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I am currently going over this and got me thinking about a scanario where you have A -> BC

Where A is S = 0, L=0, B is S = 1 L=0, C is S=1 L =0

(I'll use S = intrinsic spin, L = angular momentum, J = Total Angular momentum, |L-S|=< J =< L+S)

Maybe such a decay doesn't exist, but I'm just trying to test the "boundaries" of what I know about this topic.

For this reaction to happen the total angular moment must be J=0 (ie 2-2 = 0 as J = 0 on LHS so L=2 on RHS for total system)

[itex]\hat{P}|B> = (-1)(+1)(-1)^{L}[/itex]

L = 0

[itex]\hat{P}|B> = -1[/itex]

and like wise:

[itex]\hat{P}|C> = -1[/itex]

For charge conjugation

[itex]\hat{C}|B> = (-1)^{L+S}[/itex]

[itex]\hat{C}|B> = (-1)^{2} = +1[/itex]

[itex]\hat{C}|C> = (-1)^{2} = +1[/itex]

Now put them together:

[itex]\hat{P}|BC> = (-1)(-1)(-1)^{L}=(-1)^{2}= +1[/itex]

[itex]\hat{C}|BC> = (-1)(-1)(-1)^{L+S} = (-1)^{4} = +1[/itex]

Hence CP:

[itex]\hat{C}\hat{P}|BC> = (+1)(+1) = +1[/itex]

BUT

If we do the LHS using L = 0, S = 0 we get CP(A) = -1

I could be doing these calculations wrong, though this method has worked for easier examples (maybe by chance..). Or maybe it's not suppose to work ...?

[Ps this isn't homework, i'm just reading a book on it!]

Thanks for any help

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# CP Operators Mesons

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