Parity violation in lambda baryon decay

[Veles]

Homework Statement

In the weak decay of the lambda baryon to a proton and pion, parity is not conserved, allowing for s and p waves in the orbital wave function of the pion-proton system. Using non-relativistic wavefunctions, find the angular distribution of the protons relative to the lambda's spin, which points along the z-axis.

2. Homework Equations

The Attempt at a Solution

Define the z'-axis as the direction of the proton's momentum.
Define L_z' as the projection of the orbital angular momentum of the pion-proton system along z'.
Define s_z' as the projection along the z'-axis of the proton's spin.
Define J_z' as the total angular momentum along z'.

J_z' can be +1/2 or -1/2 (so J=1/2, and angular momentum is conserved).
Therefore the following combinations of [L_z', s_z'] are allowed: [1, -1/2], [0,1/2], [0,-1/2], [-1, 1/2].

Chirality is conserved at the weak interaction vertices. However, as it is the constituent quarks interacting, not the proton/baryon, I can't see what limitations this places on the chirality of the proton.

 

[member 553083]

I then thought that I could use the Wigner-Eckart theorem to find the angular distribution, but I'm not sure how. As I understand it, the general form for transition matrix elements is given by <J_fM_f|T_q^q|J_iM_i> = (-1)^(j_i - m_i)<j_f || T_q^q || j_i> * <m_f || j_f, m_i>where T_q^q is the operator given by the weak interaction. However, I don't know how to relate this to the angular distribution of the proton. Any help would be greatly appreciated.