T2K sees ~3 sigma evidence for neutrino CP violation

[mfb]

TL;DR Summary

Measurements clearly favor non-zero CP violation in the neutrino sector.

Publication: Constraint on the matter–antimatter symmetry-violating phase in neutrino oscillations
Edit: arXiv: Constraint on the Matter-Antimatter Symmetry-Violating Phase in Neutrino Oscillations
Article: Neutrino Asymmetry Passes Critical Threshold
Previous measurements already hinted at this, now we have a relatively strong single measurement.
CP violation is linked to matter/antimatter asymmetries. They are small for quarks, but it looks like they are larger in the neutrino sector. The measurement favors the maximal CP violation that was still within the range set by other parameters.
DUNE will measure this parameter more precisely in the future.

Significant CP violation in the neutrino sector might be an explanation for the matter/antimatter asymmetry today (our universe has matter but nearly no antimatter).

The other big open question in neutrino mixing is the mass ordering - two light neutrinos and a (relatively) heavy one, as most people expect, or one light neutrino and two heavier ones? This measurement favors the former slightly, just like many others did in the past, but more measurements will be needed. DUNE will help there, too.

 

[Orodruin]

It is worth pointing out that the measurement is not very precise. It is just barely ruling out the CP-conserving values of $\delta$ at $3\sigma$, the $3\sigma$ confidence interval being $[-3.41,-0.03]$ (CP-conservation would be 0 or $-\pi$ (equivalent to $\pi$). That is almost half the range still allowed, so if one wants to be mean one could say that the title should be "Almost no constraint on ...". A better title would have been "Strongly disfavouring matter-antimatter symmetry in the lepton sector" in my opinion.

Significant CP violation in the neutrino sector might be an explanation for the matter/antimatter asymmetry today (our universe has matter but nearly no antimatter).

This has to come with a huge caveat. While CP-violation is one of the Sakharov conditions, it is not directly clear how the particular CP-violating phase measured in oscillation experiments relates to the generation of a matter/antimatter asymmetry. For example, in the simplest forms of leptogenesis, the phase measured in oscillation experiments is completely decoupled from the resulting asymmetry. Instead, the asymmetry builds upon other CP-violating phases that relate to the high-energy part of the theory, i.e., the part of the Casas-Ibarra parametrisation that is not accessible through oscillation experiments. Those phases could theoretically be probed through probing the dimension six effective operators that are in principle accessible to oscillation experiments, but in practice way out of the sensitivity of current or planned future generation experiments.

The other big open question in neutrino mixing is the mass ordering - two light neutrinos and a (relatively) heavy one, as most people expect, or one light neutrino and two heavier ones? This measurement favors the former slightly, just like many others did in the past, but more measurements will be needed. DUNE will help there, too.

Not only DUNE, but many of the future planned experiments, including reactor experiments such as JUNO and experiments looking at atmospheric neutrinos. There are current hints in global fits that seem to favour the normal mass ordering. DUNE would do very well on the mass ordering front (something like 10 sigma establishment if I do not misremember). There are also other proposed future accelerator experiments that have somewhat different setups than DUNE and are more tailored to CP violation, such as T2HK and ESSnuSB. Those experiments would a priori have very poor sensitivity to the mass ordering in the accelerator data, but that would to a large extent be offset by the huge sample of atmospheric neutrinos.

 

[Dr.AbeNikIanEdL]

It is just barely ruling out the CP-conserving values of δδ\delta at 3σ3σ3\sigma, the 3σ3σ3\sigma confidence interval being [−3.41,−0.03][−3.41,−0.03][-3.41,-0.03] (CP-conservation would be 0 or −π−π-\pi (equivalent to ππ\pi)

Moreover, $-\pi$ is in that range. The paper only claims to have ruled out the CP-conserving values at 95% confidence level.

 

[Orodruin]

Moreover, $-\pi$ is in that range. The paper only claims to have ruled out the CP-conserving values at 95% confidence level.

You are right, my mind for some reason swapped the order of the decimals in the 3.41 ...

 

[mfb]

"Almost no constraint on ..."

I think that is too weak. It rules out half of the range with >3 sigma and disfavors a good part of the other half as well. This is not a search for a new particle/process where you can safely dismiss 3 sigma hints because of the look-elsewhere effect. It's a measurement of a free parameter.

This has to come with a huge caveat.

That's why I said "might": We don't know if it is linked to baryogenesis.

 

[ohwilleke]

FWIW, the open access pre-print of the article was released on October 10, 2019.

The best fit value is -0.60π + 0.22π -0.18π (in radians). This is consistent at a one standard deviation level with maximal CP violation which is -0.50π. It is inconsistent with zero CP violation at almost, but not quite, three sigma significance.

This result is in line with previous results from the T2K experiment. In July of 2018, T2K found that the best fit value for a CP violating phase based upon those T2K measurements was -0.6π ± -.20π. Zero CP violation (zero or π) was already excluded at more than two sigma significance in 2018. T2K also announced similar results in the summer of 2016.

The new result is also, uncoincidentally, consistent within error bars with the Particle Data Group value, although it has chosen to report the equivalent value within the 0 to 2π range. The result in the new paper is 1.40π + 0.18π - 0.22π in that reporting convention, while the PDG global average value is 1.37π +0.18π - 0.16π (which is more than three sigma from zero CP violation). The PDG value is based on three prior results, the 2018 measurement from T2K and 2018 measurements from NOVA and SKAM which are much less precise, and hence got much less weight in computing the global average. As PDG notes, the 2018 values it used to computer its averages were (in units of π radians):

1.33 +0.45−0.51		1​	ABE ​ 2018​ B	SKAM	Normal mass ordering, θ13 constrained
1.40 ±0.20		2​	ABE ​ 2018​ G	T2K	Normal mass ordering, θ13 constrained
1.21 +0.91−0.30		3​	ACERO ​ 2018​	NOVA	Normal mass ordering; octant II for θ23

There is good reason to hope for future narrowing of this range in the reasonably near future, and not just from DUNE, because most of the uncertainty is statistical and can be reduced simply by collecting more data.

The key results from the body text of the paper (in radians, emphasis added) are as follows:

We find the data shows a preference for the normal mass ordering with a posterior probability of 89%, giving a Bayes factor of 8. We find sin2 (θ23) = 0.53+0.03 −0.04 for both mass orderings. Assuming the normal (inverted) mass ordering we find ∆m2 32 = (2.45 ± 0.07) × 10^−3 (∆m2 13 = (2.43±0.07)×10^−3 ) eV^2 /c^4. For δCP our best fit value and 68% (1σ) uncertainties assuming the normal (inverted) mass ordering are −1.89 +0.70 −0.58 (−1.38 +0.48 −0.54), with statistical uncertainty dominating. Our data show a preference for values of δCP which are near maximal CP violation (see Figure 3), while both CP conserving points, δCP = 0 and δCP = π, are ruled out at T2K measurement [8]. Here, we also produce 99.73% (3σ) confidence and credible intervals on δCP . In the normal ordering the interval contains [−3.41,−0.03] (excluding 46% of the range of parameter space), while in the inverted ordering the interval contains [-2.54,-0.32] (excluding 65% of the parameter space). The 99.73% credible interval marginalized across both mass orderings contains [−3.48,0.13] (excluding 42% of the parameter space). The CP-conserving points are not both excluded at the 99.73% level. However, this is the first time closed 99.73% (3σ) intervals on the CP-violating phase δCP have been reported (taking into account both mass orderings) and a large range of values around +π/2 are excluded.

While this paper favors Normal Ordering over Inverted Ordering for neutrino masses 89% to 11%, combined with all other sources of data a March 18, 2020 pre-print updating the data contained in a previous paper on the subject estimates that the preference for a normal ordering is about 3.5 sigma.

 

[ohwilleke]

Significant CP violation in the neutrino sector might be an explanation for the matter/antimatter asymmetry today (our universe has matter but nearly no antimatter).

The paper's abstract in Nature and press accounts inevitable tack this onto any discovery regarding CP violation. But, this is marketing and hype without much substance to it.

Even with maximal CP violation for neutrinos you basically cannot meet the three Sakharov conditions (CP violation, baryon number violation, and lack of thermal equilibrium, all to a sufficient extent) without beyond the Standard Model physics for which there is no positive evidence whatsoever. See e.g., Paolo S. Coppi, "How Do We Know Antimatter Is Absent?" (2004). (N.B. Yoshimura is also sometimes given credit for the conditions now commonly called Sakharov's conditions.)

In particular, no experimental evidence has ever shown any violation of conservation of baryon number (see, e.g., Lafferty (2006) citing S. Eidelman et al. (Particle Data Group), Phys. Lett. B592 (2004)), or conservation of lepton number.

Sphaleron interactions which do not conserve baryon number but do conserve baryon number minus lepton number, are permitted in theory by the Standard Model, but have never been observed experimentally (and we wouldn't expect to be able to in the Standard Model because "The minimum energy required to trigger the sphaleron process is believed to be around 10 TeV; however, sphalerons cannot be produced in existing LHC collisions, because although the LHC can create collisions of energy 10 TeV and greater, the generated energy cannot be concentrated in a manner that would create sphalerons." See also, e.g., Koichi Funakub, "Status of the Electroweak Baryogenesis" ("[W]e find that the sphaleron process is in chemical equilibrium at T between 100 GeV and 10^12 GeV.").

But, these interactions cannot by themselves explain matter-antimatter imbalance in the universe with the CP violation allowed in the CKM matrix, even with maximal CP violation in the PMNS matrix which would not be inconsistent with the latest measurement.

Cosmology observations, including those supporting the Big Bang Nucleosynthesis hypothesis (which is largely but not perfectly confirmed with observational evidence) also dramatically constrains the time frame in which baryogenesis and leptogenesis need to happen after the Big Bang: In the conventionally accepted chronology of the Universe, this has to happen sometime in the first microsecond after the Big Bang (or less, given temperature constraints, etc.), and possibly much much less (on the order of 10^-32 seconds or less) given temperature considerations.

This simply isn't enough time in conventional Big Bang cosmology, at sufficient energies, to have enough sphaleron interactions to produce the matter-antimatter asymmetry seen in baryons in the universe from a starting point of no asymmetry.

Footnote Re Another Implication Of A SM Solution To Baryon Asymmetry

Baryon asymmetry explained solely from sphaeleron interactions would also imply that the number of anti-leptons in the universe minus the number of leptons in the universe would have to be identical to the number of baryons in the universe. And, because the asymmetry in charged leptons is also identical to the asymmetry of baryons in the universe, the number of anti-neutrinos in the universe would have to exceed the number of neutrinos in the universe by almost exactly twice the number of baryons in the universe. Since the the number of baryons in the universe is about 4×10^79, and the number of neutrinos in the universe is about 1.2×10^89, the number of neutrinos and anti-neutrinos in the universe must be equal to more than nine orders of magnitude of precision for this scenario to be true.

As a practical matter, it would be impossible to prove exactly to the necessary level of precision, but could be disproved if the ratio of neutrinos to antineutrinos in the universe were measured to be sufficiently statistically significantly different from 1-1.

No estimate of matter-antimatter asymmetry in neutrinos in the universe based upon astronomy observations is sufficiently precise to do that right now, but the available evidence points to an observable excess of antineutrinos over neutrinos in the universe which would be inconsistent with the baryon asymmetry of the universe having a Standard Model physics origin from a zero asymmetry starting point at the Big Bang. See Dominik J. Schwarz, Maik Stuke, "Does the CMB prefer a leptonic Universe?" (Submitted on 28 Nov 2012 (v1), last revised 11 Mar 2013 (this version, v3)) (published version here). A 2002 paper, meanwhile, puts an upper bound on electron neutrino asymmetry at 3% of the number of electron neutrinos, and a bound on muon and tau neutrino asymmetry at 50% of the combined number of such neutrinos. So, one would need a sub-percent level precision measurement of the proportions of neutrinos that are neutrinos and anti-neutrinos to resolve the question at the three to five sigma level needed to be considered definitive.

 

[Lord Crc]

Are there any plausible SM extensions that predict or can reasonably accommodate these results along with the neutrino oscillation results so far?

 

[Orodruin]

Are there any plausible SM extensions that predict or can reasonably accommodate these results along with the neutrino oscillation results so far?

The issue is usually not accommodating any particular set of oscillation parameters. The problem is typically that the SM extensions tend to have a large parameter space and therefore not be very predictive in the low-energy regime (i.e., anything below the scale at which neutrino masses originate).

 

[Lord Crc]

So nothing really ruled out by current results, is what you're saying. So any that would be if improved measurements show (near) maximal CP violation is the true state of nature? If not, what are these measurements helping us with?

Any relation between the CP violation and oscillations, or are they completely orthogonal in most/all extensions?

 

[ohwilleke]

Are there any plausible SM extensions that predict or can reasonably accommodate these results along with the neutrino oscillation results so far?

The result is completely consistent with the Standard Model. It is a measurement of one of the four parameters of the PMNS matrix, each of which is a fundamental experimentally determined physical constant of the Standard Model (of which there are a couple dozen). This result is also consistent with all prior measurements of CP violation in connection with neutrino oscillation at the one standard deviation level.

So nothing really ruled out by current results, is what you're saying.

Roughly half the possible parameter space is ruled out at the three sigma level. The best fit value at plus or minus one sigma, is about 20% of the possible parameter space. The existence of CP violation in neutrino oscillations is established at just slightly less than three sigma, but close to 98-99% likelihood.

So any that would be if improved measurements show (near) maximal CP violation is the true state of nature? If not, what are these measurements helping us with?

Ultimately, to understand the neutrino sector in the Standard Model, including virtual loops in almost every other Standard Model process (often not very important ones relative to the full result in processes that are not "about" neutrinos), we need to know the values of all of the fundamental Standard Model parameters. The best fit value gives us a number to put into these calculations. The margin of error measurement, when flowed through the calculations, tells us how much the uncertainty concerning the best fit value impacts a calculation that includes an interaction with a neutrino, either on shell or off shell (i.e. either "real" or "virtual").

Any relation between the CP violation and oscillations, or are they completely orthogonal in most/all extensions?

When you are at a given starting point in a physical event involving a neutrino, you need to use the PMNS matrix to determine what the probability is of the neutrino undergoing an oscillation of a particular type. This is determined by entries in the PMNS matrix, each of which is an algebraic combination of one or more of the four PMNS parameters (the exact combination depends upon which of the mutually equivalent schemes are used to do the parameterization, even the CP violation component can be parameterized in different ways). The most common parameterization is as follows (per the link to the PMNS matrix above in this comment):

in which s refers to Sine, c refers to Cosine, the subscripts identify which of the three other PMNS parameter angles is being used, e is Euler's constant, i is the imaginary number, and the CP violating parameter appears in the exponent of the Euler's constant terms (note that e^iπ=-1).

In the absence of CP violation, the probability of going from State A to State B is also identical to the probability of going from State B to State A (and the Euler's constant term in each of the PMNS matrix is equal to 1 because anything other than zero, to an exponent of zero is equal to 1). In the presence of a non-zero CP violation parameter, the probability of going from State A to State B is different in a quantifiable manner, from the probability of going from State B to State A.

Another way to state the same thing is that the CP violation parameter quantifies the amount by which the oscillations of neutrinos differ from the oscillations of antineutrinos.

In four of the nine PMNS matrix entries (it is a 3 x 3 entry matrix), the CP violation parameter's contribution is negligible. But, in the other five those nine matrix entries, the CP violation parameter is more significant.

The parameters themselves are not observables. The experiments attempt to discern the CP dependence of particular entries of the PMNS matrix where CP violation is more significant (by counting the number of events of each type compared to what would be expected with no CP violation given our best estimate of the other neutrino oscillation parameters and the relative neutrino mass eigenstates) and use that data to try to infer the value of that parameter.

For example, suppose that you are wondering if there is a fifth force that impacts the number and type of neutrinos that are emitted in complex nuclear fission reactions that emit both neutrinos and antineutrinos. You would set up a detector near the reactor and measure how many neutrinos of each type were emitted from the reactor to your detector (this is not easy as a practical matter, but we can assume that it has been done and done properly for these purposes). Then, you need to figure out how many neutrinos are expected in each of your detector bins in the Standard Model.

To get the right prediction, you need to know how many neutrinos of each type you predict will end up in each bin, and how many antineutrinos of each type you predict will end up in each bin, and then you need to compare your experimental measurement to the theoretical prediction (in light of the margins of error in your parameter measurements and in your experimental measurements).

But, because the CP violation parameter is non-zero, the proportions of neutrinos in each bin will be different from the proportion of antineutrinos in each analogous bin for antineutrinos. Without making that adjustment, you would think you are seeing a fifth force when you are really just seeing results that are completely consistent with the Standard Model.

On the other hand, if the observed number of neutrinos and antineutrinos in the bins for each respective type are different to a statistically significant extent from the numbers predicted by the Standard Model including the CP violation parameter, then you have observed evidence of "new physics" beyond the Standard Model and need to figure out how to explain that anomaly.

So far, we would only be able to see huge deviations from the Standard Model expectation, because neither our parameter measurements, nor our experimental measurements are super precise. And, we haven't seen that. But, science is a cumulative process. Each new generation of scientists sits on the shoulders of the giants who came before. And, gradually, over time, with each new experiment, the margin of error in the parameters shrinks and the precision of the experimental apparatuses that are used grows greater. And, prior results can allow us to focus our attention where experience has taught us to look, optimizing our experiments for that part of the parameter space. As that happens, potential deviations from the Standard Model can be confirmed or ruled out to greater precision.

 

[Orodruin]

The result is completely consistent with the Standard Model. It is a measurement of one of the four parameters of the PMNS matrix, each of which is a fundamental experimentally determined physical constant of the Standard Model (of which there are a couple dozen).

Well, technically, the SM extended with neutrino masses.

The existence of CP violation in neutrino oscillations is established at just slightly less than three sigma, but close to 98-99% likelihood.

It is important to note the difference between confidence level and likelihood. The T2K result is frequentist in nature and does not give a probability for or against CP violation.

 

[Lord Crc]

Thank you for the responses, that helped clear things up.

I was under the impression that CP violation was BSM. So it would then be correct to say that all (most?) SM extensions that introduce neutrino masses allow for CP violation?

 

[Orodruin]

I was under the impression that CP violation was BSM.

Neutrino masses by themselves are generally considered to be BSM physics. Therefore, anything that has to do with oscillations is technically going to be BSM, including CP-violation in the PMNS matrix.

Note that the SM does have CP violation though and that this has been observed for a long time in the CKM matrix, which describes the mixing of quarks.

 

[Vanadium 50]

Neutrino masses by themselves are generally considered to be BSM physics.

Yes, but this (as I have discussed previously) was a relatively late addition to the SM. It happened just before neutrino masses were discovered to be non-zero. I've detailed the history elsewhere, but the 1978 review article Bilenky and Pontecorvo (the P of PMNS) jumps straight into masses without even suggesting that in the SM they are supposed to be zero. There was just never a time when people were walking around thinking neutrinos were massless.

Onto this result. I was sitting next to Chris Quigg on a flight to or from Geneva a while back and one of the topics of our conversation was "the only interesting number for the CP phase is zero". The point of this is that any 3 family mixing has a CP phase, and it has to be something. But if it is identically zero, there is some new symmetry making it zero.

You don't see papers saying "if the neutrino CP phase is between x and y it explains the matter-antimatter asymmetry of the universe". It doesn't work this way. The thinking is that there is some unknown physics that drives the matter-antimatter asymmetry, and one low-energy consequence of this is reflected in the neutrino CP phase.

 

[Orodruin]

Yes, but this (as I have discussed previously) was a relatively late addition to the SM. It happened just before neutrino masses were discovered to be non-zero. I've detailed the history elsewhere, but the 1978 review article Bilenky and Pontecorvo (the P of PMNS) jumps straight into masses without even suggesting that in the SM they are supposed to be zero. There was just never a time when people were walking around thinking neutrinos were massless.

That neutrino masses were not expected to be zero does not mean that they are non-zero in the SM. There are a number of different ways of incorporating neutrino masses in the SM, but it is not clear which would be the "standard" way to do this.

You don't see papers saying "if the neutrino CP phase is between x and y it explains the matter-antimatter asymmetry of the universe". It doesn't work this way. The thinking is that there is some unknown physics that drives the matter-antimatter asymmetry, and one low-energy consequence of this is reflected in the neutrino CP phase.

I would give a stronger statement: Even if the CP phase of the PMNS arises from a high-energy theory that predicts the baryon asymmetry, there is no a priori argument that the low-energy CP phase is relevant to that generation mechanism.

 

[Vanadium 50]

There are a number of different ways of incorporating neutrino masses in the SM, but it is not clear which would be the "standard" way to do this.

I'm not sure I would argue "I'm not sure if the mass is Dirac or Majorana, therefore it must be zero!"

Even if the CP phase of the PMNS arises from a high-energy theory that predicts the baryon asymmetry, there is no a priori argument that the low-energy CP phase is relevant to that generation mechanism.

That is absolutely true.

One argument goes like this: we've measured the quarks pretty well, and are still uncertain about what's going on, so let's look at the leptons. They may be cleaner, and in any event, it's a second data point.

The other argument goes like this: we love the see-saw mechanism. This provides a natural way to connect the high energy physics we care about to the neutrinos we can measure. I would argue that see-saw love is misplaced, but I'm in the minority here.

 

[Orodruin]

I'm not sure I would argue "I'm not sure if the mass is Dirac or Majorana, therefore it must be zero!"

That is not what I am arguing. I am arguing that whatever mechanism it is, it is not part of the Standard Model as it is typically phrased today. That historically nobody expected neutrinos to be massless does not mean that the Standard Model predicted neutrino masses. The Standard Model must not describe Nature perfectly.

 

[Vanadium 50]

does not mean that the Standard Model predicted neutrino masses.

I agree, it didn't.

But it didn't predict quark or charged lepton masses either. I would argue only one fermion has a sensible mass, the top quark. Everything else has something going on we don't understand. Maybe the top does too.

 

[Orodruin]

But it didn't predict quark or charged lepton masses either.

This depends on what you mean by "predict" and "Standard Model".

 

[ohwilleke]

Well, technically, the SM extended with neutrino masses.

The terminology in that case is vexing. I'd say that this statement is both true and not true.

The Standard Model, 1979-1990ish edition, has massless neutrinos, although more as a default assumption than as a strong empirically motivated conclusion. But, even then, I don't think there was ever majority support for the idea that real world neutrinos were actually massless.

The current consensus in the scientific community is that there are massive neutrinos which oscillate and have oscillations including CP violation in connection with oscillations that is well described by the PMNS matrix and by the measured differences in mass between the mass eigenstates. The evidence from more than one independent line of evidence is moving strongly towards a widespread belief that there is "normal mass hierarchy" and towards a fair modest range masses for the lightest of the neutrino mass eigenstates, from which the other two can be determined with considerable precision given everything else we know. Figuring out if one parameter which is definitely not exactly 45º is a little more than or a less less than 45º is just a measurement thing and not fundamental. So, operationally, that gets us what people in many contexts would call the neutrino portion of the Standard Model.

The problem with the picture, of course, is that we have a nice neat theory to explain the masses of all of the other fundamental particles of the Standard Model that have non-zero mass with the Yukawas of those particles coupling to the Higgs field, while neutrinos stubbornly refuse to fit neatly into the model.

The "shut up and calculate" school of physics would argue - neutrino mass is. We have no affirmative evidence sufficient to make any meaningful statements about why neutrino mass is. So, we do not speak of that until we get some affirmative evidence to inform us.

But, all of the most obvious fixes to neutrino mass have problems, until somebody has an a-ha moment and comes up with a better one.

The Higgs mechanism presumes that massive fermions come in left parity-right parity pairs of identical mass, with the same electromagnetic charge and same particle v. antiparticle status. But, that doesn't work for what we have observed about neutrinos. Neutrinos don't have electromagnetic charge. Neutrinos don't have strong force charge. Left handed neutrinos and right handed antineutrinos have weak force charge; but right handed particles and left handed antiparticles do not. All available evidence supports the conclusion that neutrino oscillation via the PMNS matrix conserves matter v. antimatter status. So, if right handed neutrinos did exist, they would not interact via any of the Standard Model forces or interactions. Thus, even if we operationally treat left handed neutrinos and right handed antineutrinos as if they had Dirac mass (which is basically what the PMNS matrix treatment that is the conventional wisdom used on a daily basis does), fitting neutrinos in the Higgs mechanism doesn't work elegantly the way it does for all of the other massive fundamental particles of the Standard Model.

A Majorana mass solution to neutrino mass isn't much better. This implies lepton number violation outside of sphaleron processes, for example, in neutrinoless double beta decay or tree level flavor changing neutral currents, which have never ever been observed. This introduces two additional CP violation phases that we again have zero experimental motivation to introduce. While the Higgs mechanism at least has some answer to why fundamental particles of different generations have different masses, even if it is question begging (they have different Yukawas, which is barely better than "because Nature says so"), to get a Majorana mass solution to do that you have to come up with something even uglier.

The see-saw mechanism introduces new particles that don't fit existing patterns and definitely introduces beyond the Standard Model physics that we don't need for fit experimental data and that are only motivated as a way to somehow explain neutrino mass.

I'd like to hope we come up with better solutions than any of these someday, and I have a few possibilities in mind that I think are promising, even though they aren't fully worked out. But, this is not the place to spin speculations about what that would look like.

Until then, I think that the fair answer is that neutrino mass and neutrino oscillation via a four parameter PMNS matrix plus three neutrino mass eigenstates is part of the Standard Model, 2020 edition, as that term is commonly used in a wide variety of contexts, but that the Standard Model just doesn't tell us where those masses or any of the other neutrino physics parameters come from, just as it doesn't tell us where the other Standard Model parameters come from.

The Standard Model, 2020 edition, is like a scarf made by an impatient knitter with a knife. It has lots of loose ends, even though it basically comes together as a whole into something very pretty and useful.

This would all be much more troubling if we had any decent theory to explain why most of the Standard Model experimentally measured fundamental parameters take the values that they do. But, since it isn't all that different to say that muons have the mass that they do for no reason at all, and to say that muons have the mass that they do because of the Higgs field Yukawa which has the value it does for no reason at all,* not having a ready answer for why neutrino masses are what they are doesn't tarnish the integrity of the Standard Model all that much anyway. It would be nice to know and we could even make some predictions about some very hard to observe and obscure phenomena if we did, but we can manage just fine without that knowledge for now. Knowing the CP violating phase of the PMNS matrix with greater precision would be a lot more useful in the short to medium term.

* I recognize that the math of the Standard Model needs to have massless fermions and a Higgs field rather than intrinsically massive fermions to work properly and that in that sense, it is very different. I just mean that it is not all that different with respect to haven't an ultimate answer to where these numbers comes from. I also understand that the same logic means that having intrinsically massive neutrinos, even if the masses are tiny, is, in some theoretical consistency sense more undesirable than the Higgs mechanism that has been worked out for all of the other fermions even with that mechanism's question begging Yukawas. But, it would be a lot more frustrating to not have a neutrino mass mechanism figured out if we actually had some sensible explanation for why the fundamental particle masses and CKM and PMNS matrix parameters and the three coupling constants, took the values that they do.

I would argue that see-saw love is misplaced, but I'm in the minority here.

I totally agree. If you are in the minority here, you are at least in a minority of not less than two. I've read enough see-saw papers that now, when I see one on arXiv, I immediately go . . . "on to the next thing, let's find someone who has something more novel and worthwhile to add to the great discussion" without even reading anything else about the article.

It is important to note the difference between confidence level and likelihood. The T2K result is frequentist in nature and does not give a probability for or against CP violation.

Fair enough. Slightly sloppy language. Mea culpa. Mea maxima culpa.

 

[Orodruin]

Thus, even if we operationally treat left handed neutrinos and right handed antineutrinos as if they had Dirac mass (which is basically what the PMNS matrix treatment that is the conventional wisdom used on a daily basis does), fitting neutrinos in the Higgs mechanism doesn't work elegantly the way it does for all of the other massive fundamental particles of the Standard Model.

The Dirac mass mechanism would work just as well for neutrinos as for the quarks or charged leptons. The big difference is that the right-handed field would be a SM singlet. This a priori allows a Majorana mass term for the right-handed field, with a mass parameter that is not a priori related to anything else in the SM. Letting this Majorana mass be large naturally results in the seesaw mechanism, but it is quite natural to discuss the phenomenology in any range for the right-handed Majorana mass.

The Higgs mechanism presumes that massive fermions come in left parity-right parity pairs of identical mass, with the same electromagnetic charge and same particle v. antiparticle status.

This is not really correct. Before symmetry breaking, neither of the left/right-handed fields have mass. Once you introduce the EW symmetry breaking via the Higgs mechanism, the mechanism itself results in a Dirac mass for the left/right-handed pair. Gauge symmetry for SM non-singlets prevent the Majorana masses and therefore leave Dirac pairs so this is a prediction of the Higgs mechanism if the field charges are such that no fields are singlets under the gauge groups. Since the right-handed neutrinos would be singlets, there is no reason a priori to expect a Dirac pair.

A Majorana mass solution to neutrino mass isn't much better. This implies lepton number violation outside of sphaleron processes, for example, in neutrinoless double beta decay or tree level flavor changing neutral currents, which have never ever been observed. This introduces two additional CP violation phases that we again have zero experimental motivation to introduce. While the Higgs mechanism at least has some answer to why fundamental particles of different generations have different masses, even if it is question begging (they have different Yukawas, which is barely better than "because Nature says so"), to get a Majorana mass solution to do that you have to come up with something even uglier.

Again, I do not agree with this. The Majorana mass that violates lepton number in the seesaw (which is a natural consequence of introducing a right-handed neutrino field) is rather natural as there is absolutely nothing to forbid it. B-L is an accidental symmetry of the SM and was never imposed, there is no theoretical reason to a priori believe that it should be conserved. The apparent conservation of lepton number at low energies is therefore something that any UV completion of the SM has to deal with, such as through a suppression of those processes by a large scale (as in the seesaw).

Instead, I would say that the seesaw is rather natural. It essentially follows directly from the introduction of right-handed neutrinos into the SM for a perfectly viable range for the new parameter space that includes the Majorana mass term for the right-handed neutrino field, which also naturally suppresses lepton number violation. (In fact, if the right-handed mass would be lower than the characteristic scale for double beta-decaying nuclei, it would also suppress the rate of neutrinoless double beta decay.)

The see-saw mechanism introduces new particles that don't fit existing patterns and definitely introduces beyond the Standard Model physics that we don't need for fit experimental data and that are only motivated as a way to somehow explain neutrino mass.

I do not agree. All it does is to introduce right-handed neutrinos, which is very much in the same spirit as the SM where quark SU(2) doublets are accompanied by two SU(2) singlets, whereas the lepton doublets are only accompanied by one singlet. The big difference is that those new fields would be complete SM singlets and therefore allow an additional Majorana term. So the (type-I) seesaw actually just extends the field content of the SM in a rather natural way. It is just that that extension allows a mass term that is unrelated to the Higgs mechanism. In essence, it directly follows from the will to put Dirac masses on neutrinos.

 

[mfb]

NOvA measured the same parameter, and their result is nearly a perfect opposite of what T2K sees (but with larger uncertainties). Presented at Neutrino 2020 (virtual conference)
Slides
Here are both in one image (from slide 29)

Interestingly: T2K has the same preferred regions for the inverted mass ordering (one light neutrino, two "heavy" neutrinos), but for NOvA this is inverted. With the inverted hierarchy both experiments favor the same region. The inverted hierarchy is disfavored from other measurements, however.

 

[ohwilleke]

Eyeballing the image, there is a point at roughly 1.15pi and sin^2theta(23)=0.55 (about 48º) that is within the one sigma range of both experiments.

The collective evidence disfavoring an inverted hierarchy is too strong to be displaced much by these two results with big error bars.