How to apply explicit spinor forms for definite helicity fermions

[lefebvre]

Homework Statement

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.

 

[Orodruin]

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