Understanding Transversely Polarized Quarks Inside Longitudinally Polarized Nucleons

We review the current understanding of transversely polarized quarks inside longitudinally polarized nucleons from the perspective of the longi-transversity distribution function and transverse-momentum-dependent (TMD) factorization. Employing the recently developed TMD evolution formalism for the unpolarized and longi-transversity distribution functions, we present the theoretical formalism for the relevant physical observables, namely the $A_{LL}^{\cos 2\varphi }$ asymmetry in the Drell–Yan process and the $A_{UL}^{\sin 2{\varphi }_h}$ asymmetry in the semi-inclusive deep inelastic scattering process. The phenomenological results are presented numerically.