- #1
Einj
- 470
- 59
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.
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 V3 (is the same thing that happens for the usual isospin), but why exactly 1? Consider for example the third component of isospin. As K0 has I3=1/2 I'd expect that matrix element to be 1/2. Why is 1?
Thanks
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 V3 (is the same thing that happens for the usual isospin), but why exactly 1? Consider for example the third component of isospin. As K0 has I3=1/2 I'd expect that matrix element to be 1/2. Why is 1?
Thanks