We apply QCD effective theories to study the physics of jets and quarkonium production. The thesis contains work in the following two related directions.
The first direction is jet physics. We introduced a function called fragmentation function to a jet (FFJ) to describe inclusive jet production from a parton and studied FFJs in different phase space and momentum regions. One of the limits we investigated is the situation where the jet radius was small. The smallness of radius r leads to large log(r) corrections that need to be resummed. Another limit we investigated was the large z limit, where z is defined to be the fraction of energy carried by the jet from the mother parton. This is the limit where QCD dynamics gradually becomes non-perturbative and large log(1-z) would appear. We found that the emergence of this log(1-z) was due to the gluon radiations that were both collinear and soft and could be described by the collinear-soft mode within the soft-collinear effective theory (SCET) framework. We formulated factorization theorems and used renormalization group techniques to deal with these types of logarithms.
The second direction is quarkonium production in jets. This direction naturally combines jet physics with quarkonium production. Since quarkonium production in a jet is inclusive in the jet, we can still use inclusive quarkonium fragmentation functions that are perturbatively calculable based on the Non-relativistic QCD (NRQCD) factorization formalism. We did both analytic calculations and Monte Carlo simulations and compared them with the recent LHCb measurement of J/psi production in jets. We found that currently existing event generators are not sufficient to study the details of the dynamics of quarkonium production in jets and proposed a modification to PYTHIA. Both our analytic calculations and the modified PYTHIA agreed reasonably well with the LHCb data. We also studied other observables related to quarkonium production in jets that could have the potential power to discriminate different quarkonium production mechanisms and test which long distance matrix element extractions are preferable.