# Decay rate of a scalar particle under scalar/pseudoscalar lagrangian

1. Mar 18, 2009

### torus

Hi,
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
$$L_a = g \varphi \bar{\Psi}\Psi$$
$$L_b = g \varphi \bar{\Psi}i\gamma_5 \Psi$$.
Now the decay rates $$\Gamma_{a/b}$$ of the process $$\varphi \rightarrow e^+ e^-$$ are to be calculated and compared. It turns out $$\Gamma_b > \Gamma_a$$, 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 $$L_a/L_b$$ is scalar/pseudoscalar under parity, but I don't see why this should affect the decay rate.

Any help is welcome.

Regards,
torus