As rob pointed out in a comment in my previous question :
"There were hints about sterile or missing neutrinos in LSND, in the low-statistics region of MiniBoone, and in a number of other neutrino results, but the community was rightly skeptical."
Sounds quite true. But why “rightly skeptical” ?
More recently, the BEST experiment results shows serious arguments for the existence of one sterile neutrino in the eV/c^2 mass range.
But this has not produced much excitement in the astrophysical community, in particular with respect to the possibility of sterile neutrinos as Dark Mater candidates.
Please don’t belabour the obvious and shower me with arguments that eV/c^2 mass range sterile neutrinos are useless in astrophysics. I can do elementary arithmetics, thanks.
But there are three families of fermions. Including three ordinary neutrinos. Would not the most natural extension of the Standard Model to accommodate neutrino masses consist in introducing three sterile neutrinos ? If the lightest is in the eV/c^2 mass range couldn’t either the intermediate mass one, or the heaviest one be an interesting candidate for Dark Matter ?
Very roughly, mass ratios for second to first, and third to second families are
- for 2/3 charge quarks 500 and 150
- for -1/3 charge quarks 40 and 20
- for charged leptons 200 and 20
Since for usual neutrinos only mass differences can be obtained from neutrino oscillations data the ratio from second to first cannot be known. However, assuming that the first is not very close to the second one can guesstimate the mass to the second one to be reasonably close to $\sqrt{\Delta m^2_{12}}$, and the mass of the third one to be close to $\sqrt{\Delta m^2_{23}}$, leading to a ratio “third to second” of the order of 5.
So these ratios vary a lot and one cannot make an estimate of the mass of the second and third sterile neutrinos if they really exist, except that they are significantly heavier than the lightest one.
But doesn’t il look promising ?
Also, the three eigenstates of neutrino mass (1, 2, and 3 just above) do not coincide with the there neutrino “flavors”, electronic, $\mu$-onic and $\tau$-onic. There is a rather complicated $3\times 3$ matrix relating them.
If the masses of the neutrinos, ordinary and sterile, come from a see-saw mechanism, wouldn’t it stand to reason than their masses would come from the diagonalisation of a $6\times 6$ matrix ? In which case the argument against “reasonable mass” sterile neutrinos, namely that that the heaviest mass should be in the GUT range (because the sum of the eigenvalues is the trace, and the trace is predicted in the GUT range) fails for a $6\times 6$ matrix. Indeed just one super-heavy sterile neutrino is needed to take care of the bulk of the trace of the matrix, leaving two others. The lightest one, the one found in BEST, in the eV/c^2 range, and the intermediate one that can have any mass whatsoever ! In particular, an astrophysical interesting mass, in the keV/c^2 range, for a Dark Matter candidate.
Why hasn’t anyone yet jumped on such an attractive possibility ? (Dont count me, I am retired, and my field was not astrophysics anyway, it is just a “hobby” for me)
Edit : I have read the paper suggested by anna v in her comment below.
This paper predates the results of the BEST experiment, but mentions older results as well as the "gallium anomaly" which is the very point of BEST.
The author did consider the $6\times 6$ matrix I have suggested above. But for some reason he considers only the cas of one reasonably light sterile neutrino and two very heavy ones. But with now solid (if not yet conclusive) evidence for one sterile neutrino in the eV/c^2 mass range and the need of another one in the keV/c^2 mass range to account for (tepid) Dark Matter, is there any proposal in the direction of the $6\times 6$ matrix having only one very heavy eigenvalue ?
