UV Divergence of the Quasi-Pdf Operator under the Lattice Regularization

Even since the "quasi" parton distribution function (PDF) was proposed underthe large-momentum effective theory (LaMET) framework, its renormalizationunder the lattice regularization has been a central challenge to be solved dueto the linear divergence. Thus, we investigate several possible ways torenormalize the quasi-PDF operators in high accuracy with non-perturbativecalculation using the quench configurations at several lattice spacings. Wefind that the ratio of the UV divergences obtained from the Wilson loop andoff-shell quasi-PDF operator is not a constant of the Wilson link length z.Although the linear divergence in them may be consistent to each othernumerically, there is some additional UV divergence in the quasi-PDF operator.