Electromagnetic properties of the pion as a composite Nambu-Goldstone boson

Abstract

Motivated by the Nambu--Jona-Lasinio model of light mesons, we introduce a covariant separable interaction to model the structure of relativistic quark-antiquark systems. The Schwinger-Dyson equation for the quark self-energy is solved analytically, generating a dynamical quark mass through spontaneous breaking of chiral symmetry, and yielding a pion which has zero mass in the chiral limit. The Bethe-Salpeter vertex function for this qq\ifmmode\bar\else\textasciimacron\fi{} pion, which has a momentum distribution and composite structure associated with the interaction, is obtained analytically. Using this vertex function, and a similar one for the \ensuremath{\rho} meson, we calculate the electromagnetic observables of this composite Nambu-Goldstone boson, including effects from \ensuremath{\rho}-meson dominance processes. Our calculation takes the composite structure of the mesons into account. The \ensuremath{\rho}-meson effects are found to be very small in the pion charge form factor, but substantial in the charge radius. Using the model, predictions are made for ${\ensuremath{\gamma}}^{\mathrm{*}}$${\mathrm{\ensuremath{\pi}}}^{0}$\ensuremath{\rightarrow}\ensuremath{\gamma} and \ensuremath{\rho}\ensuremath{\pi}\ensuremath{\gamma} transition form factors.