Baryonic content of the pion

TL;DR

This paper investigates the baryonic structure of charged pions caused by isospin symmetry breaking, estimating the baryon mean square radius through phenomenological models and experimental data analysis.

Contribution

It provides the first estimates of the pion's baryon mean square radius, highlighting a positive radius for π+ and a negative for π-, based on form factor analysis.

Findings

The baryon mean square radius for π+ is estimated as (0.03-0.04 fm)^2.

The outer pion region has a net baryon, inner region a net antibaryon, balancing total baryon number.

The effect is opposite for π−, with similar magnitude estimates.

Abstract

The baryon form factor of charged pions arises since isospin symmetry is broken with unequal up and down quark masses, $m_d>m_u$, as well as electromagnetic effects. We obtain estimates for this basic property in two phenomenological ways: from simple constituent quark models, as well as from fitting the $e^+e^- \to \pi^+ \pi^-$ data. All our methods yield the result that the baryon mean square radius, extracted from the slope of the form factor, is positive for $\pi^+$, hence a picture where the outer region has a net baryon, and the inner region a net antibaryon density, both compensating each other such that the total baryon number is zero. For $\pi^-$ the effect is equal and opposite. We estimate the corresponding mean squared baryon radius as $\langle r^2 \rangle_B^{\pi^{+}} = (0.03-0.04~{\rm fm})^2$.