Renormalization in Large Momentum Effective Theory of Parton Physics

TL;DR

This paper proves that non-local QCD operators used in LaMET, which include Wilson lines, renormalize multiplicatively to all orders in both dimensional and lattice regularizations. By introducing an auxiliary heavy-quark field, the Wilson line is recast into heavy-light current structures, with renormalization controlled by standard HQET-like factors, including $Z_j$ and $Z_O$, in the continuum. On the lattice, a linear self-energy divergence necessitates a mass counterterm that introduces a $z$-dependent exponential, while the remaining renormalization constants are z-independent and consistent with heavy-light current anomalous dimensions. Together, these results establish a robust path to define a continuum limit for quasi-PDFs and improve lattice extractions of parton physics within the LaMET framework.

Abstract

In the large-momentum effective field theory approach to parton physics, the matrix elements of non-local operators of quark and gluon fields, linked by straight Wilson lines in a spatial direction, are calculated in lattice quantum chromodynamics as a function of hadron momentum. Using the heavy-quark effective theory formalism, we show a multiplicative renormalization of these operators at all orders in perturbation theory, both in dimensional and lattice regularizations. The result provides a theoretical basis for extracting parton properties through properly renormalized observables in Monte Carlo simulations.