We discuss in detail a method to study transverse momentum dependent parton distribution functions (TMDs) using lattice QCD. To develop the formalism and to obtain first numerical results, we directly implement a bilocal quark-quark operator connected by a straight Wilson line, allowing us to study $T$-even, “process-independent” TMDs. Beyond results for $x$-integrated TMDs and quark densities, we present a study of correlations in $x$ and ${\mathit{k}}_{\perp }$. Our calculations are based on domain wall valence quark propagators by the LHP Collaboration calculated on top of gauge configurations provided by the MILC Collaboration with $N_f=2+1$ asqtad-improved staggered sea quarks.

• Received 22 November 2010

DOI:https://doi.org/10.1103/PhysRevD.83.094507