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

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The discussion focuses on the amplitudes of meson decay, specifically the transition from K to ee and K to π ee. The amplitude M=sγ5d ee represents pure leptonic decay, while M=sd ee pertains to semileptonic decay. Parity conservation plays a crucial role, as both K and pion have negative parity, while the final state of two electrons has positive parity. Consequently, for the PS to PS decay, only currents with positive parity can contribute, leading to the replacement of sγ5d ee with sd ee in the amplitude. This highlights the necessity of including parity-violating operators in the pure leptonic decay transition.
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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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