Why does sd replace sγ5d ee in the amplitude of meson decay?

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SUMMARY

The discussion clarifies the transition of the amplitude from M=sγ5d ee in pure leptonic decay of the pseudo scalar meson K→ee to M=sd ee in the semileptonic decay K→π ee. It emphasizes that the K meson and pion both possess negative parity, while the electron pair has positive parity, necessitating a current with negative parity for the decay process. The transition K→π conserves parity, while the K→Vacuum transition in pure leptonic decay violates parity, requiring the inclusion of a parity-violating operator.

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M=sγ5d ee
is the amplitude of pure leptonic decay of pseudo scalar meson(say K→ee), while
M=sd ee
is the amplitude of the semileptonic decay of K→π ee. Kindly explain why does sd replace sγ5d ee in the amplitude?
 
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It's about the parity conservation. The K has negative parity, as does the pion (pseudoscalars). On the right hand side, two electrons have positive parity, so the current should have negative parity, -1*-1=1.

Then for the PS to PS decay you have a final state with negative parity, so only currents with positive parity can contribute.

The gamma5 is negative parity.
 
I understand that the transition K→π conserves parity. While in pure leptonic decay, the quark current transition K→Vacuum does not conserve parity so it must include parity violating operator.
 

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