Understanding parity and parity conservation

[center o bass]

I am struggling with the concept of parity. I understand the analogies with spinning balls etc. and that the physics in the mirror should also be found in the world. I also understand that a wavefunction is an eigenfunction of parity if under the parity operator it looks the same. (indicating only that the probability of finding a particle at -r is equal to the probability of finding it at r, or something more?)

What I am not understanding is the leap from this to statements like: parity is conserved in the strong reaction:

$$p + p \to \pi^+ + n + p$$
What does one really mean with such a statement?

It seems one rather arbitrarly assign numbers to the particles on the right hand side and makes sure they agree with the numbers assigned on the left hand side (which was assigned so that they agreed with the numbers on the right hand side).

In the texbook 'Introduction to high energy physics I read:
"In strong as well as electromagnetic interactions, parity is found to be conserved.
This is true, for example, in the strong reaction
$$p + p \to \pi^+ + n + p$$
in which a single boson (pion) is created. In such a case, it is necessary to assign an intrinsic parity to the pion in order to ensure the same parity in initial and final states, in
just the same way that we assign a charge to the pion in order to ensure charge
conservation in the same reaction. As shown below, the intrinsic parity is P(pi) = -1.
What about the intrinsic parities of the proton and neutron? By convention,
neutrons and protons are assigned the same value, P(n) = + 1. The sign here is
simply due to convention, because baryons are conserved and the nucleon parities
cancel in any reaction."

Here there seem to be a lot of convensions. And the concept of instrinsic parity seems to be important. I've seen some trying to explain this is terms of a free particle wavefunction, where one can see that a free particle is a eigenstate of parity if it has zero momentum.. So one can assign an eigenvalue to the particle in it's restframe. Anyhow, what significance does this have in relation to the reaction above? All the particles are certainly not at rest.

After what I've read my current understanding on the statement above is that;
One observes that parity transformed strong reactions(i.e how a reaction would look like in the mirror also occur in nature), therefore there is a symmetry and thus also a conservation law. One must then find the number being conserved. A canidate is the intrinsic parity of the different particles. Trough the dirac equation one gets the requirement that the composite system of a particle and antiparticle must have parity -1, therefore one assigns +1 to a particle and -1 to it's antiparticle.

How does that sound?

I would really apprechiate if someone could enlighten me on this concept.

BTW: When I assign +1 to proton and neutron and -1 to the pion the parity on the left side is +1 while it is -1 on the other side. It does not seem to be conserved after all? :)

 

[LightHero]

Your understanding of the concept is mostly correct. The statement that parity is conserved in the strong reaction means that the parity (as an intrinsic property) of the particles on the left side of the reaction are the same as the parity of the particles on the right side. For the reaction you mentioned, the parities are indeed conserved since the proton and neutron carry a parity of +1, while the pion carries a parity of -1. In this case, the parities are conserved because of the Dirac equation, which states that the composite system of a particle and its antiparticle must have a parity of -1. In other words, the parity of the particle is related to the parity of its antiparticle in such a way that they cancel out when the two interact. So, by assigning a parity of +1 to the proton and neutron, and -1 to the pion, the parities on the left and right sides of the reaction are equal. In general, parity conservation is a symmetry principle which states that the laws of physics should remain unchanged when spacetime is reflected across a plane. This means that if a reaction occurs in one direction, then the same reaction should also occur in the opposite direction. Thus, for the conservation of parity to hold, the parities of the particles on both sides of the reaction must be equal.