In Lattice gauge theories , to calculate the PDFs from first principles
it is convenient to consider the Ioffe-time distribution defined through gauge-invariant bi-local operators with spacelike separation. Lattice calculations provide values for a limited range of the distance separating the bi-local operators. In order to perform the Fourier transform and obtain the pseudo- and the quasi-PDFs, it is then necessary to extrapolate the large-distance behavior.
I will discuss the formalism one may use to study the behavior of the Ioffe-time distribution at large distances and show that the pseudo-PDF and quasi-PDF are very different at this regime. Using light-ray operators, I will also show that the higher twist corrections of the quasi-PDF come in not as inverse powers of $P$ but as inverse powers of $x_B P$.