(I am at the introductory level of particle physics)
I know that the parity is conserved in strong and electromagnetic interaction, so I would like to show that the charge parity is violated.
I would like to show that the product of the charge conjugation parity of proton and its antiparticle is $-1$, which doesn't equal to the charge parity of $\pi^0 + \pi^0$
problem I have encountered:
by definition $\hat C |p, \Psi\rangle = C_p |p,\Psi\rangle$ and $\hat C |p, \Psi\rangle = |\bar p,\Psi\rangle$ then $\hat C^2 |p, \Psi\rangle = C_p^2 |p,\Psi\rangle = |p,\Psi\rangle = C_\bar p |\bar p,\Psi\rangle$
applying $\bar C$ once again
$C_p|p,\Psi\rangle = C_\bar p |\bar p,\Psi\rangle \implies C_p = C_\bar p \implies C_pC_\bar p = 1$ which doesn't lead to the result I wanted.
What went wrong for me?