Correct Feynman rules for one loop diagram?

[CAF123]

Consider the diagram attached for the process quark + quark -> photon + quark + quark. I want to check I have the correct expression for the amplitude for this process by using the Feynman rules. $i,j,m,n,l,p$ are colour indices. $k$ is the loop momentum. I don't care about overall factors of -1 or i. All momenta are incoming.

$$\mathcal M = e_q g_s^4 \int \frac{d^dk}{(2\pi)^d} \left( \bar u(-p_5) \gamma^{\nu} t_a^{jl} \frac{\not k + \not p_4 + m}{(k+p_4)^2 - m^2} \gamma^{\delta} \frac{\not k + m}{k^2-m^2} \gamma^{\mu} t_b^{il} v(-p_3) \right) g^{\nu \rho} g^{\mu \sigma} \frac{1}{(k+p_4+p_5)^2 (k-p_3)^2} \times \left(\bar u(-p_2) \gamma^{\rho}t_a^{mp} \frac{-(\not k + \not p_4 + \not p_5 + \not p_2) + m}{(k+p_4+p_5+p_2)^2-m^2} \gamma^{\sigma}t_b^{np} u(p_1)\right) \epsilon_{\delta}(p_4)$$

(I think) the structure there is correct but, in particular, I just wanted to check that the order in which I write down the two fermion lines doesn't matter? Because the part in each brackets is just 1x1 (a number) so commutes with the other. Basically I am using software that will do all these types of integrals for me but to begin with I want to evaluate one by hand and check my results with what the software gives me.

Thanks!

 

[LightHero]

Yes, the order in which you write down the two fermion lines does not matter. This is because the part in each bracket is a number and therefore commutes with the other. As long as you are consistent with your notation, the order of the fermion lines will not affect the amplitude.