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

by torus
Tags: decay, lagrangian, particle, rate, scalar
 P: 21 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

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