How to apply explicit spinor forms for definite helicity fermions

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lefebvre
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Homework Statement


Text problem statement, Problem 3: decay width of fermion f(a) into fermion f(b) and spinless particle M, with interaction Hamiltonian H_I(x) = h phi(x) psibar(b)(x) Gamma psi(a)(x) + H.c., and two cases Gamma = I and Gamma = -i gamma^5 asking for decay amplitudes and angular momentum.


Homework Equations

The Attempt at a Solution


I've started from writing out the amplitude. Here I know that fermion has definite helicity so I can't sum over spins but I should input explicit forms of spinors. Am I correct? How to do this?
I would be grateful for helping me with this step. I'll manage the rest of the problem.
 
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Discussion

You insert the expression for a spinor of the appropriate spin. It should be described in your textbook how such a spinor looks.