On the structure of the pion: A QCD--inspired point of view

TL;DR

This paper presents a QCD-inspired model of the pion's structure, deriving a relativistic light-cone wave function that enables analytical calculations of its form factor and radius, highlighting the pion's highly relativistic constituents.

Contribution

It introduces a new up-down-model for quark-antiquark interactions in mesons, replacing previous methods, and applies it to the pion using only fundamental QCD parameters.

Findings

The pion's constituents are highly relativistic.

The model allows analytical calculation of the pion's form factor.

The pion's mean-square radius is derived analytically.

Abstract

The effective interaction between a quark and an anti-quark as obtained previously with by the method of iterated resolvents is replaced by the so called up-down-model and applied to flavor off-diagonal mesons including the pion. The only free parameters are those of canonical quantum chromo-dynamics (QCD), particularly the coupling constant and the masses of the quarks. The so obtained light-cone wave function can be used to calculate the pion's form factor, particularly its mean-square radius can be computed analytically. The results allow for the exciting conclusion that the pion is built by highly relativistic constituents, in strong contrast to composite systems like atoms or nuclei with non-relativistic constituents.