Effective Field Theories For J/ψ Production

Abstract

We discuss the history of Nuclear Physics and introduce QCD as the modern theory of strong nuclear forces. The idea of factorization allows us to make predictions by separating nuclear processes into independent parts occurring at different energies. We approach the calculations in different regions by setting up NRQCD, which is an effective field theory. Using these ideas, we then calculate the matching, at leading order, of the transverse momentum-dependent fragmentation functions (TMDFFs) for light quarks and gluons fragmenting to a $J/\psi$ onto polarized nonrelativistic QCD (NRQCD) TMDFFs. Using the results we obtain, we make predictions for the light quark fragmentation contribution to the production of polarized $J/\psi$ in semi-inclusive deep inelastic scattering (SIDIS) both for unpolarized and longitudinally polarized beams of electrons colliding with protons. We then compare the relative importance of different mechanisms for polarized $J/\psi$ production in semi-inclusive deep inelastic scattering processes at large $Q^2$. We study the leading contributions from light quark fragmentation to polarized $J/\psi$ production, and compare to direct production via photon-gluon fusion, which can proceed through color-singlet as well as color-octet mechanisms. We identify kinematic regimes where light quark fragmentation dominates, allowing for the extraction of the $^3S_1$ matrix element, as well as regimes where photon gluon fusion dominates, suggesting that the gluon TMD parton distribution function can be probed.