Meson-Baryon-Baryon Vertex Function and the Ward-Takahashi Identity

Abstract

Ohta proposed a solution for the well-known difficulty of satisfying the Ward-Takahashi identity for a photo-meson-baryon-baryon amplitude ($γ$MBB) when a dressed meson-baryon-baryon (MBB) vertex function is present. He obtained a form for the $γ$MBB amplitude which contained, in addition to the usual pole terms, longitudinal seagull terms which were determined entirely by the MBB vertex function. He arrived at his result by using a Lagrangian which yields the MBB vertex function at tree level. We show that such a Lagrangian can be neither hermitian nor charge conjugation invariant. We have been able to reproduce Ohta's result for the $γ$MBB amplitude using the Ward-Takahashi identity and no other assumption, dynamical or otherwise, and the most general form for the MBB and $γ$MBB vertices. However, contrary to Ohta's finding, we find that the seagull terms are not robust. The seagull terms extracted from the $γ$MBB vertex occur unchanged in tree graphs, such as in an exchange current amplitude. But the seagull terms which appear in a loop graph, as in the calculation of an electromagnetic form factor, are, in general, different. The whole procedure says nothing about the transverse part of the ($γ$MBB) vertex and its contributions to the amplitudes in question.