# How to find theoretically the decay width of a particle-decay process? [closed]

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, GertAug 18 at 23:43

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• en.wikipedia.org/wiki/Particle_decay#Decay_rate – G. Smith Aug 6 at 18:58
• What is your conceptual problem with three particles in the final state? – G. Smith Aug 6 at 19:01
• How to calculate the amplitude $|M|^2$? – Daniel Vainshtein Aug 6 at 19:30
• Can you draw the Feynman diagram? Have you learned how to write the amplitude for a Feynman diagram? – G. Smith Aug 6 at 19:33
• 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? – Daniel Vainshtein Aug 7 at 5:00