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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?

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

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

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