Transverse Quark Spin Effects in Azimuthal Asymmetries in SIDIS and Drell Yan

The connection between quark orbital angular momentum and final state interaction for transversely polarized quarks in unpolarized hadrons suggests significant $\cos 2\phi$ azimuthal asymmetries in pion production in semi-inclusive deep inelastic scattering (SIDIS) ($e\ p\rightarrow e^\prime \ X \ \pi$) and in di-lepton production in Drell Yan ($p\ \bar{p}\rightarrow \ell^+ \ \ell^- \ X$) scattering. When transverse momentum of the reaction, $P_{T}$ is on the order of or less than $\Lambda_{\rm qcd}$, that is where $P_T\sim k_T$, where $k_T$ is intrinsic transverse quark momentum, these effects are characterized in term of naive time reversal odd (so called $T$-odd) transverse momentum dependent (TMD) parton distribution and fragmentation functions. At these moderate transverse momentum scales we estimate the size of the $\cos 2\phi$ azimuthal asymmetry in SIDIS and Drell Yan scattering in the parton spectator framework. In the former case we consider this so called ``Boer-Mulders'' effect for a proposed experiment at the upgraded CLAS-12 GeV detector at Jefferson LAB. In the latter case we consider this asymmetry for proton anti-proton experiments.