p_\mu/2)
  -i r \sin(-k_\mu/2 + p_\mu/2) \} \delta_{st},\end{aligned}$$ where $k$ and $p$ represent incoming momentum into the vertex (see Fig. 1 of Ref.[@AIKT98]). $T^A$ $(A=1,\dots,N^2-1)$ is a generator of color SU($N$). The fermion propagator originally takes $N_s\times N_s$ matrix form in $s$-flavor space. In the present one-loop calculation, however, we do not need the whole matrix elements because we consider Green functions consisting of the physical quark fields. The relevant fermion propagators are restricted to following three types: $$\begin{aligned}
&&
{\langle q(-p) {\overline{q}}(p) \rangle} = 
 \frac{-i\gamma_\mu \sin p_\mu + \left(1-W e^{-\alpha}\right) m}
{-\left(1-e^{\alpha}W\right) + m^2 (1-W e^{-\alpha})}
 \equiv S_q(p),
\label{eqn:phys-prop}
\\&&
{\langle q(-p) {\overline{\psi}}(p,s) \rangle} 
=
\frac{1}{F}
\left( i\gamma_\mu \sin p_\mu - m \left(1 -W e^{-\alpha} \right)
\right)
\left( e^{-\alpha (N_s-s)} P_R + e^{-\alpha (s-1)} P_L \right)
{\nonumber}\\&&\qquad
+\frac{1}{F} \Bigl[
m \left(i\gamma_\mu \sin p_\mu  -m \left(1-W e^{-\alpha}\right)\right)
- F \Bigr] e^{-\alpha}
\left( e^{-\alpha (s-1)} P_R + e^{-\alpha (N_s-s)} P_L \right),
\\&&
{\langle \psi(-p,s) {\overline{q}}(p) \rangle} 
=
\frac{1}{F}
\left( e^{-\alpha (N_s-s)} P_L + e^{-\alpha (s-1)} P_R \right)
\left( i\gamma_\mu \sin p_\mu - m \left(1 - W e^{-\alpha} \right)
\right)
{\nonumber}\\&&\qquad
+\frac{1}{F}
\left( e^{-\alpha (s-1)} P_L + e^{-\alpha (N_s-s)} P_R \right) e^{-\alpha}
\Bigl[
m \left(i\gamma_\mu \sin p_\mu  -m\left(1- We^{-\alpha}\right) \right)
- F 