium production using Non-relativistic QCD (NRQCD) and the study of jet substructure observables using the Soft-Collinear Effective Theory (SCET). The concept of Fragmenting Jet Functions (FJF), which describe a hadron's energy distribution inside a jet of measured substructure, is extended to jets where the angularity is measured or where the transverse momenta of a hadron relative to the jet axis is measured. Predictions of the energy distribution of $J/\psi$ in jets at the LHC using FJFs are compared with the latest LHCb data using various extractions of the non-perturbative NRQCD long-distance-matrix-elements (LDMEs) in the literature. These distributions are also calculated using a modification of the Pythia Monte Carlo, which is shown to have an unphysical model of quarkonium production and gives results consistent with our FJF calculations. Our predictions of the energy of $J/\psi$ produced in jets fit the data much better than default Monte Carlo results. We also demonstrate that LDMEs extracted from high transverse momentum data do a better job at predicting the LHCb measurements.