In the Compton scattering quark($p_1$) + gluon ($q_1$)-> quark($p_2$) + gluon($q_2$), there is three gluon vertex contribution. If we choose the physical polarisation sum $\sum_{\lambda} \epsilon^a(\lambda) \epsilon^{*b}(\lambda)=-g^{ab}+\frac{(p_1^a q_1^b+p_1^b q_1^a)}{(p_1.q_1)}$ for the incoming gluon, and $\sum_{\lambda} \epsilon^a(\lambda) \epsilon^{*b}(\lambda)=-g^{ab}+\frac{(p_2^a q_2^b+p_2^b q_2^a)}{(p_2.q_2)}$ for the outgoing gluon. Then, how does this affect the propagator of the virtual gluon in the three gluon vertex? should it be $\frac{-i g_{ab}}{(q_1-q_2)^2}$ ?


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