# Pion Distribution Amplitude and Quasi-Distributions

## TL;DR

This paper develops a theoretical framework connecting pion distribution amplitudes with quasi-distributions using VDA formalism, providing models and evolution patterns to aid lattice QCD studies.

## Contribution

It introduces a VDA-based method to relate pion transverse momentum dependent distributions to quasi-distributions, with models and evolution analysis for lattice applications.

## Key findings

- Established a connection between TMDA and QDA for pions.
- Provided models for QDAs based on VDA models of soft TMDAs.
- Analyzed the $p_3$ dependence and evolution patterns for various pion DA models.

## Abstract

We extend our analysis of quasi-distributions onto the pion distribution amplitude. Using the formalism of parton virtuality distribution amplitudes (VDAs), we establish a connection between the pion transverse momentum dependent distribution amplitude (TMDA) $\Psi (x, k_\perp^2)$ and the pion quasi-distribution amplitude (QDA) $Q_\pi (y,p_3)$. We build models for the QDAs from the VDA-based models for soft TMDAs, and analyze the $p_3$ dependence of the resulting QDAs. As there are many models claimed to describe the primordial shape of the pion DA, we present the $p_3$-evolution patterns for models producing some popular proposals: Chernyak-Zhitnitsky, flat and asymptotic DAs. Our results may be used as a guide for future studies of the pion distribution amplitude on the lattice using the quasi-distribution approach.