- #1
GL_Black_Hole
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- 0
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.