Factorization, evolution and inverse matching of the quasi-PDF

In this talk, we discuss the factorization formula of the quasi-PDF in the large-momentum effective theory (LaMET). We show that by employing the momentum evolution equation of the quasi-PDF, we can derive the inverse matching formula that allows one to directly calculate the PDF from the quasi-PDF in the x-space. By deriving the next-to-next-to-leading order matching coefficient for the recently proposed hybrid scheme, we implement this inverse matching on a lattice QCD calculation of the pion valence quark PDF. The results show nice perturbative convergence and scale-uncertainty reduction, which is a promising step towards improving the precision of such calculations.