Constructing scalar-photon three point vertex in massless quenched scalar QED

Abstract

Nonperturbative studies of Schwinger-Dyson equations require their infinite, coupled tower to be truncated in order to reduce them to a practically solvable set. In this connection, a physically acceptable Ansatz for the three point vertex is the most favorite choice. Scalar quantum electrodynamics (sQED) provides a simple and neat platform to address this problem. The most general form of the three point scalar-photon vertex can be expressed in terms of only two independent form factors, a longitudinal and a transverse one. Ball and Chiu have demonstrated that the longitudinal vertex is fixed by requiring the Ward-Fradkin-Green-Takahashi identity while the transverse vertex remains undetermined. In massless quenched sQED, we construct the transverse part of the nonperturbative scalar-photon vertex. This construction (i) ensures multiplicative renormalizability of the scalar propagator in keeping with the Landau-Khalatnikov-Fradkin transformations, (ii) has the same transformation properties as the bare vertex under charge conjugation, parity and time reversal, (iii) has no kinematic singularities and (iv) reproduces the one-loop asymptotic result in the weak coupling regime of the theory.