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

[plasmon]

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?

 

[Hepth]

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.

 

[plasmon]

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.