Working principle of symmetry operations of a system with given physical situations

In the book I read some explanations about symmetry of a system.

We can make an experiment using lambda particle, A^. A^ can disintegrate into one proton and one pion - A^ and proton have same spin state, and pion doesn't have any spin. By conservation of momentum, when the proton moves toward (0,0,+z) direction the pion will move toward (0,0,-z) direction. Then we now have two choices - A^ spin up/down.

(1) // A^ (spin up) → proton (spin up, +z) pion(-z) // probability amplitude of disintegration : a

(2) // A^ (spin down) → proton (spin down, +z) pion(-z)// probability amplitude of disintegration : b

The problem is what the book explains -

"The disintegration of (1) is just the reflection - in, say, the yz-plane - of (2). If parity were conserved, b would have to be equal to a or to -a."

Question 1) Because all particles and their spins are located along z-axis, I think reflection in yz-plane cannot change the spin state and this means that (1) cannot become (2). Why (1) is the reflection of (2)?

Question 2) What is the relationship between the conservation of parity and those amplitudes though we cannot determine the parity of the states, (1) and (2) - Odd, Even or No Parity.

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 Welcome, true. We have the MathJax rendering engine active on the site which means that you can write LaTeX alike markup. In particular \Lambda marks up as $\Lambda$. Editing to use MathJax would probably make this more comprehensible. – dmckee♦ Aug 23 '12 at 17:12