# Neutrino result heralds new chapter in physics

This will now direct physicists towards even more interesting theories to help explain how the Universe came to be.

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I did not find the linked article to be particularly informative. Here’s another one that seems a bit better:

In particular, I was rather confused about how they were expecting anything other than a failure to detect a particle that doesn’t interact with matter in any way (except through gravity, which is too weak to use directly). Apparently they are looking for discrepancies in the oscillations of the other neutrino flavours. As far as I know this is consistent with other negative results that have looked for signatures of 4th neutrino flavours in cosmology (e.g. through their impact on the early evolution of the universe, via the CMB).

Also as far as I know (though perhaps one of the @physicists can correct me) this doesn’t rule out the most straightforward explanation of neutrino mass, which is that neutrinos have right-handed and left-handed versions interacting via the Higgs field just like the other leptons, but that the right-handed ones otherwise only interact via gravity - I think they are also sometimes called sterile neutrinos, but that doesn’t seem to be what they are talking about here?

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Thanks for that. I’d seen a number of pop-sci article with screaming headlines about new physics, but this is actually informative.

This is because there is a historical background: there were some results from Los Alamos and Fermilab stating that there is evidence for sterile neutrinos at some modestly high sigma (which I can’t remember how high). The reason this new study (MicroBooNE) is newsworthy is because it contradicted the previous results.

If you are talking about sterile neutrinos = right handed neutrinos, that’s also what they are talking about.

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In that case I am confused about how these measurements are evidence against their existence, or how the previous measurements could have been evidence for them.

If neutrinos get their mass from the same mechanism as quarks and the other leptons (in Standard Model + right-handed neutrinos), isn’t just about any oscillation pattern possible, since the masses and mixing parameters are arbitrary parameters of the model? In which case these measurements just constrain those parameters, instead of ruling out the existence of right-handed neutrinos?

Granted, I am not well-versed in the details of this model, nor am I very familiar with other models of how neutrinos get mass…

Neutrinos oscillate because their flavor eigenstates are not the same with their mass eigenstates, so flavor oscillation experiments is connected to the masses. For MiniBooNE, the salient point is this: if there are only three neutrinos, then \Delta m_{13}^2 = \Delta m_{12}^2 + \Delta m_{23}^2, where \Delta m_{13} is the difference between the mass of neutrino flavor 1 and neutrino flavor 3, and so on. What they found was an excess, i.e., that this equation does not hold. This implies that there are not three neutrinos. The one and two neutrino models have been disfavored, so if this excess is real there should be more than three neutrinos.

So, what are these new neutrinos? There are two ways that neutrinos can get mass (or at least, two popular ways):

1. There is the possibility that neutrinos are Majorana particles with a Majorana mass instead of a Dirac mass. If they are Majorana, then you can get mass terms for the left-handed particles when you integrate out (i.e., form an effective field theory) some high energy scale. The stuff integrated out this way might be, but not necessarily, the right handed neutrinos.
2. If neutrinos are Dirac particles, then the right-handed neutrinos are required to form the Dirac mass term

Regardless of 1) or 2), the idea is that RH neutrinos → can generate mass → if it exists (and interacts in the way that we expect), it will cause \Delta m_{13}^2 = \Delta m_{12}^2 + \Delta m_{23}^2 to be violated. Obviously it’s not the only way you can get a violation, but evidence is not equal proof, as we theists very well know. Such violation is evidence in the Bayesian sense for the existence of RH neutrinos, and a lack of violation is evidence against.

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Thanks for that explanation! I am still confused, though: if adding RH neutrinos causes a violation of \Delta m_{13}^2 = \Delta m_{12}^2 +\Delta m_{23}^2, but the two popular ways for the neutrino to have mass (and thus, oscillations between flavours) usually both involve adding RH neutrinos, under what model is \Delta m_{13}^2 = \Delta m_{12}^2 +\Delta m_{23}^2 actually predicted? How do neutrinos get their mass in that scenario?

I had assumed that the most basic extension of the SM with neutrino masses was that they were Dirac particles, with three RH neutrinos (interacting only via gravity and Higgs) which just have the same three masses as the (mass eigenstates of the) LH neutrinos. Is that incorrect?

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The existence of sterile RH neutrinos explains neutrino masses, but it’s not the only mechanism to produce neutrino masses.

The violation of \Delta m_{13}^2 = \Delta m_{12}^2+\Delta m_{23}^2 means that there are sterile neutrinos (which for most physicists means RH neutrinos, more on in my last paragraph). There are other ways to produce this violation, but they are quite exotic, such as a violation of CPT. This violation does not mean that the active LH neutrinos don’t have mass, just that there exist sterile neutrinos.

There are ways for the active neutrinos to gain mass without the help of sterile neutrinos. For example, if the neutrino is a Majorana particle, then it is its own antiparticle (allowed since neutrinos are electrically neutral). Majorana masses of the neutrino can be formed by interactions of the form ~HLL, where “H” is the Higgs, and the two “L”'s are the left-handed neutrinos, with proper complex conjugation etc where necessary. Note that terms of the form HLL is not actually allowed due to symmetry reasons concerning the Higgs field, so if we want that term, the Higgs field also has to be modified (to get technical, the Higgs cannot be a ‘doublet’ of SU(2)_L). The question of whether the neutrino is a Dirac or a Majorana particle is the holy grail of neutrino physics.

Note that in my first sentence, I specify sterile RH neutrinos instead of just RH neutrinos because I’m sure there are crazy theories in which there are active RH neutrinos. There are also theories with sterile LH neutrinos, of course. For what it’s worth, there are also ways for \Delta m_{13}^2 = \Delta m_{12}^2+\Delta m_{23}^2 to be true, but the right-handed neutrinos ALSO exists – for example, maybe the usual active neutrinos \nu_e, \nu_\tau, \nu_\mu do come in both LH and RH variants, we just haven’t found the RH variants yet (somehow), and that there is no relationship between flavor and handedness (e.g., there are no fourth flavor that is only RH). Most of these theories are pretty ad hoc, and most of the time not taken seriously (whether that’s a good thing or not is beyond this discussion).

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Ah, this is what I assumed to be the most natural extension of SM - like the other fermions, the neutrinos come in LH and RH variants, and like the other fermions, only the LH neutrinos interact with the weak force. This leaves the RH neutrinos with no interactions beyond the Yukawa interaction with the LH partners and Higgs, and the gravitational force, since the neutrinos are electrically neutral. Which (again, this is my assumption) is why we haven’t found the RH variants - basically, their only effect on the particles we can interact with in any meaningful way is to give the LH neutrinos mass.

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That theory requires a larger extension of SM than at first glance. Dirac masses for the neutrino requires that the SM gauge group is larger than we think – the lepton number conservation (or more precisely, the combination of baryon number - lepton number) has to be upgraded from an accidental symmetry to an actual, fundamental symmetry of nature. The Yukawa coupling required is also extremely small, much smaller than the other couplings in the standard model (7 order of magnitude smaller than the electron’s). I suppose “natural” is in the eye of the beholder, every neutrino theory requires some level of ad-hocness.

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