There are two definitions of the parity transformation acting on the Dirac spinors: $\Psi_P = \eta \gamma^0 \Psi$ with $\eta = i$ ($P^2=-1$ as in Srednicki) and $\eta=1$ ($P^2=+1$ as in Peskin & Schroeder).
Both definitions result in the same parities of the sesquilinear forms such as $\bar\Psi \Phi$.
However, the bilinear form $\overline{\Psi_C} \Phi$ (à la pseudoscalar diquark) is scalar under $P^2=-1$ inversion and pseudoscalar under the one with $P^2=+1$, since $\Psi_{CP} = -\eta^* \gamma^0 \Psi_C$; $C$ is charge conjugation.
Does it mean that the two definitions are physically inequivalent (and $P^2=-1$ is incorrect)?
Or...
Do I miss something that makes $\overline{\Psi_C} \Phi$ a pseudoscalar even for $\eta = i$?