(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider the decay A -> B + C (where A is not at rest). In the rest frame of A, B is emitted in a random direction (all directions have equal probability) and I need to show that in the lab frame, the energy distribution of B is uniform.

(We assume that B has negligible mass)

2. Relevant equations

(Let c=1)

3. The attempt at a solution

So I started by writing down the 4-momenta of A and B in the rest frame of A (choosing the momentum of B to be along the x axis):

P_{A}' = (m_{A},0,0,0)

P_{B}' = (E_{B}',E_{B}',0,0)

In the lab frame:

P_{A}= (E_{A},(E_{A}^{2}-m_{A}^{2})^{1/2},0,0)

P_{B}= (E_{B},E_{B},0,0)

Lorentz boosting along the x-axis, I can determine the maximum and minimum energy that B can have:

[tex]

E_B^{\mathrm{min,max}} = \frac{E_A}{2} \bigg(1-\frac{m_C^2}{m_A^2}\bigg) \bigg(1 \pm \sqrt{1-\frac{m_A^2}{E_A^2}}\bigg)

[/tex]

using:

[tex]

\gamma = \frac{E_A}{m_A}\>,\gamma \beta = \frac{p_A}{m_A},\>E_A' = \frac{m_A^2-m_C^2}{2m_A}

[/tex]

I could also Lorentz boost in all other directions to get expressions for the energy. But I have no idea how to show that each of these energies in equally probable?

Any help would be appreciated.

Thanks!

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# Homework Help: Particle Decay

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