$\rho\omega$--Mixing and the Pion Electromagnetic Form Factor in the Nambu--Jona-Lasinio Model

Abstract

The $\rho\omega$--mixing generated by the isospin breaking of the current quark masses $m_{u} \neq m_{d}$ is studied within the bosonized NJL model in the gradient expansion. The resulting effective meson lagrangian naturally incorperates vector meson dominance. By including pion loops an excellent description of both the pion electromagnetic form factor and of the $\pi^+\pi^-$ phase shifts in the vector--isovector channel is obtained. The $\rho\omega$--mixing can be treated in the static approximation but is absolutely necessary to reproduce the fine structure of the electromagnetic form factor, while the pion loops are necessary to obtain the correct energy dependence of the phase shifts.