Gauge-covariant Diagonalization of Π-A_1 Mixing and the Resolution of a Low Energy Theorem

Using a recently proposed gauge covariant diagonalization of ora l -mixing, we show that the low-energy theorem F-pi = ef(pi)(2)F(3 pi) of current algebra, relating the anomalous form factor F gamma ->pi+pi 0 pi- = F-3 pi and the anomalous neutral pion form factor F-pi 0 ->gamma gamma = F-pi, is fulfilled in the framework of the Nambu-Jona-Lasinio (NJL) model, solving a long-standing problem encountered in the extension including vector and axial-vector mesons. At the heart of the solution is the presence of a gamma pi(q) over barq vertex which is absent in the conventional treatment of diagonalization and leads to a deviation from the vector meson dominance (VMD) picture. It contributes to a gauge-invariant anomalous tri-axial (AAA) vertex as a pure surface term.