Understanding Neutrino Mass and its Impact on Beta Decay Observations

[granpa]

when beta decay is observed it is noticed that some of the energy and some of the momentum is missing.
it is thought that this missing energy and momentum is carried away by a neutrino.
the neutrino mass is still unknown.

if you know how much momentum (mv) is missing and
you know how much energy (mc² + mv²) is missing then
dont you automatically know how much mass the neutrino must have?

why is the neutrino mass still unknown?

 

[bcrowell]

Relativistic energy is not given by E=mc^2+mv^2, it's E=\sqrt{m^2+p^2} (in units with c=1). The neutrinos emitted in radioactive decay are ultrarelativistic, so m² is negligible compared to p², and E=p to an extremely good approximation. Therefore you can't extract any information about m.

Neutrino masses are not completely unknown. We know that there are mass differences between neutrino flavors.

 

[granpa]

:-(

hmm. well, that clears it up.
Thanks for the reply.

 

[phyzguy]

The mass and momentum are related by the relation E^2 = p^2 c^2 + m^2 c^4 . In a typical beta decay, the energy and momentum are both in the MeV range, and since the neutrino mass is in the eV range or less, within experimental error the data are related by E^2=p^2 c^2. In other words, the experimental data are consistent with a neutrino mass of zero. There have been attempts to look at the very end of the decay spectrum, where the electron carries away almost all of the energy, and the neutrino has only a very small energy, but only about 1 in 10^14 decay events are in this range. The best that has been done this way, to my knowledge, is to put an upper bound on the neutrino mass of about 2eV.

 

[Bob S]

The Kurie plot has been extensively used to study the shape of the electron energy spectrum in beta decay. Any curvature at the end is due to a finite neutrino mass. See

http://books.google.com/books?id=ws...v=onepage&q=Kurie point neutrino mass&f=false

Bob S