# Mass of an anti electron neutrino

I can't seem to find the mass of an anti electron neutrino in MeV. I found that in beta radiation one down quark breaks into an up quark, an electron, and an anti electron neutrino. The mass in MeV of a down quark is 4.8, the mass of an up quark is 2.4 MeV, the mass in MeV of an electron is 0.511 MeV. So the mass of an anti electron neutrino should be 1.889 MeV. However I can't find a place to make sure I am right. Thank you and forgive me if i'm wrong.

## Answers and Replies

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Your calculation ignores the fact that the beta decay products typically carry kinetic energy. This makes it hard to use beta decay to measure the neutrino mass, since the neutrino masses are very small, probably around a few hundredths of an eV. The kinetic energy of the electron, for example, is typically at least a few % of its mass, so around a few thousand eV, which is around 5 orders of magnitude larger than the expected neutrino mass. An experiment would need a high sensitivity to measure the small neutrino mass.

Furthermore, because of neutrino oscillations, current experiments have not been able to measure the value of the electron neutrino flavor eigenstate.

There is a proposal for a new experiment sensitive to a mass of around ##0.2~\mathrm{eV}##. A review of this and other experiments is here. It may be possible in the next few years to have a direct measurement of a neutrino mass.

Mentor
In addition to the good post of fzero: you cannot consider the quarks as isolated particles. The decay is a process of the whole nucleon or even the whole nucleus (if you don't have a free neutron). The released energy corresponds to the mass difference between initial and final nucleus (or neutron->proton for a free neutron).

Those light quark masses are problematic anyway - it is hard to measure them as you cannot see them as isolated quarks, and the values have a large uncertainty.

Nick666
So the measurements that suggests that the electron neutrino may have a negative mass-squared value are wrong ?

Mentor
There are no measurements that are incompatible with real and positive neutrino masses.

And how is this related to the old thread from 2013?

Nick666
I didnt want to open a new thread ...

So what are these guys talking about ?

http://www.sciencedirect.com/science/article/pii/S0370269398008247
"The unphysical result of the negative mass square of the electron neutrinos recently reported in several tritium β-decay experiments, is one of the most attractive subjects among remaining physical problems"

http://arxiv.org/ftp/arxiv/papers/0909/0909.2104.pdf
"In view of erroneous and unphysical mass results obtained by some earlier experiments in β-decay"

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Beta decay experiments set out to determine the neutrino mass found their best fit was for negative mass squares. However, the result were still compatible with positive mass squares and so there was never really a big problem. The expriments are therefore not wrong, they are simply not sensitive enough to make a definite statement.

As is often the case, physicists like to theorize what could cause a result for which there is only a weak hint in case more precise measurements would confirm it.

Mentor
Those are old measurements - the linked paper is from 1998 and refers to papers from 1991 to 1995.

A more recent and more precise measurement has been done in Mainz, they quote a squared mass of ##-1.6 \pm 2.5 \pm 2.1 eV^2## - this is an example where the best fit value is negative, but a small positive mass is well in agreement with the measurement (less than 1 sigma away).

Gold Member
The combination of neutrino oscillation based mass eigenstate differences, Planck cosmic background radiation measurements, and other astronomy data, suggests a lightest neutrino mass eigenstate of about 0.001 eV or less in a normal mass hierarchy, and a bit more (but still well under 0.01 eV) in the case of an inverted neutrino mass hierarchy. Determining the mass hierarchy definitively should be possible within the next few years. Direct measurement of the absolute neutrino masses will take a longer period of time.

As noted above, however, in the vast majority of circumstances, neutrinos will have much more kinetic energy than they have rest mass. A neutrino with GeV kinetic energy (travelling at very nearly the speed of light) wouldn't be terribly exceptional.

I can't seem to find the mass of an anti electron neutrino in MeV. I found that in beta radiation one down quark breaks into an up quark, an electron, and an anti electron neutrino. The mass in MeV of a down quark is 4.8, the mass of an up quark is 2.4 MeV, the mass in MeV of an electron is 0.511 MeV. So the mass of an anti electron neutrino should be 1.889 MeV. However I can't find a place to make sure I am right. Thank you and forgive me if i'm wrong.

Wait, actually I have a question of my own, how did you know the mass of an electron is .511? Is that the rest mass? But if it is why would you want rest mass since in β rad. it also has momentum?

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Determining the mass hierarchy definitively should be possible within the next few years.

If by "the next few" you mean within 2 or 3 years, I am afraid this statement is misleading. The current generation of neutrino oscillation experiments simply do not have the sensitivity to provid this kind of measurement unless you are very lucky with statistical fluctuations (conversely you could also get unlucky and rule out the correct hierarchy). There most certainly will be a hint or two, but a measurement at 3 (or preferably 5) sigma will probably have to wait for the new generation of experiments. The NOvA experiment which just recently started getting events and will run for 6 years would reach 3 sigma only if they are lucky *and* the CP phase is favorable (see this figure). All other experiments with sensitivity to the mass hierarchy are still on the drawing table:

JUNO: New reactor neutrino experiment in China. They are looking for teeny tiny changes in the oscillation pattern as a function of energy. It is still not clear to me whether they will be able to reduce the energy uncertainties and control the linearity of their energy scale to high enough precision to make the measurement. But it seems they are going to build it anyway, it worked for the Daya Bay experiment ...

PINGU: Measurement of atmospheric neutrino oscillations by a low energy extension of IceCube/DeepCore. Could measure the mass hierarchy very fast if it is constructed and the parameters are favorable. It needs to find funding and to be constructed. The american community did not seem overly enthusiastic about the idea.

INO: Indian magnetized iron detector. They have significantly improved their prospects of measuring the mass hierarchy using atmospheric neutrinos by suggesting inclusion of hadronic information directly into their analysis. Still needs to be built but India seems intent on doing so. Could perhaps have a 3 sigma result around 2025 or so.

Future long baseline experiments: Accelerator based experiments being suggested for different locations and configurations. The far detector of these experiments could most likely measure the mass hierarchy using atmospherics even if the long baseline experiment itself could not (as is the case in T2HK). None of these experiments are currently approved/funded and they will need additional time for construction. I would be surprised if they have significant results by 2025.

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