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Neutrino Mass

Only the very highest energy β-electrons contribute to the neutrino mass measurement, i.e. those with energies very close to the end-point energy. Unfortunately, as shown below, only a very small fraction of decays result in the electron having an energy of within 1 eV of the Q-value.

Beta End Point

 

The effect of a non-zero neutrino mass can be seen to distort the tail part of the spectrum above, but in itself this is difficult to observe due to the degree in which one has to "zoom in" on the tiny tail end part of the spectrum. It is more easily demonstrated below, in what is known as a Kurie Plot.

 

Kurie Plot

 

The Kurie plot is usually defined as:

Kurie Plot Definition

It arises by plotting the square root of the number of β-particles, N(E), whose momenta (or kinetic energy, Te) lie within a certain narrow range, scaled by the Fermi function, F(Z,E) - against β-particle energy. It is a straight line for "allowed" transitions, i.e. those in accordance with the Fermi theory. "Forbidden" decays have a distorted Kurie plot.

The departure from linearity in the tail of the Kurie plot is a much better visual guide to the existence of a non-zero neutrino mass. However one must be careful because energy resolution effects, excited final states and other backgrounds can all cause a "blurring" at the tail end. It is imperative, therefore, for an experiment such as AMBER to have the best possible energy resolution, in order to minimise this blurring at the end-point which may lead to an erroneous mass measurement.

Diagrams borrowed from Andrea Giuliani's talk Review of Neutrino Mass Measurements, INFN, 2005.