Helicity problem in decay

Hi I have to calculate the total decay width for a fermion(a) decaying in to a fermion(b) and a scalar. I assumed that I am in the rest frame of the decaying fermion, so the decaying fermion a has no helicity and definite spin 1/2. Now to calculate the total decay rate I need to: 1. Boost the fermion b spinor 1/2 with the helicity operator and then obtain the decay width for λ=1/2. 2. Boost the fermion b spinor -1/2 with the helicity operator and then obtain the decay width for λ=-1/2. 3. Sum the obtained modulus squares of matrix elements. Is it the right approach? I guess if the fermion a does not have any initial helicity the decay product fermion b can have helicity λ= -1/2. Thanks for any help in advance. If there are any ambiguities according to the explanation of my problem I will clarify in the comments.