# Tau lepton decay problem - weird answer?

1. Nov 23, 2009

### jeebs

Hi,
I've got a tauon weak-decaying into a charged pion and a neutrino. The tauon has total energy $$\ E_{\tau} = 2.5GeV$$, rest mass $$\ m_{\tau} = 1.777GeV/c^2$$, and the pion has rest mass $$\ m_{\pi} = 0.1396GeV/c^2$$.
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.

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

and so $$\ E_{\pi} = \sqrt{p_{\pi}^2 + m_{\pi}^2}$$

This gives me the result that $$\ E_{\pi} = 1.764GeV$$.
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.