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I Correct Feynman rules for one loop diagram?

  1. Jun 5, 2017 #1

    CAF123

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    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!
     

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  3. Jun 10, 2017 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
     
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