[Diogo_Afonso_Leitao (OP)]

Hello everyone!

I just had a little thought in the decay of the W Boson. I read an article saying it could decay into one kind of neutrino and a positron, anti-muon or anti-tau. However, these are different particles with different masses. The law of conservation of energy says that the mass before the decay has to be the same as the mass after the decay. So, if positrons, anti-muons and anti-taus have different masses, the three neutrinos need to have different masses aswell for the law of conservation of energy to work.
Therefore, we confirm at least two of the kinds of neutrinos are massive.

What do you think?

[evan_au]

So, if positrons, anti-muons and anti-taus have different masses, the three neutrinos need to have different masses as well for the law of conservation of energy to work.

The energy carried away from a nuclear decay is in the form of:
- the particles' "rest-mass", for which you have to bring the particle to rest. You can consider this mass to have an equivalent energy, according to Einstein's iconic E=mc²
- the particles' "kinetic energy". You can consider this energy to have an equivalent mass, according to Einstein's iconic E=mc². (...although physicists prefer to talk about momentum rather than kinetic energy)

The energy of the decay is divided among the debris in a somewhat random way, with the kinetic energy of the neutrino mostly far exceeding it's rest mass.

Take the example of neutron decay, which is better-understood than Higgs decay, with much lower energy: n⁰ → p⁺ + e⁻ + ν_e + 0.78MeV
In some cases, the electron carries off almost all the energy; in other cases, the neutrino carries off almost all the energy.

However, the mass of the neutrino is thought to be somewhere around 0.1-0.25eV (it's really hard to measure).

So a neutron decay where the neutrino rest mass is 0.1eV, and the kinetic energy is anywhere up to 782,343eVą13,000eV makes it really hard to pin down the rest mass of the neutrino. The error bars are far larger than the thing you are trying to measure!

Trying to pin down the rest mass of 3 neutrinos from the very infrequent (and very high energy: 126GeV) decay of the Higgs is even more problematic.

Other experiments have constrained the difference in mass of the different neutrino types, and it appears that they are fairly similar to each other. So distinguishing the masses via different paths of Higgs decay is especially tricky!

For current guesstimates of neutrino mass, see: http://en.wikipedia.org/wiki/Neutrino#Mass
It is hoped that the KATRIN & MARE experiments should pin down the mass of the electron neutrino more accurately, over the next couple of years.