  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.
