Abstract
It has been demonstrated that, contrary to the commonly accepted viewpoint, electromagnetic interactions cannot be consistently included in the Nambu–Jona-Lasinio model within vector meson dominance. This refers to the procedure for removing the πa1 transition in the effective meson Lagrangian. By the example of the a1(1260)→γπ+π- radiative decay, it has been demonstrated that the gauge invariance condition for the amplitude gives rise to an electromagnetic vertex describing the direct emission of a photon and a pion by a quark–antiquark pair. Surface terms appearing in the calculation of an anomalous triangular quark diagram, where one of the vertices is the interaction violating the vector-dominance hypothesis, play a key role in satisfying the Ward identities.
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