# Decay of tauon into pion and neutrino

1. Nov 21, 2011

### shroom

Decay of tauon into pion and neutrino....

Hello all.

I have a question.

One of the weak decays of a tauon(energy 20GeV) is to a charged pion(rest mass 139.6Mev/c^2) and a neutrino(take the neutrino to be massless).

What condition results in the maximum energy of the pion after the decay?

Sketch how the decay appears in this case, and calculate the energy.

Attempt at solution.

Ok so I got that in the lab frame, the energy of the pion would be maximised if the neutrino remained stationary. Is this correct? The reason I am questioning is that if I am taking the neutrino as massless, can a massless particle be stationary? Because then by the relativistic relation

E^2=p^2 +m^2 since m is zero and p is zero as it's stationary then it has...well nothing.

Is there something obvious I am missing?

Shroom

2. Nov 21, 2011

### vela

Staff Emeritus
Re: Decay of tauon into pion and neutrino....

If the neutrino is massless, it moves at the speed of light.

3. Nov 22, 2011

### shroom

Re: Decay of tauon into pion and neutrino....

So the neutrino can never be stationary? I thought that would be the case. If this is so, then how do you go about maximising the energy of the pion?

4. Nov 22, 2011

### vela

Staff Emeritus
Re: Decay of tauon into pion and neutrino....

Try analyzing the decay in the center-of-mass frame first.