Compton Scattering Feynman diagram integral expression

I'm trying to write down the integral expression according to the feynman-rules for this Diagram of an electron with compton scattering and a one-loop correction:

Feynman Diagram http://s8.postimg.org/qd1n6zt9v/DSCN9963.jpg ![Compton Scattering][1]

$$(-ie)^4\int \frac{d^4k}{2\pi} \gamma_{\mu}\frac{i}{p-k-m+i\epsilon}\gamma_{\nu}\frac{-ig^{\mu \nu}}{k^2 + i \epsilon}\gamma_{\sigma}\frac{-ig^{\sigma\rho}}{k_1^2+i\epsilon}\frac{i}{p+k_1-m+i\epsilon}\\\gamma^{\alpha}\frac{-ig^{\alpha \beta}}{k_2^2+i\epsilon}\frac{i}{p+k_1+k_2-m+i\epsilon}$$

Is that somehow correct? I have the impression that the indices are not balanced. Is it correct that i only integrate over the first part with the loop?

From right to left:

• outgoing electron $e^-$ spinor: $\bar{u}(p_2)$
• QED vertex: $ie\gamma^\nu$
• outgoing photon: $e^*(k_2)$
• electron propagator: $\frac{i}{\not{q}-m+i0}$
• incoming photon: $e(k_1)$
• QED vertex: $ie\gamma^\mu$
• incoming electron $e^-$ spinor: $u(p_1)$

There is no photon propagator in this process, and also, only one electron propagator. You should rewrite your expression since it's wrong.

• So for the diagram without the photon loop, I get: $(ie)^2 u(p+k_1+k_2) \gamma^{\nu}e^{*}(k_2) \frac{i}{\gamma^{\nu}(p+k_1)-m+i\epsilon} e(k_1)\gamma^{\mu}u(p)$ ... is that correct? Commented Jun 20, 2015 at 10:47
• Yes. It's correct. And there is no integral here. But when there exist a loop correction in Compton scattering, you should insert a loop integral in this amplitude. That integral will be divergent. To deal with this divergence, you should use one of regularization methods, and then renormalization. Commented Jun 20, 2015 at 12:45
• @LêDũng I am under impression that OP is trying to calculate loop corrections, not the tree-level diagram. Commented Jun 20, 2015 at 12:55
• Can you load your diagram again? I cannot see your diagram Mechanix Commented Jun 20, 2015 at 12:59
• i was trying to add a picture from here: s8.postimg.org/qd1n6zt9v/DSCN9963.jpg That's my diagram. The only difference is that i have a loop correction in the incoming electron. Commented Jun 20, 2015 at 13:02