Baryonic content of the pion

Abstract: The baryon form factor of charged pions arises since isospin symmetry is broken with unequal up and down quark masses, $m_d&gt;m_u$, 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 $$e^{+e^-} \to \pi⁺ \pi<sup>-$$ data. All our methods yield the result that the baryon mean square radius, extracted from the slope of the form factor, is positive for $\pi<sup>+$, 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 $\pi<sup>-$ the effect is equal and opposite. We estimate the corresponding mean squared baryon radius as $$\langle r² \rangle_B^{{\pi^{+}}} = (0.03-0.04~{\rm fm})<sup>2$$.