[en] NJL model ; rho pi pi coupling constant ; low energy pi pi scattering lengths ; pion electromagnetic form factor
[en] We calculate the low energy pipi scattering lengths a(0)(0), a(0)(2), b(0)(0), b(0)(2) and a(1)(1), the coupling of the rho to the pion g(rhopipi), the total width of the rho, the low q(2) 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 rho meson is generated from a four-quark tensor interaction. Such a simple model avoids the mathematical complication related to pi - a(1) mixing. Two types of regularization are discussed, mainly affecting the values of a(0)(0) and b(0)(0). We find rather good agreement with data. The p meson described in this way does not account for the meson vector dominance model: it does not contribute to the a(0)(0), a(0)(2) 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 rho pole does not account for the p --> pipi decay but only reflects the q (q) over bar structure of the rho.