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Tau lepton decay problem - weird answer?

  1. Nov 23, 2009 #1
    Hi,
    I've got a tauon weak-decaying into a charged pion and a neutrino. The tauon has total energy [tex]\ E_{\tau} = 2.5GeV[/tex], rest mass [tex]\ m_{\tau} = 1.777GeV/c^2[/tex], and the pion has rest mass [tex]\ m_{\pi} = 0.1396GeV/c^2[/tex].
    This is everything I am told.
    I have to find the maximum energy the pion can have after the decay.

    So, what I said was that the pion will get the most energy by retaining all of the tauon's momentum, ie.

    [tex]\ p_{\tau} = \sqrt{E_{\tau}^2 - m_{\tau}^2} = p_{\pi} = 1.758GeV/c[/tex]

    and so [tex]\ E_{\pi} = \sqrt{p_{\pi}^2 + m_{\pi}^2} [/tex]

    This gives me the result that [tex]\ E_{\pi} = 1.764GeV [/tex].
    However, the neutrino that is also produced has a tiny mass and I have assumed it to have zero momentum, so where has most of the 2.5GeV tauon energy gone?

    I had 2.5GeV before the decay, but now I have not much more than 1.764GeV after the decay, so where has the rest of this energy magically disappeared to?

    Thanks.
     
  2. jcsd
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