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(Pz₃,z₃²) as a function of the Ioffe time ν=Pz₃ and the distance z₃. The next step is to divide M(Pz₃,z₃²) by the rest-frame density M(0,z₃²). Our lattice calculation shows a linear exponential z₃-dependence in the rest-frame function, expected from the Z(z₃²) factor generated by the gauge link. Still, we observe that the ratio M(Pz₃,z₃²)/M(0,z₃²) has a Gaussian-type behavior with respect to z₃ for 6 values of P used in the calculation. This means that Z(z₃²) factor was canceled in the ratio. When plotted as a function of ν and z₃, the data are very close to z₃-independent functions. This phenomenon corresponds to factorization of the x- and k_⊥-dependence for the TMD F(x,k_⊥²). For small z₃≤4a, the residual z₃-dependence is explained by perturbative evolution, with αₛ/π=0.1.