# Pion generalized parton distribution from lattice QCD

## TL;DR

This paper reports the first lattice QCD calculation of the pion's valence-quark generalized parton distribution using LaMET, providing insights into the pion's internal structure in the zero-skewness limit.

## Contribution

It introduces a novel lattice QCD approach to compute the pion GPD using LaMET, with results connecting to the pion's parton distribution and form factor.

## Key findings

- Reproduces the pion PDF and form factor as GPD limits
- Highlights large statistical errors and the need for higher-statistics data
- Provides a first exploratory lattice calculation of pion GPD

## Abstract

We present the first lattice calculation of the valence-quark generalized parton distribution (GPD) of the pion using the large-momentum effective theory (LaMET) approach. We focus on the zero-skewness limit, where the GPD has a probability-density interpretation in the longitudinal Bjorken $x$ and the transverse impact-parameter distributions. Our calculation is done using clover valence fermions on an ensemble of gauge configurations with $2+1+1$ flavors (degenerate up/down, strange and charm) of highly improved staggered quarks (HISQ) with lattice spacing $a \approx 0.12$ fm, box size $L \approx 3$ fm and pion mass $m_\pi \approx 310$ MeV. The parton distribution function and the form factor are reproduced as special limits of the GPD as expected. Due to the large errors, this exploratory study does not show a clear preference among different model assumptions about the kinematic dependence of the GPD. To discriminate between these assumptions, future studies using higher-statistics data will be crucial.