More on large-momentum effective theory approach to parton physics

Xiangdong Ji,Jian-Hui Zhang,Yong Zhao

doi:10.1016/j.nuclphysb.2017.09.001

Abstract

Large-Momentum Effective Theory (or LaMET) advocated by the present authors provides a direct approach to simulate parton physics in Euclidean lattice QCD theory. Recently, there has been much interest in this theory in the literature, with some questioning its validity and effectiveness. Here we provide some discussions aiming at a further exposition of this approach. In particular, we explain why it does not have the usual power divergence problem in lattice QCD calculations for the moments of parton distributions. The only power divergence in the LaMET approach comes from the self-energy of the Wilson lines which can be properly factorized. We show that although the Ioffe-time distribution provides an alternative way to extract the parton distribution from the same lattice observables, it also requires the same large momentum (or short distance) limit as in LaMET to obtain a precision calculation. With a proper quantification of errors, both extraction methods shall be compared with the same lattice data.

Highlights

The parton model invented by Feynman has been one of the most useful languages in describing the physics of strong interactions at high energy [1]
The√space-time z)/ 2), which involves an explicit time dependence [3]. (We use ξ μ = (t, x, y, z) (μ = 0, 1, 2, 3) to denote space-time coordinates, x, y, and z are commonly used to denote momentum fractions as well.) In physics, the time-dependent correlations are in a class by themselves because the time evolution calls for the presence of the interaction-dependent Hamiltonian H, and the observables are called “dynamical”
All parton physics can be accessed from equal-time correlations in a large-momentum hadron state which are calculable in Euclidean Monte Carlo simulations

Summary

Introduction

The parton model invented by Feynman has been one of the most useful languages in describing the physics of strong interactions at high energy [1]. All remainder dynamics is included in the boosted hadron wave function, not in the probe operators In this way, all parton physics can be accessed from equal-time correlations in a large-momentum hadron state which are calculable in Euclidean Monte Carlo simulations. To see that the nucleon matrix elements of the quasi-distribution calculated from lattice QCD does capture the correct IR physics in perturbation theory, one has to perform an analytical continuation of the matrix elements after the Euclidean loop integrals are done, not before. We provide an example to illustrate the above point: We calculate a one-loop integral appearing in the Euclidean quasi-distribution and show that the collinear divergence becomes manifest after an analytic continuation from pE2 to pM2 with pMμ and pEμ being the Minkowskian and Euclidean momenta. It can be matched perturbatively to the normal distributions in the MS scheme, where the matching factor can be computed in Minkowski space

Power divergences and renormalization of quasi-distributions in lattice QCD

Conclusion