Transverse Spin and Classical Gluon Fields: Combining Two Perspectives on Hadronic Structure

In recent decades, the spin and transverse momentum of quarks and gluons were found to play integral roles in the structure of the nucleon. Simultaneously, the onset of gluon saturation in hadrons and nuclei at high energies was predicted to result in a new state of matter dominated by classical gluon fields. Understanding both of these contributions to hadronic structure is essential for current and future collider phenomenology. In this Dissertation, we study the combined effects of transverse spin and gluon saturation using the Glauber-Gribov-Mueller / McLerran-Venugopalan model of a heavy nucleus in the quasi-classical approximation. We investigate the use of a transversely-polarized projectile as a probe of the saturated gluon fields in the nucleus, finding that the transverse spin asymmetry of produced particles couples to the component of the gluon fields which is antisymmetric under both time reversal and charge conjugation. We also analyze the effects of saturation on the transverse spin asymmetry (Sivers function) of quarks within the wave function of the nucleus, finding that gluon saturation preferentially generates the asymmetry through the orbital angular momentum of the nucleons, together with nuclear shadowing.