Sivers and Boer-Mulders observables from lattice QCD

Abstract

We present a first calculation of transverse momentum-dependent nucleon observables in dynamical lattice QCD employing nonlocal operators with staple-shaped, ``process-dependent'' Wilson lines. The use of staple-shaped Wilson lines allows us to link lattice simulations to TMD effects determined from experiment, and, in particular, to access nonuniversal, naively time-reversal odd TMD observables. We present and discuss results for the generalized Sivers and Boer-Mulders transverse momentum shifts for the SIDIS and DY cases. The effect of staple-shaped Wilson lines on T-even observables is studied for the generalized tensor charge and a generalized transverse shift related to the worm-gear function ${g}_{1T}$. We emphasize the dependence of these observables on the staple extent and the Collins-Soper evolution parameter. Our numerical calculations use an ${n}_{f}=2+1$ mixed action scheme with domain wall valence fermions on an Asqtad sea and pion masses 369 MeV as well as 518 MeV.