Generalized parton distributions of the pion

TL;DR

This paper computes the generalized parton distributions of the pion using chiral quark models, ensuring theoretical constraints are met, and evolves these results to higher scales to compare with experimental and lattice data.

Contribution

It provides explicit low-energy expressions for pion GPDs that satisfy all theoretical constraints and demonstrates their evolution to match experimental observations.

Findings

GPDs satisfy polynomiality, positivity, and sum rules.

Evolved distributions agree with experimental and lattice data.

Quark-model scale is approximately 320 MeV.

Abstract

Generalized Parton Distributions of the pion are evaluated in chiral quark models with the help of double distributions. As a result the polynomiality conditions are automatically satisfied. In addition, positivity constraints, proper normalization and support, sum rules, and soft pion theorems are fulfilled. We obtain explicit expressions holding at the low-energy quark-model scale, which exhibit no factorization in the t-dependence. The crucial QCD evolution of the quark-model distributions is carried out up to experimental or lattice scales. The obtained results for the Parton Distribution Function and the Parton Distribution Amplitude describe the available experimental and lattice data, confirming that the quark-model scale is low, around 320 MeV.