I New Upper Bound of Neutrino Mass

[fresh_42]

TL;DR Summary

Direct neutrino-mass measurement based on 259 days of KATRIN data. The paper claims a model-independent measurement of less than 0.45 eV mass with 90% confidence.

For the press:

The international KArlsruhe TRItium Neutrino Experiment (KATRIN) at the Karlsruhe Institute of Technology (KIT) has once again surpassed its own achievements. The latest data establish an upper limit of 0.45 eV/c2 (equivalent to 8 x 10-37 kilograms) for the neutrino mass. With this result, KATRIN, which measures neutrino mass in the laboratory using a model-independent method, has once again set a world record. The researchers have published their results in the journal Science.

https://www.kit.edu/kit/english/pi_...trinos-weigh-less-than-0-45-electronvolts.php


For physicists:

That neutrinos carry a nonvanishing rest mass is evidence of physics beyond the Standard Model of elementary particles. Their absolute mass holds relevance in fields from particle physics to cosmology. We report on the search for the effective electron antineutrino mass with the KATRIN experiment. KATRIN performs precision spectroscopy of the tritium β-decay close to the kinematic endpoint. On the basis of the first five measurement campaigns, we derived a best-fit value of $m^2_\nu=-0.14^{+0.13}_{-0.15} \;\mathrm{eV^2},$ resulting in an upper limit of $m_\nu<0.45\;\mathrm{eV^2}$ at $90\%$ confidence level. Stemming from 36 million electrons collected in 259 measurement days, a substantial reduction of the background level, and improved systematic uncertainties, this result tightens KATRIN’s previous bound by a factor of almost two.

https://www.science.org/doi/10.1126/science.adq9592

 

[mad mathematician]

$m_\nu^2<0$ imaginary numbered mass?!

 

[Orodruin]

$m_\nu^2<0$ imaginary numbered mass?!

No, it is just about how tritium decay experiments work when measuring the end-point energy. They depend on a factor of the neutrino mass squared, but continuously so they fit that expression agnostically with $m_\nu^2$ as a free parameter. That free parameter comes out with a negative best-fit. It has for every tritium neutrino decay experiment so far. 20 years ago this led me down a trail of thought I still think might have been my only Nobel prize worthy original thought ever should it have panned out in the future. Of course, on looking through the literature, it turned out Weinberg had had the same thought in the 80s, but still. I got a paper out of working on it a bit.

But yes, I would also like to see them make a fit where it is restricted to be positive.

 

[Hornbein]

TL;DR Summary: Direct neutrino-mass measurement based on 259 days of KATRIN data. The paper claims a model-independent measurement of less than 0.45 eV mass with 90% confidence.

For the press:

https://www.kit.edu/kit/english/pi_...trinos-weigh-less-than-0-45-electronvolts.php


For physicists:

https://www.science.org/doi/10.1126/science.adq9592

One trentillionth of a gram.

 

[ohwilleke]

FWIW, the result was announced on June 19, 2024, with no material changes in the nearly ten months between the pre-print and the final published peer reviewed version. M. Aker, et al., "Direct neutrino-mass measurement based on 259 days of KATRIN data" arXiv:2406.13516 (June 19, 2024).

The experiment is expected to ultimately bound it to 0.2 eV or less, which is the limit of its capacity to measure it. This is on the order of 200 times the true value, if cosmology based estimates have a sound scientific basis.

 

[Orodruin]

This is on the order of 200 times the true value, if cosmology based estimates have a sound scientific basis.

Please support this by references. As far as I am aware there is no current consensus on a definitive discovery of neutrino masses from cosmology. You are also saying this true value should be 0.001 eV, which would be incompatible with oscillation results requiring at least one state to have a mass of at least 0.049 eV. Cosmology bounds typically address the sum of neutrino masses so a result significantly below this should be taken with an enormous pinch of salt. It is more likely to stem from not understanding the cosmology well enough than from actual neutrino masses.

 

[ohwilleke]

Please support this by references. As far as I am aware there is no current consensus on a definitive discovery of neutrino masses from cosmology.

There are many cosmology based upper bounds on the sum of the three neutrino masses which taken together with neutrino oscillation data imply an upper bound on the lightest neutrino mass eigenstate.

Like most particle physics questions with multiple measurements of a physical constant, it isn't a matter of a "consensus" so much as it is a compilation of the best fit to the measurements that have been made to date, discarding earlier estimates that have been superseded by the same research groups. Essentially all of the recent cosmology based estimates are in the same ballpark and are summarized by the Particle Data Group. The most recent results from that summary are as follows:

The most recent estimate, which is a representative example of a bound on the sum of neutrino masses from cosmology is:

From DESI.

The DESI estimate matches a pre-DESI result from 2020.

Another cosmology based limit on the sum of the three neutrino masses is an upper bound of 87 meV at 95% confidence (which would rule out the inverted hierarchy at low significance). See Eleonora Di Valentino, Stefano Gariazzo, Olga Mena "On the most constraining cosmological neutrino mass bounds" arXiv:2106.16267 (June 29, 2021) (previously discussed in this PF thread). See also In V. Ghirardini, et al., "The SRG/eROSITA All-Sky Survey: Cosmology Constraints from Cluster Abundances in the Western Galactic Hemisphere" arxiv.org/abs/2402.08458 (Feb. 13, 2023) (sum < 0.11 eV) which also states:

the constraints on the mass of the lightest neutrino eigenstates are similar: for both mass hierarchy we obtain m(light) = 0.01 +0.020 −0.005 eV (68% confidence intervals)

Then there is this estimate from 2020 (sum < 0.14 eV) and this estimate from 2018 (which lists multiple bounds based upon the assumptions made). Back in 2014, the Plank CMB measurements put a cap on the sum of the neutrino masses of 0.26 eV, but that has been greatly tightened in the last eleven years with more astronomy data.

The PDG review article on cosmology based neutrino mass estimates is short and states in its entirety:

Converting an upper bound on the sum of the three neutrino masses to bounds on the smallest of the three neutrino mass eigenstates:

A limitation on the sum of the neutrino masses of a certain amount implies a maximum lightest neutrino mass based upon oscillation data.

The 95% confidence interval minimum value of the mass difference between the second and third neutrino mass eigenstate is 48.69 meV, and the corresponding value of the mass difference between the first and second neutrino mass eigenstate is 8.46 meV. This implies that with a first neutrino mass eigenstate of 0.1 meV, a sum of the three neutrino masses is 0.01 + 8.47 + 57.16 = 65.64 meV in a normal hierarchy and 0.01 + 48.70 + 57.16 = 105.87 meV in an inverted hierarchy.

There are probably half of dozen different estimates of the sum of the three neutrino masses from cosmology in the same ballpark, plus or minus a dozen or two meV, as the DESI estimate cited above of < 0.13 eV, which implies an upper bound of 8 meV on the lightest neutrino mass in an inverted hierarchy and an upper bound of 24.5 meV in a a normal hierarchy (given neutrino oscillation data). The two hierarchies are illustrated respectively in the following chart:

You are also saying this true value should be 0.001 eV, which would be incompatible with oscillation results requiring at least one state to have a mass of at least 0.049 eV.

KATRIN is measuring the lightest of the three neutrino masses, not the sum of the three neutrino masses, or a simple mean of the neutrino mass eigenstates (arguably, they could be said to be measuring the electron neutrino mass which would be a PMNS matrix weighted mix of the three neutrino mass eigenstates, which would still be much lower that the heaviest neutrino mass eigenstate).

Neutrino oscillation data doesn't place a floor (or ceiling) on the absolute mass of the lightest neutrino mass.

Realistically, almost no neutrino physics scientists actually believe that the lightest neutrino mass is anywhere near the upper bound of 0.45 eV recently established by KATRIN or the upper bound of 0.2 eV which is KATRIN's maximum sensitivity. This is simply a function of the most sensitive direct neutrino mass detection experiment that we are able to build at the moment.

Cosmology bounds typically address the sum of neutrino masses so a result significantly below this should be taken with an enormous pinch of salt. It is more likely to stem from not understanding the cosmology well enough than from actual neutrino masses.

Given the amount of the uncertainty in the cosmology based bounds, however, the best fit value is generally on the order of 1-10 meV, and the balance of the upper bound is two sigmas of observational uncertainty.

Pretty much all of the evidence from both oscillation studies and cosmology favors the normal hierarchy over the inverted hierarchy, but not at a decisive 5 sigma level. A 2018 estimate put the preference at 3.5 sigma. Di Valentino (2021), cited above, implies a 2.2-2.7 sigma preference for a normal ordering. See also here and here.

All of the cosmology estimates include some assumption, such as an assumption that neutrino masses must not be negative, and sometimes, that the minimum sum of neutrino masses is the minimum in the normal hierarchy. But the observational pull is generally towards a best fit closer to the lower values. See, e.g., Nathaniel Craig, Daniel Green, Joel Meyers, Surjeet Rajendran, "No νs is Good News" arXiv:2405.00836 (May 1, 2024).

The fact that the cosmology based upper bound estimates of sum of the neutrino masses, and the neutrino oscillation experiment estimates of the minimum sum of the three neutrino masses, are of the same order of magnitude, lends some confidence to the idea that the cosmology based bounds are probably not grossly off the mark, even if it isn't logically necessary that this be the case if the cosmology based bounds are unsound (and they are certainly model dependent, although they are more robust to changes in the model than you might think). See Eleonora di Valentino, Stefano Gariazzo, Olga Mena, "Model marginalized constraints on neutrino properties from cosmology" arXiv:2207.05167 (July 11, 2022).

Footnote: Evidence for exactly three neutrinos that oscillate with each other under 10 eV or so.

As an aside, data from W and Z boson decays likewise tightly constrain the number of active neutrinos with masses of less than 45,000,000,000,000 meV/c^2 to exactly three.

Neutrino oscillation experiment anomalies suggesting the existence of a light sterile neutrino are mutually inconsistent with each other.

Cosmology data also strongly supports the hypothesis that there are exactly three generations of neutrinos (with no sterile neutrinos having a mass of 1,000,000,000 meV/c^2 or less) (also here). These cosmology bounds are very robust to issues that could arise from a specific set of instrumentation or the details of the model used.

 

[Orodruin]

There are many cosmology based upper bounds on the sum of the three neutrino masses which taken together with neutrino oscillation data imply an upper bound on the lightest neutrino mass eigenstate.

Sure, but that was not your statement. Your statement was that the KATRIN result was two orders of magnitude larger than the true value of the neutrino mass. This is very different from claiming an upper bound. It is claiming having zoned in on a particular finite mass range.

This is on the order of 200 times the true value

So you are now essentially retracting this claim?

As I said, it is also not 200 times the range required by oscillations, which is at least 48 meV. 200 x 48 meV would be 9.6 eV.

Again, you know that I am a neutrino physicist, right? Posting a long essay on things I am aware of and does not support your claim regarding the true value of the neutrino mass only serves the purpose of derailing rather than focusing the discussion on what is important. In particular when you start talking about things not related to the actual question asked such as Neff and the Z decay width.

 

[mfb]

The 95% confidence interval minimum value of the mass difference between the second and third neutrino mass eigenstate is 48.69 meV

I can't find that at the PDG.

A sum of 80 meV is perfectly compatible with cosmology limits, and would put the lightest neutrino at over 10 meV and the heaviest at over 50 meV. Which is still too light for KATRIN to measure as non-zero, but not 200 times lighter.

 

[ohwilleke]

Sure, but that was not your statement. Your statement was that the KATRIN result was two orders of magnitude larger than the true value of the neutrino mass. This is very different from claiming an upper bound. It is claiming having zoned in on a particular finite mass range.

The upper bound claimed by KATRIN is about 200 times greater than the best fit value from cosmology, which can be determined from efforts to determine the upper bound of the sum of the three neutrino masses from cosmology, and assuming that masses cannot be negative and assuming that the sum of the three neutrino masses can't be lower than the minimum lower bound from neutrino oscillation experiments.

So you are now essentially retracting this claim?

No.

As I said, it is also not 200 times the range required by oscillations, which is at least 48 meV. 200 x 48 meV would be 9.6 eV.

This is not correct. You are confused about KATRIN is measuring. KATRIN is not measuring the highest neutrino mass eigenstate (which is in very round number about 0.05 eV more than the lowest neutrino mass eigenstate). KATRIN is measuring some close approximation of the lowest neutrino mass eigenstate. There is no contradiction.

Again, you know that I am a neutrino physicist, right?

I am not.

Posting a long essay on things I am aware of and does not support your claim regarding the true value of the neutrino mass only serves the purpose of derailing rather than focusing the discussion on what is important.

You are the one who is confused, as your comparison of the mass difference for the highest neutrino mass eigenstate to the KATRIN result implies, and as your statement that there is no consensus of the sum of the neutrino masses from cosmology suggests.

In particular when you start talking about things not related to the actual question asked such as Neff and the Z decay width.

It is an interesting side point that goes to the solidity of cosmology based data and the soundness of the three neutrino model.

 

[ohwilleke]

I can't find that at the PDG.

A screenshot of the relevant text (from here) is as follows:

You have to take the positive square root of the two mass differences (because masses can't have a negative absolute value), and then add them to each other with an appropriate value for the lowest neutrino mass eigenvalue, and then add two sigma of uncertainty above the square root to get the upper bound on the minimum value of the sum of the three neutrino masses.

A sum of 80 meV is perfectly compatible with cosmology limits, and would put the lightest neutrino at over 10 meV and the heaviest at over 50 meV. Which is still too light for KATRIN to measure as non-zero, but not 200 times lighter.

The lightest neutrino mass is the only one that KATRIN is measuring, so the mass of the heaviest one is irrelevant to the comparison.

The best fit values of the lightest neutrino mass in the cosmology estimates is at the bottom of the allowed range (as noted by multiple references cited above). Without the imposed boundaries of non-zero mass and mass at least as great as the minimum normal hierarchy mass, the DESI best fit value is actually negative.

 

[Orodruin]

The upper bound claimed by KATRIN is about 200 times greater than the best fit value from cosmology, which can be determined from efforts to determine the upper bound of the sum of the three neutrino masses from cosmology, and assuming that masses cannot be negative and assuming that the sum of the three neutrino masses can't be lower than the minimum lower bound from neutrino oscillation experiments.

You should know better than to use the best-fit as the ”true value”. There is simply no statistical basis for that and confounding them is simply wrong.

Even if it were not the case, I’d trust cosmology bounds about as far as I can throw them … at least until cosmology is better understood.