We calculate the low energy π π scattering lengths [Formula: see text] and [Formula: see text], the coupling of the ρ to the pion gρ π π, the total width of the ρ, the low q2 behavior of the pion electromagnetic form factor, and the pion scalar form factor within a chiral SU(2) f NJL-type Lagrangian where the spin 1 ρ meson is generated from a four-quark tensor interaction. Such a simple model avoids the mathematical complication related to π - a1 mixing. Two types of regularization are discussed, mainly affecting the values of [Formula: see text] and [Formula: see text]. We find rather good agreement with data. The ρ meson described in this way does not account for the meson vector dominance model: it does not contribute to the [Formula: see text] scattering lengths, and the charge radius of the pion is mainly ascribed to the bare photon quark coupling. Even if the shape of the electromagnetic form factor is well reproduced, the strong increase near the ρ pole does not account for the ρ→ππ decay but only reflects the [Formula: see text] structure of the ρ.
Vector dominance model and Gari-Krümpelmann formula for the nucleon electromagnetic form factor