Lattice QCD exploration of parton pseudo-distribution functions

We demonstrate a new method of extracting parton distributions from lattice calculations. The starting idea is to treat the generic equal-time matrix element M(Pz(3), z(3)(2)) as a function of the Ioffe time nu = Pz(3) and the distance z(3). The next step is to divide M(Pz(3), z(3)(2)) by the rest-frame density M(0, z(3)(2)). Our lattice calculation shows a linear exponential z(3)-dependence in the rest-frame function, expected from the Z(z(3)(2)) factor generated by the gauge link. Still, we observe that the ratio M (Pz(3), z(3)(2))/M(Pz(3), z(3)(2)) has a Gaussian-type behavior with respect to z(3) for 6 values of P used in the calculation. This means that Z (z(3)(2))factor was canceled in the ratio. When plotted as a function of nu and z(3), the data are very close to z(3)-independent functions. This phenomenon corresponds to factorization of the x-and k(perpendicular to)-dependence for the TMD F(x, k(perpendicular to)(2)) . For small z(3) <= 4a, the residual z(3)-dependence is explained by perturbative evolution, with alpha(s)/pi = 0.1.