What is the Speed of the CM Frame in Particle Decay?

In summary, we are given a problem where a particle with mass M decays into two daughter particles, one of which is produced at rest in the Lab frame. Using the conservation of 4-momentum and the relativistic energy momentum relation, we can find the energy of the parent particle in the Lab frame. We are also asked to show that the speed of the CM frame, vcm, is equal to 0.6c. By finding the energies and velocities of the two daughter particles in the CM frame and assuming no energy loss, we can deduce that vcm must be equal to 0.6c.
  • #1
Katie1990
6
0

Homework Statement



A particle of mass M, traveling horizontally through the laboratory, decays into two daughter
particles, each of mass 0.4M. One of the daughters, A, is produced at rest in the Lab frame.

Show that vcm , the speed with which the CM frame moves in the Lab frame, is equal to
0.6c, and find the energy of the parent particle in the Lab frame.

Homework Equations



Conservation of 4-momentum, Relativistic energy momentum relation


The Attempt at a Solution



I have found the energys and velocities of the two daughter particles in the com frame, but am unsure how to show that Vcm is equal to 0.6c. I tried finding the energy by writing the momentum of the the stationary daughter as p1 = P - p2 and finding the square of that then rearranging to get energy but this didn't work.
 
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  • #2
Hi Katie1990! :smile:

If the speed is v, what is the energy of the two 0.4M particles?

Then assuming no energy is lost, what must v be? :wink:
 

FAQ: What is the Speed of the CM Frame in Particle Decay?

1. What is particle decay using 4-momentum?

Particle decay using 4-momentum is a process in which a particle decays into two or more smaller particles, while conserving momentum and energy. This is described by the 4-momentum vector, which takes into account the particle's mass, energy, and momentum in all directions.

2. How is 4-momentum used to describe particle decay?

4-momentum is used to describe particle decay by taking into account the conservation laws of energy and momentum. The initial 4-momentum of the parent particle is equal to the sum of the 4-momentum of the daughter particles after decay.

3. What types of particles can undergo decay using 4-momentum?

Any type of particle can potentially undergo decay using 4-momentum, as long as it is unstable and has enough energy to produce the daughter particles. This includes both elementary particles, such as quarks and leptons, and composite particles, such as mesons and baryons.

4. How is particle decay using 4-momentum important in particle physics?

Particle decay using 4-momentum is important in particle physics as it helps us understand the fundamental properties of particles, such as their mass and spin. It also plays a crucial role in the study of the Standard Model, as it allows us to test its predictions and search for new particles.

5. Can particle decay using 4-momentum be reversed?

In theory, particle decay using 4-momentum can be reversed if the daughter particles are recombined with enough energy. However, this is not a common occurrence in nature and is typically only observed in high-energy particle collisions. In most cases, particle decay is an irreversible process.

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