Constructing Scalar-Photon Three Point Vertex in Massless Quenched Scalar QED

TL;DR

This paper constructs a non-perturbative transverse scalar-photon vertex in massless quenched scalar QED, ensuring key physical properties and consistency with known asymptotic behavior, aiding Schwinger-Dyson equation studies.

Contribution

It provides a novel, physically consistent ansatz for the transverse part of the scalar-photon vertex in massless quenched scalar QED, satisfying multiple theoretical constraints.

Findings

Ensures multiplicative renormalizability of the scalar propagator.

Maintains correct transformation properties under discrete symmetries.

Reproduces one-loop asymptotic results in weak coupling regime.

Abstract

Non perturbative studies of Schwinger-Dyson equations (SDEs) require their infnite, 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 (WFGTI), while the transverse vertex remains undetermined. In massless quenched sQED, we construct the transverse part of the non perturbative scalar-photon vertex. This construction (i) ensures multiplicative renormalizability (MR) of the scalar propagator in keeping with the Landau-Khalatnikov-Fradkin transformations (LKFTs), (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 one loop asymptotic result in the weak coupling regime of the theory.