Ambiguity in assigning intrinsic parity We know that, fermions can have intrinsic parity either $\eta_P=+1$ or $=-1$. How does one then fix the intrinsic parities ofthe elementary particles, uniquely? Again, the intrinsic parity of a baryon is the product of the intrinsic parities of the quarks. But unless one can fix the intrinsic parity of the quarks, uniquely, it remains ambiguous. Should we take $\eta_P=+1$ for all of them or $\eta_P=-1$ for all of them? How to fix this?
 A: If you're referring to elementary fermions (described by the Dirac equation), there is no ambiguity: fermions have an intrinsic parity +1 while antifermions have -1. This is easy to establish by starting from the Dirac equation, you deduce that the parity operator is $\gamma^0$ and using the general solutions for spinors $u$ (particles) and $v$ (anti-particles) you can check that:
$$u(-\vec{p}) = \gamma^0 u(\vec{p}), ~~~v(-\vec{p}) = -\gamma^0 v(\vec{p})$$
hence, the sign of the intrinsic parity. 
For the parity of the baryons, it's not so straightforward because it is defined as the product of the intrinsic parity of the 3 quarks (giving +1) and the product of the angular momentum between 2 of the 3 quarks (giving $(-1)^{l_{1,2}}$) and the angular momentum between the third and the barycenter of the first 2 (giving another $(-1)^{l_{3,1-2}}$).
A: According to the CPT thoerem, the choice of positive parity for particles and negative parity for antiparticles is just as arbitrary as the choice of positive charge for protons and negative charge for electrons.
