Relativistic Dalitz Plot

[iloveflickr]

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

Decay of particle A into three particles of equal mass, prove that the Dalitz plot is a equilateral triangle with height Q/2, inscribed within a triangle with height Q.

2. Relevant equations

Q = MassA - 3(MassB)

3. The attempt at a solution

For relativistic kinematics, T (kinetic energy) is = E = p (in natural units)

I'm not sure where to go from here. Thanks,

[clem]

The Dalitz plot is not a triangle unless A decays into massless particles, or A is so much heavier than B that Bhas E>>M. Then as you write E~p for each decay particle. Also then, Q=M_A.
The maximum energy of any decay particle is when the other two are in the opposite direction with equal energy. This should get you the maximum energy of any decay particle, which you can relate to the altitude of the triangle.