2
$\begingroup$

I want to work out in detail the paper by Lavoura to get some real practice as a beginning student. I have stumbled upon several problems as I am moving along with the arguments. Firstly, I am not yet sure how to write down or guess the very general form of the amplitude, equation (1). Next I have trouble working out the self-energy type diagrams where the photon attaches itself with the external fermions. My calculation immediately gives me a divergent answer, and there is no finite part left to be extracted from the self-energy diagrams. However, the paper says that the divergence in the self-energy diagrams will exactly cancel the divergence in the three-point diagrams and there must be some additional finite part from the self-energy type diagrams that will be added to the contribution from the other diagrams. This isn't making sense to me.

Improve this question
$\endgroup$
4
  • $\begingroup$ The reaction you wrote isn't even possible by the way as QED conserves lepton number. Did you mean $e\to e\gamma$? $\endgroup$
    – Triatticus
    Commented Apr 4 at 19:55
  • $\begingroup$ @Triatticus Your alternative $e\to e\gamma$ can't conserve energy in the rest frame of the initial electron. The decay in the question, $\mu\to e\gamma$, does preserve lepton number. It doesn't separately conserve lepton flavor, like the more familiar leptonic decay $\mu\to e\nu\bar\nu$. However, flavor is well-known to be non-conserved in the neutrino sector, so there should be some (very small) branching ratio for a decay without the neutrino pair in the final state. $\endgroup$
    – rob ♦
    Commented Apr 6 at 13:04
  • 1
    $\begingroup$ @rob I'm aware of the energy concerns, and I didn't catch in time that I said lepton and not muon/electron number unfortunately much longer after I commented. I'm guessing the reaction is muon $\to$ electroweak blob $\to$ some final state fermions including real radiation. $\endgroup$
    – Triatticus
    Commented Apr 6 at 13:49
  • $\begingroup$ @Triatticus No I meant what I mentioned. This is possible in BSM scenarios, $\endgroup$
    – Hubert John
    Commented May 28 at 17:17

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.