T-odd Parton Distribution Functions and Azimuthal Anisotropy at High Transverse Momentum in p-p and p-A Collisions

Various azimuthal anisotropies (v₁, v₂, v₃, v₄), at high transverse momentum (high-pT), are shown to arise from the asymmetric scattering of transverse polarized quarks and gluons, arising from unpolarized nucleons (the Boer-Mulders' effect) and resulting in unpolarized hadrons (the Collins effect). Combined with the asymmetric scattering of partons from polarization independent but transverse momentum dependent (TMD) distributions, we obtain a possible mechanism to understand the azimuthal anisotropy of hadrons at large transverse momentum observed in p-p collisions. Constraining the ratio of polarization dependent TMD distributions to polarization independent distributions by comparing with the data from p-p collisions, we find that a simple A1/3 enhancement of the intrinsic transverse momentum (k_⊥²) distribution, of the initial state partons from the proton, straightforwardly yields the azimuthal anisotropy at high pT in p-A collisions.