Proton anti-proton pair and CP eigenstate

[merrypark3]

$p\bar{p}$ pair is a CP eigenstate?

As $p$ and $\bar{p}$ are fermions (the pair is assumed to be at S-state), the pair seems to be C's eigenstate with eigenvalue of -1.

As they have opposite intrinsic parity, the pair state seems to be P's eigenstate with eigenvalue -1. Then isn't it CP eigenstate with eigenvalue of 1?

But why the $p$$\bar{p}$ pair cannot produce $K_S$ or $K_L$ but only $\bar{K}^0$?

 

[Vanadium 50]

pbar-p pair is a CP eigenstate?

Not necessarily. The rest of the message assumes this, so there's no point in commenting on it.