The VPP-interaction form factor and the low-energy theorems in the effective chiral Lagrangians based on the extended Nambu-Jona-Lasinio model

In this paper the problem of simultaneous description of the low-energy theorems for the ππ-scattering amplitude and that which connects the γ → 3π and π0 → γγ decay amplitudes is discussed in the framework of the effective chiral Lagrangians. It is shown that to satisfy these low-energy theorems it is necessary to shift the vector-meson fields. This shift leads to the nontrivial form factor of the VPP interaction, which vanishes at the low-energy limit. An additional result of this shift is the appearance of unphysical interactions from the effective Wess-Zumino Lagrangian, which slightly violate low-energy theorems. It is shown that these interactions can be removed which slightly violate low-energy theorems. It is shown that these interactions can be removed by the regularization procedure in the framework of the extended Nambu-Jona-Lasinio model, which reproduces completely all low-energy phenomenological vertices of meson interactions in the effective chiral Lagrangians in terms of one-loop diagrams with virtual constituent quarks