Ward-Green-Takahashi identities and the axial-vector vertex

Understand

The colour-singlet axial-vector vertex plays a pivotal role in understanding dynamical chiral symmetry breaking and numerous hadronic weak interactions, yet scant model-independent information is available.

• We therefore use longitudinal and transverse Ward-Green-Takahashi (WGT) identities, together with kinematic constraints, in order to ameliorate this situation and expose novel features of the axial vertex: amongst them, Ward-like identities for elements in the transverse piece of the vertex, which complement and shed new light on identities determined previously for components in its longitudinal part.
• Such algebraic results are verified via solutions of the Bethe-Salpeter equation for the axial vertex obtained using two materially different kernels for the relevant Dyson-Schwinger equations.
• The solutions also provide insights that suggest a practical Ansatz for the axial-vector vertex.