Quantifying finite-momentum effects in meson quasi-PDFs

TL;DR

This paper uses a constituent quark model to systematically analyze finite-momentum effects in meson quasi-PDFs, providing insights into their size and behavior, which is crucial for validating LaMET calculations.

Contribution

It is the first dedicated study of finite-momentum effects in meson quasi-PDFs, extending LaMET analysis beyond nucleons using a constituent quark model.

Findings

Finite-$p_z$ effects are potentially smaller for lighter mesons.

Systematic estimation of the size and $x$ dependence of finite-$p_z$ corrections.

Provides guidance for future lattice QCD calculations of meson PDFs.

Abstract

The recently proposed large momentum effective theory (LaMET) of Ji has led to a burst of activity among lattice practitioners to perform and control the first pioneering calculations of the quasi-PDFs of the nucleon. These calculations represent approximations to the standard PDFs defined as correlation functions of fields with lightlike separation, being instead correlations along a longitudinal direction of the operator $\gamma^z$; as such, they differ from standard PDFs by power-suppressed $1 \big/ p^2_z$ corrections, becoming exact in the limit $p_z \to \infty$. Investigating the systematics of this behavior thus becomes crucial to understanding the validity of LaMET calculations. While this has been done using models for the nucleon, an analogous dedicated study has not been carried out for the $\pi$ and $\rho$ quark distribution functions. Using a constituent quark model, a systematic calculation is performed to estimate the size and $x$ dependence of the finite-$p_z$ effects in these quasi-PDFs, finding them to be potentially tamer for lighter mesons than for the collinear quasi-PDFs of the nucleon.