to each fermion of the loop, and so the effective vertices are calculated with the help of the Feynman rules

$$\begin{aligned}
\chi^{\mu\lambda} &=& \chi^{\mu\lambda}_{(L)} + \chi^{\mu\lambda}_{(R)} = i g_{s} e e_{q} (t^{a})_{{\cal{A}}{\cal{B}}} \left\{ (\gamma^{\mu})_{ij} \left[ \frac{({\not{\hbox{\kern-.3pt $l_{1}$}}}- {\not{\hbox{\kern-1.5pt $q$}}})_{jk}}{(l_{1} - q)^{2}} \right] (\gamma^{\lambda})_{kl} + (\gamma^{\lambda})_{lk} \left[ \frac{({\not{\hbox{\kern-.3pt $l_{1}$}}}- {\not{\hbox{\kern-1.5pt $k$}}})_{kj}}{(l_{1} - k)^{2}} \right] (\gamma^{\mu})_{ji} \right\},\end{aligned}$$

and $$\begin{aligned}
\chi^{\nu\sigma} &=& \chi^{\nu\sigma}_{(L)} + \chi^{\nu\sigma}_{(R)} = i g_{s} e e_{q} (t^{b})_{{\cal{B}}{\cal{A}}} \left\{ (\gamma^{\sigma})_{mn} \left[ \frac{({\not{\hbox{\kern-1.5pt $k$}}}- {\not{\hbox{\kern-.3pt $l_{2}$}}})_{np}}{(k - l_{2})^{2}} \right] (\gamma^{\nu})_{pq} + (\gamma^{\nu})_{qp} \left[ \frac{({\not{\hbox{\kern-1.5pt $q$}}}- {\not{\hbox{\kern-.3pt $l_{2}$}}})_{pn}}{(q - l_{2})^{2}} \right] (\gamma^{\sigma})_{nm} \right\},\end{aligned}$$ \[eff-vertex\]

where the indices obey the assignment as follows: ($\mu, \nu, \sigma, ...$) for the four-vectors, ($a, b$) are the color indices, ($i, j, k, ...$) are the matrix-elements of the four-vectors, and (${\cal{A}}, {\cal{B}}, {\cal{C}}, ...$) for the elements of the color matrices.

Attaching each side of the diagram, there will be two distinct contributions to the fermion loop, which can be computed whether one couples the diagrams in the Fig. \[fig:eff-diag\] at each side of the central line. The product of the diagrams in the left-hand side with the right- ones results in a possible diagram for the fermion loop, being the latter the complex conjugate of 