Studying the Sivers and Boer-Mulders Function with Lattice QCD

Transverse momentum dependent parton distribution functions (TMDs) characterize the intrinsic momentum distribution of quarks inside the nucleon. However, they also encode final or initial state interactions of the processes in which they are measured, such as semi-inclusive deep inelastic scattering (SIDIS) or the Drell–Yan process (DY). Consequently certain TMDs are process-dependent and predicted to be equal but opposite in sign for SIDIS and DY. Extending our method on the lattice to non-local operators with U-shaped Wilson lines, we can study these naively time-reversal odd TMDs, in particular the Sivers- and the Boer-Mulders function. We express our results in terms of Fourier-transformed TMDs that appear naturally in the Fourier transformed cross section of, e.g., SIDIS, and in Bessel-weighted asymmetries. We discuss the method, its limitations and preliminary results from an exploratory calculation using lattices generated by the MILC and LHP collaborations.