I'm studying the semileptonic decay of the kaon and I'm currently reading about the Ademollo-Gatto theorem. The question is probably silly. However, here it is.(adsbygoogle = window.adsbygoogle || []).push({});

The proof starts by just considering that [itex][V_-,V_+]=V_3[/itex], where V is the V-spin. Now, we consider the matrix element [itex]\langle K^0|V_3|K^0\rangle=1[/itex].

I understand that the [itex]|K^0\rangle[/itex] state is an eigenstate of V_{3}(is the same thing that happens for the usual isospin), but why exactly 1? Consider for example the third component of isospin. As K^{0}has I_{3}=1/2 I'd expect that matrix element to be 1/2. Why is 1?

Thanks

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# Doubt on Ademollo-Gatto theorem proof

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