Ultra-Relativistic Particle Decaying to Identical Particles

In summary, it is impossible for an ultra-relativistic particle with ##pc>>Mc^2## to disintegrate into two identical massive particles of mass m, regardless of the ultra-relativistic condition. This is due to the fact that the energy of the decay products is always equal to half of the parent particle's mass, which cannot be greater than 2m. Therefore, the question is either incorrect or missing important information.
  • #1
GL_Black_Hole
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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.
 
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  • #2
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.
 

FAQ: Ultra-Relativistic Particle Decaying to Identical Particles

What is an ultra-relativistic particle?

An ultra-relativistic particle is a particle that travels at speeds close to the speed of light, typically above 0.99c. These particles have high energies and can only be accurately described by Einstein's theory of relativity.

What is particle decay?

Particle decay is the process by which a particle spontaneously transforms into one or more different particles. This can occur due to the instability of the particle or through interactions with other particles.

What are identical particles?

Identical particles are particles that cannot be distinguished from one another, even in theory. This means that they have the same properties and behave in the same way. Examples include electrons and photons.

What is the significance of a particle decaying to identical particles?

When a particle decays into identical particles, it allows for the conservation of certain physical quantities, such as energy and momentum. This can provide valuable information about the initial particle and its properties.

How do scientists study ultra-relativistic particle decay to identical particles?

Scientists use particle accelerators to create and observe ultra-relativistic particles and their decays. These decays can also be studied through high-energy collisions in these accelerators. The resulting data is analyzed using mathematical models and simulations to understand the behavior of these particles.

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