# Complete Matching for Quasi-distribution Functions in Large Momentum Effective Theory

## TL;DR

This paper advances the extraction of parton distribution functions using large momentum effective theory by deriving a comprehensive factorization formula and matching kernels, enabling more accurate lattice QCD calculations.

## Contribution

It provides a general factorization formula and one-loop matching kernels for quasi-PDFs with mixing, applicable to both polarized and unpolarized distributions.

## Key findings

- Derived a general factorization formula for quasi-PDFs with mixing.
- Calculated the hard matching kernel at order α_s in a regularization-independent scheme.
- Facilitates extraction of flavor-singlet quark and gluon PDFs from lattice QCD.

## Abstract

We complete the procedure of extracting parton distribution functions (PDFs) using large momentum effective theory (LaMET) at leading power accuracy in the hadron momentum. We derive a general factorization formula for the quasi PDFs in the presence of mixing, and give the corresponding hard matching kernel at $\mathcal O(\alpha_s)$, both for the unpolarized and for the polarized quark and gluon quasi-PDFs. Our calculation is performed in a regularization-independent momentum subtraction scheme. The results allow us to match the nonperturbatively renormalized quasi-PDFs to normal PDFs in the presence of mixing, and therefore can be used to extract flavor-singlet quark PDFs as well as gluon PDFs from lattice simulations.