Ultra-Relativistic Particle Decaying to Identical Particles

[GL_Black_Hole]

Homework Statement

Show that it is impossible for an ultra-relativistic particle with $pc>>Mc^2$ to disintegrate into two identical massive particles of mass m.

Homework Equations

Conservation of four momentum

The Attempt at a Solution

The four momentum of the ultra-relativistic particle in its rest frame is $p^{\mu} = (M,0)$ and the decay products will have identical energy and momenta so writing the four momentum of the second particle in terms of the first and the parent particle: $p_2^{\mu} = p^{\mu} -p_1^{\mu}$ we can take magnitudes and find: $-m^2+m^2 = -M^2 +2ME$ where $E$ is the energy of the decay products. So $E =M/2$ and the magnitude of the daughter's four momenta are: $|p| = \frac{\sqrt{M^4 -4M^2 m^2}}{2M}$.
I don't see how to use the ultra-relativistic condition to reach a contradiction here.

 

[Orodruin]

The question is wrong or missing information. You can always go to the rest frame of the decaying particle so whether it is ultra relativistic or not is irrelevant. The only relevant thing is whether or not M > 2m.