The problem is devided into two parts:

First part: There is an interaction Lagrangian for real scalar fields given by L=$\lambda_1 \phi_1 \phi_2\phi_3+\lambda_2\phi_1^2\phi_3$. I need to know how to calculate the decay width of the process $\phi_2 \to \phi_1\phi_1\phi_1$. I know that there are 2 vertices with corresponding couplings $\lambda_2,\lambda_1 $ and that $\phi_3$ is an internal line. However, I never seen any calculation of amplitude including the decay of one particle to three.. (only similar case of coupled quantum harmonic osciilators but this not quiet the problem).

Second part: Kind of the same problem but now this is decay of the lepton tau particle as: $\tau \to \nu_{\tau}+ \hat\nu_{e}+e$. Now the propogator is $W^{-}$ gauge boson, and we have two vertices with corresponding coupling for each - $\frac{g}{\sqrt2}$. The problem is similar: how to calculate the amplitude?


closed as off-topic by G. Smith, Jon Custer, ZeroTheHero, Aaron Stevens, Gert Aug 18 at 23:43

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. We want our questions to be useful to the broader community, and to future users. See our meta site for more guidance on how to edit your question to make it better" – G. Smith, Jon Custer, ZeroTheHero, Aaron Stevens, Gert
If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ en.wikipedia.org/wiki/Particle_decay#Decay_rate $\endgroup$ – G. Smith Aug 6 at 18:58
  • $\begingroup$ What is your conceptual problem with three particles in the final state? $\endgroup$ – G. Smith Aug 6 at 19:01
  • $\begingroup$ How to calculate the amplitude $|M|^2$? $\endgroup$ – Daniel Vainshtein Aug 6 at 19:30
  • $\begingroup$ Can you draw the Feynman diagram? Have you learned how to write the amplitude for a Feynman diagram? $\endgroup$ – G. Smith Aug 6 at 19:33
  • $\begingroup$ Yes, but this type of diagrams I donwt understand from where to where the momentum go in the graph? and does I need to multiply at each vertice coupling as the harmonic osccilator? $\endgroup$ – Daniel Vainshtein Aug 7 at 5:00

enter image description here

For the first part, I think this is what you want to ask. In any case, the couplings should be in the vertices.


Not the answer you're looking for? Browse other questions tagged or ask your own question.