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Hello, for my bachelor thesis I have to calculate $|M|^2$ of this Feynman diagram. However, I have no understanding of QFT so far. I was told to just look up the Feynman rules and put them to use. As expected, using the Feynman rules without properly understanding the underlying formalism turned out to be rather difficult. Based on the example of $e^-e^- \rightarrow \mu^-\mu^-$ given in the book of Peskin&Schroeder I tried to write down the amplitude of the given process as follows: $u(p)(ig\gamma^{\mu}t^a)\bar{u}(p´)(-\frac{ig_{\mu\nu}}{p^2+i\epsilon})u(k)(ig\gamma^{\mu}t^a)\bar{u}(k´)$
Does this make some sense at all? For the main part I am not sure about the positioning of the fermions and if the propagator is right. I am really thankful for any sort of help since I am just getting started with the topic of QFT.

minits
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  • The $\bar u$ (which you can think of as a row vector in “spinor space”) should be to the left of the $\gamma$ matrix, because the amplitude must be just a single complex number. – G. Smith Mar 26 '21 at 22:26
  • The propagator is not that of a massive boson. You’ve got to have the mass of the $W$ in there. – G. Smith Mar 26 '21 at 22:31
  • The vertexes aren’t right for the weak interaction. – G. Smith Mar 26 '21 at 22:35
  • This question is overly broad. You need to break down your understanding into smaller pieces, such as what is the $W$ propagator, what is the $\bar qWq$ vertex, what is $t^a$, etc. – G. Smith Mar 26 '21 at 22:37
  • And first you should completely understand how to compute, say, electron scattering in QED. Then focus on how the weak interaction is different from EM. – G. Smith Mar 26 '21 at 22:39
  • I also encourage you to calculate an amplitude like this in two different ways: the abstract, formal way you see on textbooks, with traces of gamma matrices, etc., and an explicit approach where you know, for example, what every component of every spinor and every matrix is, and basically “multiply it out” and do your own spin-averaging. – G. Smith Mar 26 '21 at 22:46
  • Thanks a lot for your tips. I will try to follow your advice and make the small steps necessary to tackle the bigger problems. – minits Mar 26 '21 at 22:50

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