Double parton distributions of the pion

TL;DR

This paper calculates the valence double parton distributions of the pion using chiral quark models, revealing a simple factorized form at low energy and exploring their evolution and correlations, with potential for future lattice QCD validation.

Contribution

It provides a novel calculation of pion double parton distributions within chiral quark models, including their QCD evolution and correlation measures.

Findings

At the low-energy scale, the distributions are factorized in the chiral limit.

The distributions satisfy Gaunt-Sterling sum rules at zero transverse momentum.

Ratios of Mellin moments serve as measures of parton correlations, independent of evolution.

Abstract

We present a calculation of valence double parton distributions of the pion in the framework of chiral quark models. The result obtained at the low-energy quark model scale is particularly simple, where in the chiral limit a factorized form follows, $D(x_1,x_2, \vec{q}) = \delta(1-x_1-x_2) F(\vec{q})$ with $x_{1,2}$ standing for the longitudinal momentum fractions of the valence quark and antiquark, and $\vec{q}$ denotes the relative transverse momentum. For $\vec{q}=\vec{0}$ the result satisfies the Gaunt-Sterling sum rules. The QCD evolution to higher scales is carried out within the dDGLAP framework. We argue that the ratios of the valence Mellin moments $\langle x_1^n x_2^m \rangle / \langle x_1^n \rangle \langle x_2^m \rangle $, which do not depend on the dDGLAP evolution, provide particularly convenient measures of the longitudinal correlations between the partons. Such ratios could be probed in future lattice QCD simulations.