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Decay rate of a scalar particle under scalar/pseudoscalar lagrangian

by torus
Tags: decay, lagrangian, particle, rate, scalar
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Mar18-09, 09:18 AM
P: 21
I'm trying to solve problem 48.4 of Srednickis QFT-Book. It goes something like this:

1. The problem statement, all variables and given/known data
We have a scalar field with mass M and a Dirac field with mass m (M>2m). The interaction part of the lagrangian is
[tex]L_a = g \varphi \bar{\Psi}\Psi[/tex]
[tex]L_b = g \varphi \bar{\Psi}i\gamma_5 \Psi[/tex].
Now the decay rates [tex]\Gamma_{a/b}[/tex] of the process [tex]\varphi \rightarrow e^+ e^-[/tex] are to be calculated and compared. It turns out [tex]\Gamma_b > \Gamma_a[/tex], which should now be explained in light of parity/angular momentum conservation.
2. Relevant equations

3. The attempt at a solution
I did all the calculations but I am having a hard time with the explanation. I know that [tex]L_a/L_b[/tex] is scalar/pseudoscalar under parity, but I don't see why this should affect the decay rate.

Any help is welcome.

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