I'm trying to calculate the one loop correction to the quark-gluon vertex of QCD using euclidean formalism ($x^0 \rightarrow -ix^4$) and I'm having trouble to compute the integral in the picture below.
where$$ V_{\mu \nu \rho}(k, q, r) = (r − q)_\mu \delta_{\nu \rho} + (k − r)_\nu \delta_{\mu \rho} + (q − k)_\rho \delta_{\mu \nu}. $$
The largest order in $\epsilon = 4-D\simeq0$ should be $$\frac32C(G)t^a\gamma_\mu \frac{g^2}{8\pi^2 \epsilon}
$$ using the fact that $$i f_{abc}t^bt^c=\frac{C(G)}{2}t^a$$ for $SU(N)$. The problem is that in my calculations there's an extra $i$ in front of the result, which comes from the fermion propagator and I don't understand how to get the correct solution. The integral is already in euclidean form so there shouldn't be any $i$ coming from it, in fact I've never had this problem in all other diagrams that I've calculated.
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