# 3body decay and lorentz factor question

1. Aug 25, 2010

### mxbob468

I'm working on the decay width of a 3body decay with my professor, I'm stuck and he's not being forthcoming.

P1->P2+P3+P4

So I calculate the amplitude using FeynCalc and the form of the interaction vertex he gave me and I get this huge expression (~7000 terms) with dot products.

So I re-express all dot products in terms of masses of the particles and q2=(p1-p2)2 (p1 and p2 are 4 momenta).

So now I have to boost back to the lab frame, since the calculation is done in the rest frame of P1. This leads to my problem. In the rest frame of P1 the 4 vector dot products with p1 are just p10p20 (for example) = mP1mP2$\gamma_{P2}$.

Expressing this $\gamma_{P2}$ in terms of either masses or q2 or something like that is what I need to do and he tells me I need to:

"Start by having the parent particle at rest, and it decays to 2 particles, the daughter baryon, and the pair of leptons. You can then write down the momenta of these two particles. Then you let the 'pair of leptons' particle decay into the individual leptons, and you can again write down their momenta in their cm frame. Then you boost these cm momenta back into the overall cm frame. That's how you get he gamma factors."

and I don't understand what "boost these cm momenta back into the overall cm frame" really means? Does he want me to use a Lorentz transformation on the 3momenta that gamma is a function of?