sector this is shown to generate higher order terms of the Lagrangian [@derafael; @Yama]. Yet, if one takes a regulator of the loops integrating to a value $|\vec{q}_{max}|$ and fitting this to data, the consideration of the $q^2/m^2_V$ terms in the vector propagator is unnecessary.

Extending Eqs.  and to the charm sector is easy for the $VPP$ Lagrangian but not for the $VBB$ Lagrangian [@hofmann], but we introduce here a procedure that renders it very easy. For this, let us look at the quark structure of the $\rho^0$, $\omega$ and $\phi$ (which can be extended to $K^*$, $\rho^{\pm}$) $$\begin{aligned}
\label{waves}
\rho^0 &=& \frac{1}{\sqrt{2}} (u\bar{u} - d\bar{d})\, ,\nonumber \\
\omega &=& \frac{1}{\sqrt{2}} (u\bar{u} + d\bar{d})\, ,\nonumber \\
\phi &=& s\bar{s} \, .\end{aligned}$$ In the approximation of taking $\gamma^{\mu} \to \gamma^0$ the spin dependence disappears, and we can consider an operator at the quark level as in Eq. . We can take for instance $$\begin{aligned}
\label{wavep}
\langle p |\,g\,\rho^0\,| p \rangle \equiv \frac{1}{\sqrt{2}}\frac{1}{\sqrt{2}}
\langle \phi_{MS}\, \chi_{MS} + \phi_{MA}\, \chi_{MA} | g \frac{1}{\sqrt{2}} (u\bar{u} - d\bar{d}) |
\phi_{MS}\, \chi_{MS} + \phi_{MA}\, \chi_{MA} \rangle \, , \nonumber\\\end{aligned}$$ where $\phi_{MS}$, $\phi_{MA}$, $\chi_{MS}$, $\chi_{MA}$ are the flavor and spin mixed symmetric and mixed antisymmetric wave functions 