20 samples of 1000000 points each. We find that both results agree very well. Numerical values of $v_\Gamma$ are presented in Table \[tab:4fermi\] as a function of $M$.

We have to also calculate the corresponding continuum wave-function renormalization factor and vertex corrections in the ${{\overline {\rm MS}}}$ scheme employing the same gauge and the same infrared regulator as the lattice case. For the present calculation it seems preferable to choose Dimensional Reduction(DRED) as the ultraviolet regularization, in which the loop momenta of the Feynman integrals are defined in $D<4$ dimensions while keeping the Dirac matrices in four dimensions. In the DRED scheme we can use the same calculational techniques for the vertex corrections as the lattice case thanks to applicability of the Fierz transformation for the Dirac matrices. For the wave-function renormalization factor a simple calculation gives $$Z_2^{{{\overline {\rm MS}}}} = 1+ \frac{g^2}{16\pi^2}C_F \left[
\log (\lambda/\mu)^2 -1/2\right],$$ where $\mu$ is a renormalization scale. This result leads to $\Sigma_1^{{{\overline {\rm MS}}}}=-1/2$. For the vertex corrections we obtain $$V_\Gamma^{{{\overline {\rm MS}}}} = 1+\frac{g^2}{16\pi^2} \delta_\Gamma \left[
-\log (\lambda/\mu)^2 +1\right],$$ giving $v_\Gamma^{{{\overline {\rm MS}}}}=\delta_\Gamma$. Here we should remark that the one-loop vertex corrections yield the evanescent operators which vanish in $D=4$ for the DRED 