vertex consistent with Lorentz and CPT invariance, satisfying the Ward identity $i\Gamma_\mu(p,p) = \partial^p_\mu S^{-1}(p)$ and Ward Takahashi identity[^1] $i(p - q)_\mu \Gamma_\mu(p,q) = S^{-1}(p) - S^{-1}(q)$, and free of kinematic singularities has been given by Ball and Chiu [@BC80]. It takes the form $$\Gamma_\mu(p,q) = \Gamma_\mu^{\rm BC}(p,q) + \Gamma_\mu^{\rm T}(p,q) , 
                                        \label{genver}$$ where $$\begin{aligned}
\Gamma_\mu^{\rm BC}(p,q) & = & \frac{1}{2} \left[A(p^2) + A(q^2)\right]
                       \gamma_\mu           \nonumber \\
& + & \frac{(p + q)_\mu}{(p^2 - q^2)}\left\{ \left[A(p^2) - A(q^2)\right]
       \frac{\gamma\cdot p + \gamma\cdot q}{2} - 
          i \left[B(p^2) - B(q^2)\right] \right\},  \label{BCver}\end{aligned}$$ and $\Gamma_\mu^{\rm T}(p,q)$ is an otherwise unconstrained piece satisfying the conditions $(p - q)_\mu \Gamma_\mu^{\rm T}(p,q) = 0$ and $\Gamma_\mu^{\rm T}(p,p) = 0$.

We mention two well studied vertex Ansätze falling within this class. The first of these, introduced by Curtis and Pennington [@CP90] to ensure multiplicative renormalisability in quantum electrodynamics, is defined by setting the transverse piece $\Gamma_\mu^{\rm T}$ equal to $$\Gamma_\mu^{{\rm T}_{\rm CP}}(p,q) = \frac{A(p^2) - A(q^2)}{2d(p,q)} 
    \left[\gamma_\mu(p^2 - q^2) - (p + q)_\mu 
              (\gamma\cdot p - \gamma\cdot q ) \right], \label{CPTr}$$ with $$d(p,q) = \frac{(p^2 - q^2)^2 + \left[ M^2(p^2) + M^2(q^2)^2 \right]^2}
               {p^2 + q^2} ,$$ where $M = B/A$.

The second of these, proposed by 