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Decay rate of a scalar particle under scalar/pseudoscalar lagrangian 
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#1
Mar1809, 09:18 AM

P: 21

Hi,
I'm trying to solve problem 48.4 of Srednickis QFTBook. 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. Regards, torus 


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