# Desintegration momentum

1. Jan 17, 2014

### boddhisattva

1. The problem statement, all variables and given/known data

Given the desintegration of one particle,

1 -> 2 + 3

then show that

p1^2 = p2^2+p3² + 2cos(theta)*p2*p3

p1: momentum particle to be desintegrated
p2, p3: momentum of the two resulting particles
theta: angle between 2 & 3

2. Relevant equations

3. The attempt at a solution

I tried using conservation of quadrivector

2. Jan 17, 2014

### Polaris

I am curious as to why you attempted this via 4-momentum? Is the text you are working with promote that use?

Anyways, the way I would approach this is a lot simpler, you do not need 4-momentum. Think of this by looking at the conservation of momentum thus,

P1=P2+P3

and it follows that taking the inner product leads to

P1$\cdot$P1 = P12 = (P2+P3)$\cdot$(P2+P3).

Leaving the rest to you. Essentially this is the laws of cosines.