# QCD gluon physical polarisation sum in the three gluon vertex

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 $$\frac{-i g_{ab}}{(q_1-q_2)^2}$$ ?