Neutrino mass state = flavour state, but how come?

[Anchovy]

I understand the basics of neutrino oscillation from the starting point of each neutrino flavour state being a superposition of mass states, or vice versa. However, the introductory texts I've seen never seem to explain what motivated such an idea. What made Pontecorvo think this?

 

[Orodruin]

The same is true in the quark sector where it arises from the up and down type Yukawa couplings being different. Why would you think the lepton sector would be different when the neutrino masses likely do not even arise (solely) due to Yukawas?

 

[fzero]

There is a copy of the Pontecorvo paper here. He was suggesting mixing between neutrino and antineutrino in analogy with the neutral kaon. He had no evidence for this, but was able to suggest lines of experiments to investigate the possibility. I don't know that it's that useful to study the Pontecorvo paper beyond the historical significance, since it ignores neutrino flavors, chirality, etc, that were not well understood at the time. It was a speculative idea that turned out to be much deeper than he understood at the time of the first paper.

 

[jtbell]

Note that Pontecorvo wrote his paper in 1957, several years before Gell-Mann and Zweig invented the first version of the modern quark model in 1964.

 

[ohwilleke]

It is fair to add that the prevailing model of neutrino oscillation is very much a phenomenological model that not everyone even considers to be part of the "Standard Model" proper, because the theoretical underpinnings are not tightly bound to the rest of the Standard Model and have not been rigorously established, even though so far it seems to be able to describe all of the experimental data to date. Some people consider the non-oscillating zero mass neutrino model of the Standard Model before neutrino oscillation was discovered to be the "Standard Model" even though we now know that the neutrino piece is wrong, and consider the prevailing way of mathematically modeling neutrino oscillation to be a proposed amendment to the Standard Model that is being considered but has not yet gathered sufficient consensus support to be considered adopted as part of it.

The phenomenological model in wide use, for example, implicitly assumes that neutrino mass is Dirac in nature (rather than Majorana which would cause the PMNS matrix to be non-unitary and require the alternative to that matrix to have more than four parameters). But, there is substantial support from theoretical physicists for the possibility that the neutrino has Majorana mass, and experiments are actively investigating the question but have not resolved it because they are not yet precise enough.

Put another way, the phenomenological model in wide use to describe neutrino oscillation, unlike the initial paper that proposed the concept by analogy to meson-antimeson oscillation, is basically a black box that generates predictions based upon input data, without meaningfully articulating the mechanism or how the mechanism is connected at a deeper or theoretical level to the rest of Standard Model physics, even though there are some standard more or less heuristic descriptions of the process (and there are, of course, myriad papers discussing possible deep theoretical sources for what is observed in which there is no consensus answer).

It also isn't uncommon for even investigators in the field, particularly experimentalists, to sometimes be sloppy about the distinction between weak force flavors and mass eigenvalues.

The good news is that experimental efforts on multiple fronts are making great progress in pinning down the best fit values of each of the parameters (the three neutrino masses and the four PMNS matrix parameters) of this phenomenological model and in testing whether it is an accurate description of the experimental evidence, and other experiments are making great progress on setting experimental bounds on neutrinoless double beta decay and cosmological measurements that relate to the potential existence of additional neutrino types and to Majorana neutrino mass. In five or ten years from now a lot of the questions that can be resolved experimentally will be resolved.

 

[Orodruin]

The phenomenological model in wide use, for example, implicitly assumes that neutrino mass is Dirac in nature (rather than Majorana which would cause the PMNS matrix to be non-unitary and require the alternative to that matrix to have more than four parameters).

This is incorrect. The PMNS matrix can be unitary also for Majorana neutrinos and a non-unitary mixing matrix can arise also for Dirac neutrinos.

In the case of Majorana neutrinos, the Majorana masses would typically arise from the dimension 5 Weinberg operator upon the Higgs field taking a vev. This on its own does not imply non-unitarity of the PMNS matrix. In order to have non-unitarity, you need to look at the higher-dimensional operators, but depending on the UV completion, they may be there or not (generally they will be, but there is no way of knowing without measuring or specifying the UV completion). In the canonical type-I seesaw, and even more so in its low energy implementations, there is an additional operator at d=6 which gives rise to a kinetic term, which upon putting the original kinetic term and it on canonical form gives non-unitarity. Alternatively, you can work in the full UV complete seesaw, where non-unitarity arises due to not having enough energy to produce the right-handed neutrinos.

Although the Majorana mixing matrix contains two additional complex phases, "standard" oscillations are not able to distinguish Majorana from Dirac nature as they are insensitive to the Majorana phases. Measuring the Majorana phases would require experiments sensitive to actual lepton number violation.

In five or ten years from now a lot of the questions that can be resolved experimentally will be resolved.

In five or ten years, we will know the neutrino mass hierarchy - if we are lucky. Measuring leptonic CP-violation is a more long-term endeavour which will likely not be resolved until at least 15 years from now unless we are very very lucky with the actual value of the CP-phase.

 

[ohwilleke]

This is incorrect. The PMNS matrix can be unitary also for Majorana neutrinos and a non-unitary mixing matrix can arise also for Dirac neutrinos.

Fair point. I see that I may have oversimplified in articulating the precise circumstances in which the assumptions of the conventional PMNS matrix with four parameters do not hold. The main thrust of my point was simply to note that there are theoretically viable scenarios in which the most widely used neutrino oscillation scheme used by experimenters measuring neutrino oscillation is not a perfect fit.

I've always been a bit fuzzy on how one would detect the two additional complex Majorana phases experimentally, and from what you say it would be difficult indeed. Do you know of any papers proposing experiments to measure them? I'd love to take a look.

In five or ten years, we will know the neutrino mass hierarchy - if we are lucky. Measuring leptonic CP-violation is a more long-term endeavour which will likely not be resolved until at least 15 years from now unless we are very very lucky with the actual value of the CP-phase.

Pessimist.

Seriously, based upon the many experiments currently operating or in the works (I'm almost out of fingers counting them), I think that in ten years (around the time my kids would be in their early graduate studies if they went into physics) we will have:
* the neutrino mass hierarchy,
* a quite restrictive upper bound on the absolute neutrino masses (with the range of masses for the heaviest neutrino having a spread on the order of 50 meV),
* a correct resolution of the unresolved theta23 quadrant,
* an order of magnitude or two improvement on any potential deviations from unitarity in the PMNS matrix, and
* a measurement of the CP-violating phase to within a sufficiently small margin of error that the measurement is not meaningless and consistent with almost any value even if it may not be a precise as we'd like (maybe +/-10-15 degrees) (hey, we've still got 50% margins of error on the up and down quark masses!). At a minimum I expect to see five sigma confirmation that the CP violating phase is non-zero.

I also expect that ten years from now we will have a one to three order of magnitude improvement in precision of neutrinoless double beta decay measurements from the current state of the art, and a one order of magnitude improvement on limits on B number or L number violating processes besides neutrinoless double beta decay.

 

[Orodruin]

the neutrino mass hierarchy,

You are here relying on that atmospheric experiments like PINGU will be built or that reactor experiments such as JUNO will be able to control their energy resolution and the linearity of their energy calibration to the required level. Not unreasonable, but also far from clear. We have timeline plots like these (shameless self-promotion):

But this would require PINGU and JUNO to start data taking very soon in order to have the mass ordering (at 3 sigma) by 2025. DUNE starting this early also seems like wishful thinking at this point.

a correct resolution of the unresolved theta23 quadrant,

I would put this in the same bin as the mass hierarchy or even worse.

a measurement of the CP-violating phase to within a sufficiently small margin of error that the measurement is not meaningless and consistent with almost any value even if it may not be a precise as we'd like (maybe +/-10-15 degrees) (hey, we've still got 50% margins of error on the up and down quark masses!). At a minimum I expect to see five sigma confirmation that the CP violating phase is non-zero.

We will be lucky if we have three sigmas. The currently running generation does not have enough sensitivity for this and the DUNE and T2HK generation (if built) will not have taken enough data yet. If standard oscillations are a good description, the current T2K hint is a fluctuation regardless of the parameter values, chances are that it will either go away or not grow significantly in the coming years (if it does grow significantly we should start to question the standard oscillation framework).
The five sigma confirmation of leptonic CP violation would be something to come at the very end of the DUNE and T2HK runs (if we are lucky with the true value!) which essentially means they would have to start taking data now in order to make the 2025 deadline.