Applications of effective field theory to the transverse momentum dependent framework

Abstract

In this dissertation, I use effective field theory (EFT) to study hadron structure and production in the transverse momentum dependent (TMD) factorization framework of QCD. First, I consider how systems containing only light quarks and gluons can be studied by matching TMD parton distribution functions of light hadrons onto hadronic operators in chiral perturbation theory ($\chi$PT). In this work, I show that the TMD PDF receives long distance contributions from fluctuations into intermediate hadron states, which can be systematically calculated by evaluating objects referred to as "TMD hadronic distribution functions". I use this framework to predict and study an asymmetry between the $\bar{d}$ and $\bar{u}$ TMD PDFs in the proton, which is a novel observable. Next, I explore how EFTs can be used to study systems containing heavy quarks in the TMD framework by considering the production and polarization of the $J/\psi$ meson in NRQCD. In the region where the transverse momentum of the $J/\psi$ is greater than the soft scale of NRQCD, $P_{T,\psi} > m_c\vv$, I discuss how the TMD fragmentation functions for polarized light quarks and gluons fragmenting to a polarized $J/\psi$ meson can be matched onto the traditional long distance matrix elements (LDMEs) of NRQCD. I present phenomenological results contrasting the competing effects of TMD fragmentation vs. direct production via photon-gluon fusion in semi-inclusive deep inelastic scattering at large $Q^2$. This work will be relevant for upcoming studies at the Electron-Ion Collider. In a different limit, when $P_{T,\psi} \sim m_c\vv$, I characterize the role of soft gluon emissions from the $c\bar{c}$ pair. This leads to the categorization of new production operators, dubbed "TMD soft transition functions", that mediate the transition of charm quarks produced in color octet configurations to a $^3S_1^{[1]}$ state. These operators are enhanced in the NRQCD power counting with respect to the color octet LDMEs or even the TMD shape functions that have been used to study TMD $J/\psi$ production in previous literature. This work suggests that the TMD soft transition functions are the correct objects to match onto when studying $J/\psi$ production in the TMD framework.