A positive pion at rest decays to a positive muon and a neutrino. The kinetic energy of the muon has been measured to be T(muon) = 4.1 MeV. The mass of the muon is known from other experiments to be 105.7 MeV. Find the mass of the pion. Do this nonrelativistically, and then repeat your calculation relativistically.
Nonrelativistic: T = p^2 / 2m
Relativistic: T = E - mc^2; E^2 = (pc)^2 + (mc^2)^2
p(pion) = p(muon) + p(neutrino) = 0
The Attempt at a Solution
Since I'm given T and m for the muon, I can find p(muon) from the above formulas, both nonrelativistically and relativistically. And by conservation of linear momentum, I know that p(neutrino) = -p(muon). But from here I'm stumped. I can't find out anything more about the neutrino, because there's no further data. And even if I could, I wouldn't know what to do with it. For example, are the masses of the muon and neutrino supposed to be simply added to find the mass of the pion? I feel like I'm not being given enough information to solve this.