A What Do Direct Measurements of Flavour Neutrino Masses Reveal?

[Daaavde]

Hello everyone! I've a question regarding the neutrino masses.

When neutrinos interact they must do so in a specific flavour (e.g. e, μ,τ) and if we go to find out what their flavour is at the interaction we get a specific answer.

However, it is not clear to me what we would find out if we were, hypothetically, to directly measure their mass at the interaction.

Let's assume we know the masses of the three mass eigenstates (and let's restrict ourselves to the 3 flavours scenario). If I were to measure the mass of electron neutrinos emitted by β decays would I find a single peak centred at the linear combination (given by the elements of the PMNS matrix) of the three masses values or three peaks centred on the values of the three mass eigenstates?

 

[mfb]

You would find three peaks, corresponding to the mass eigenstates, with their relative intensities given by the composition of the electron neutrino. This is a purely hypothetical scenario of course.

 

[Daaavde]

I see, thank you very much. I was just puzzled by the KATRIN experiment.
They claim that they would potentially see a drop-off at the neutrino mass, however that confuses me.
Since the neutrino potentially carries the three masses eigenvalues, wouldn't they rather see (hypothetical infinite resolution scenario here) two kinks at the values at which the two heaviest mass eigenstates lie and then a drop-off at the lightest?

 

[Vanadium 50]

Since the neutrino potentially carries the three masses eigenvalues, wouldn't they rather see (hypothetical infinite resolution scenario here) two kinks at the values at which the two heaviest mass eigenstates lie and then a drop-off at the lightest?

Yes, but this is a detail. First they have to establish that they see something other than zero. Then people can take the next step and determine what values of mass are allowed by the data.

 

[Orodruin]

At the precision of KATRIN, you would stand essentially no chance to separate the masses. It is therefore a good approximation to work with an effective neutrino mass.

 

[mfb]

If the neutrino masses are large enough to be visible by KATRIN (>200 meV) - which would contradict limits from cosmology - then all three neutrino masses are extremely close together, within ~5 meV.
The absolute mass differences could be larger, but only with lighter neutrinos (the maximal difference is about 50 meV if one or two types are extremely light).