Intrinsic quark transverse momentum in the nucleon from lattice QCD

A better understanding of transverse momentum $(\vect{ k}_{\perp})$ dependent quark distributions in a hadron is needed to interpret several experimentally observed large angular asymmetries and to clarify the fundamental role of gauge links in non-Abelian gauge theories. Based on manifestly non-local gauge-invariant quark operators we introduce process-independent $\vect{ k}_{\perp }$ distributions and study their properties in lattice QCD. We find that the longitudinal and transverse momentum dependence approximately factorize, in contrast to the behavior of generalized parton distributions. The resulting quark $\vect{ k}_{\perp }$ probability densities for the nucleon show characteristic dipole deformations due to correlations between intrinsic $\vect{ k}_{\perp }$ and the quark or nucleon spin. Our lattice calculations are based on $N_{f} = 2+1$ mixed action propagators of the LHP Collaboration