Studies of $T_{cc}^+$ Decays and Transverse-Momentum-Dependent $J/\psi$ Production Using Effective Field Theory

We describe the application of effective field theories for quantum chromodynamics (QCD) to two bound states involving heavy quarks: the $T_{cc}^+$ exotic meson and the $J/\psi$. We study the decay of the $T_{cc}^+$ in an effective theory for hadronic molecules, and find agreement with experiment. We also use the nonrelativistic QCD (NRQCD) factorization formalism to derive the leading-order transverse momentum dependent fragmentation functions (FFs) for quarks and gluons fragmenting to $J/\psi$. We then make use of these TMD FFs to compare the $J/\psi$ production mechanisms of light quark fragmentation and photon-gluon fusion, where the conclusions we draw can motivate future experiments at the Electron Ion Collider, shedding light on the inner structure of nucleons and testing ideas from NRQCD factorization. These results showcase the utility of effective field theories in explaining experiments and testing key concepts in nuclear/particle physics.