implies that all dimensionful constants enter through the parameterization of the gluon two-point function, $D$. Here the infrared contribution to this quantity is characterized by an effective strength, $\eta $, and an effective range, $R_0$, in addition to the known ultraviolet form.

The motivation for employing the ladder approximation is provided by the following arguments. First, it offers an EM gauge-invariant description. Both the Ward-Takahashi identity (WTI), $$q_{\mu }\Gamma _{\mu }(P,q)=G^{-1}(P_{-})-G^{-1}(P_{+}),\label{WTI}$$ and the Ward identity (WI), $$\Gamma _{\mu }(P,0)=-\frac{\partial G^{-1}(P)}{\partial P_{\mu }}, \label{WI}$$ are satisfied by this approximation. This is easily demonstrated by directly substituting (\[WTI\]) or (\[WI\]) into (\[IBS\]) for the vertex, and employing (\[SDE\]). Further, it has been shown recently how gauge invariance at the quark level in the ladder approximation to the QPV fits into a gauge-invariant description of composite mesons leading to WTIs at the hadronic level[@frank94].

Second, in the vicinity of a $q\bar{q}$ resonance, the vertex obtains the form $$\Gamma _{\mu }(P,q) \approx \frac{M_V^2}{q^{2}+M_{V}^{2}}\Omega _{\mu
}(P,q),\label{pole}$$ where $\Omega _{\mu }$ is the residue at the pole, and from (\[IBS\]) satisfies $$\Omega _{\mu }(P,q)=-\frac{4}{3}g^2\int \frac{d^4K}{(2\pi
)^4}D(P-K)\gamma _{\nu }G(K_{+})\Omega _{\mu }(K,q)G(K_{-})\gamma _{\nu
},\label{BS}$$ for $q^2=-M^2_V$. This is the homogeneous Bethe-Salpeter equation in the ladder approximation for a 