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I don't understand how to solve this:

A $\pi^+$ decays into a muon and neutrino. Find the pion's energy if

  • max $E_\nu$ / min $E_\nu$ = 100/1;
  • $m_\nu = 0$
  • $m_\pi*c^2 = 140\text{ peta-eV}$
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The question seems to be ill-stated. Among the problems: $m_{\pi} c^3$ is not an energy; giving us a ration of maximum to minimum energy for a particle suggest that you are not analyzing a decay but a large number of ill-measured decays. Just what is the question here? –  dmckee May 20 '12 at 15:37
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BTW, welcome to Physics.SE. We have the MathJax rendering engine on the site, so you can write mathematical expressions in LaTeX style markup. I've done that for you text. You'll find a minimum of notes in the FAQ and the web can yield much more. –  dmckee May 20 '12 at 15:41
    
in a bunch of piones there is a disintegration hurriedly on muons and neutrino. find energy of a pion if it is known that the maximum and minimum energy at disintegration born neutrino belongs as 100:1. –  sleepy May 20 '12 at 15:43
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closed as off-topic by Jerry Schirmer, tpg2114, akhmeteli, Dimensio1n0, John Rennie Nov 9 '13 at 7:59

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1 Answer

Here's the deal. The energy of the decay products depends only on the emission angles in the laboratory frame (they always come out back-to-back in the decay frame).

First, recall that you must conserve four momentum at the vertex, and that you can look up the mass the muon (and you've been given masses for the pion and the neutrino [1] ).

So, draw the kinematics for the most and least energetic neutrino emissions (this is the part the problem expects you to think about, the rest is mechanical computation); express the neutrino energies in terms of only the masses and the pion energy; form the ratio, equate it too 100 and solve for $E_\pi$.

Done.


[1] What happens if you use the pion mass from the PDG, instead? If you allow that the neutrino actually has some mass less than 1 eV? Are these approximations reasonable?

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thanks for your answer))) i'll try to understand :). tomorrow examination and i feel i dont't understand anything in mechanics >< –  sleepy May 20 '12 at 16:10
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