Individual Neutrino Masses From a Supernova

Peter B. Denton; Yves Kini

REVIEW 4 major objections 4 minor 1 cited by

Individual Neutrino Masses From a Supernova

T0 review · 4 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A galactic supernova could measure each of the three neutrino mass states individually.

desk verdict A genuine three-mass-state framework for SN time-delay, with a clean derivation and honest caveats, but the conclusion overclaims: Table II only measures all three masses in the KATRIN/QCD corner, and the new-physics benchmark leaves m1 as an upper bound. read the letter →

arxiv 2411.13634 v2 pith:PKBCZFXC submitted 2024-11-20 hep-ph astro-ph.HE

Peter B. Denton , Yves Kini This is my paper · ORCID

classification hep-phastro-ph.HE PACS 14.60.Pq95.85.Ry97.60.Bw

keywords neutrinomasseigenstatessupernovaneutrinostime-of-flightdelayMSWeffectJUNOdetectorneutronizationburstQCDphasetransitionblackholeformation

open problems Dark Matter

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper claims that one nearby supernova, seen by the JUNO detector, can constrain the mass of each of the three neutrino mass eigenstates individually, rather than only the sum of masses or the squared mass differences that oscillation experiments measure. The idea is that each mass state travels at a slightly different speed, so a sharp feature in the supernova's neutrino signal — the neutronization burst, a QCD phase transition, or black hole formation — arrives as three time-staggered copies whose delays grow at low energy. The paper writes the supernova flavor flux with the three mass states kept separate (equations 11–14) and folds in the energy-dependent time delay of equation (27) for each state. For KATRIN-scale or heavier masses, all three masses can be measured; at the light masses allowed by oscillations or cosmology, the same data give upper bounds rather than measurements. This matters because the absolute scale and individual ordering of neutrino masses are among the last unknown parameters of the standard model and are inaccessible to oscillation experiments alone.

What carries the argument

The load-bearing object is the set of per-mass-state flux equations (11)–(14): the supernova flux at Earth is written as a sum over the heavy, medium, and light mass eigenstates, ordered by $m_H > m_M > m_L$, with each state's mixing weight shifted by its own time delay $\Delta t_i(E) \simeq (D/2)(m_i/E)^2$ (equation 28). What makes it work is that the mixing weights along the electron row (0.68, 0.30, 0.02) are never collapsed through unitarity into $1-|U_{e3}|^2$, so each mass state remains separately addressable in time. The accompanying checks — production above all MSW resonances (equation 15) and negligible jump probabilities (equations 16–22, figures 2–4) — keep the mapping from source emission to mass state to detected flavor clean enough for the time-of-flight effect to be read off.

What would settle it

Measure the energy-dependent arrival delays of a sharp supernova feature (for example, the black-hole turnoff) in a galactic supernova at a known distance with JUNO. If the low-energy tail of events is not delayed relative to the sharp cutoff by the $\propto 1/E^2$ pattern with the per-state weights 0.68/0.30/0.02, or if the delays imply mass-squared splittings that disagree with the oscillation-measured $\Delta m^2_{21}=7.4\times10^{-5}$ eV$^2$ and $\Delta m^2_{31}=2.5\times10^{-3}$ eV$^2$, the per-state time-delay picture would be falsified.

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Extended reading notes

Core claim

On its own terms, the paper shows that the standard supernova-neutrino flux formulas change character once the three mass eigenstates are followed separately. The familiar equations for $\Phi_{\nu_e}$, $\Phi_{\bar\nu_e}$, and the non-electron flavors are rewritten using the heavy/medium/light mass labels $H, M, L$ and the projections $|U_{eH}|^2, |U_{eM}|^2, |U_{eL}|^2$ (equations 11–14), so that each mass state carries its own mixing weight and its own arrival time. Each weight is then shifted in time by $\Delta t_i(E) \simeq (D/2)(m_i/E)^2$ (equation 27), and the paper shows with resonance-density and jump-probability estimates that neutrinos are produced above all level crossings, so this single-flavor mapping is valid for any mass ordering. Using the 27 $M_\odot$ supernova model of [21], JUNO's detector response, and a Poisson log-likelihood over the three sharp timing features, the paper finds (Table II) that at 10 kpc the KATRIN-scale benchmark yields 1$\sigma$ ranges such as $m_1 = 0.25$–$0.54$ eV, $m_2 = 0.32$–$0.84$ eV, and $m_3 = 0.34$–$1.52$ eV for a QCD phase transition, while the light oscillation/Planck benchmarks lead to upper bounds. The conclusion is stated plainly: a detection of a galactic supernova can measure the mass of each neutrino state, subject to statistical uncertainties.

Load-bearing premise

The paper's strongest loaded assumption is that the neutrino mixing matrix in the galactic center is identical to the one measured on Earth — the electron-row weights 0.68, 0.30, and 0.02 — even while the three masses themselves are allowed to change freely; if a dark-matter coupling alters the mixing angles together with the masses, the mapping from detected flavors to time-delayed mass states breaks down.

Editorial extensions

If this is right

For a supernova at 10 kpc observed by JUNO, each of the three mass states is constrained independently: KATRIN-scale masses are measured in all three states under a QCD phase transition, while oscillation- or Planck-scale masses give upper bounds such as $m_1 < 0.28$ eV in the normal-ordering benchmark.
Closer supernovae sharpen the measurement: at 1 kpc or less the ordering $m_3 > m_2$ becomes distinguishable even in the KATRIN scenario where it cannot be resolved at 10 kpc.
Because the three timing features come from unrelated physics, their likelihoods can be added at each point in parameter space, so a supernova that shows both a neutronization burst and a later sharp feature yields combined constraints stronger than any single feature.
The paper's per-state description implies that previous supernova analyses that assumed degenerate masses were missing the main handle: the distinct arrival-time patterns of each eigenstate, not just a single effective mass.
Part of the mass-ordering sensitivity comes from the MSW flavor conversion inside the supernova, so the same event can distinguish normal from inverted ordering even when the absolute masses are too small to time-resolve directly.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the fixed-mixing ansatz survives scrutiny, the same per-state time-delay logic should extend to any sharp neutrino transient with a known emission time — neutron-star merger signals, for example — making the technique a general probe of absolute neutrino mass rather than a supernova-specific one.
A multidetector analysis combining JUNO with the other next-generation water and liquid-argon detectors would split the difference between low thresholds and high statistics, and the paper's per-state flux formulas give those collaborations a ready-made framework; the paper itself only projects one detector.
The most interesting outcome would be a supernova whose time-delay pattern and MSW flavor pattern demand different mass orderings; under the paper's assumptions that cannot happen, so such an event would be a clean test of spatially varying neutrino masses and would falsify the fixed-mixing ansatz.
Because the delay scales as $m_i^2/D$, an independent distance measurement to the supernova (for example, from gravitational waves or the expanding shock front) is as important as event statistics for turning a detected delay into an absolute mass; the paper fixes $D = 10$ kpc rather than marginalizing over it.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

First thing to know: this is the first treatment I've seen of a galactic SN time-delay that keeps the three mass eigenstates separate instead of folding them into a single effective mass. Equations (11)-(14) are the real work, and they're correct—the MSW/jump-probability check is careful and the authors even provide a customized SNEWPY fork, which makes the numerics reproducible. For anyone planning a SN neutrino analysis, those equations and the associated time-delay implementation (eq. 28) are worth taking seriously.

The JUNO sensitivity study is a standard forecast: event rates are generated with injected benchmark masses and then fit, so the intervals in Table II are expected closures, not measurements. That's fine for a forecast, but it means the numbers inherit the chosen 27 M☉ model and the assumed sharp-feature shapes. The authors are upfront about marginalizing over the feature start time, and they don't pretend the QCD phase transition is guaranteed—but they also don't propagate the SN model uncertainty into the sensitivities. That's a real limitation, not a fatal one.

Where I part company with the paper's conclusions is the title-level claim. Table II shows that in the 'High mass' new-physics benchmark, m1 is constrained to an upper bound in every channel (m1 < 0.40 eV for QCD, <0.54 for BH, <0.80 for NB). An upper bound is not a measurement of m1. The only benchmark where all three masses get two-sided intervals is the KATRIN-scale case with a QCD phase transition. So the abstract's 'masses of each of the three mass eigenstates individually' and the conclusion's 'each separate mass state can be uniquely identified' are too strong. The stress-test note on this is right, and it lands on reading the paper.

The other soft spot is the ansatz in Section III.A: the mixing matrix stays at the terrestrial values while the masses vary arbitrarily. For a DM-coupled new-physics scenario in the galactic center that's an assumption, not a consequence. The authors flag it, but it means the high-mass benchmark program—the part that would actually measure individual masses—rests on unvalidated physics.

Net: the derivation is solid and the framework is a real step forward. The paper deserves a serious referee. It needs the conclusions and abstract toned down to match Table II, a discussion of model-systematic propagation, and ideally a clearer statement that for the standard light-mass case this is an upper-bound probe, not a measurement. I'd send it to review and would cite the three-state time-delay equations.

Referee Report

4 major / 4 minor

Summary. This paper develops a framework for using a galactic supernova observed by JUNO to constrain the three individual neutrino masses. The key theoretical step is rewriting the standard MSW-flavor-transformed supernova fluxes as sums over the three mass eigenstates (Eqs. 11-14) and applying an energy-dependent time delay to each state separately (Eqs. 27-28), with the mass-state labels assigned by the electron-row PMNS elements rather than by mass. The authors check that jump probabilities are negligible for the relevant parameter space, then simulate event rates for three sharp timing features (neutronization burst, QCD phase transition, black-hole formation) using a single 27 solar-mass fiducial model and compute 1-sigma constraints for several benchmark mass scenarios (Table II), including a speculative new-physics scenario with large masses. They conclude that a galactic supernova can measure the mass of each neutrino state individually.

Significance. If the standard-case sensitivity holds, the paper offers a new, orthogonal probe of the absolute neutrino mass scale, and the generalized treatment of separate mass states in Eqs. (11)-(14) is a useful conceptual contribution for future supernova analyses. Strengths include the transparent derivation of the flux formulas, a careful numerical check of jump probabilities, explicit treatment of arbitrary mass orderings through the H/M/L notation, and the release of customized SNEWPY code. The falsifiable prediction—that JUNO would observe energy-dependent delays of individual mass states after a sharp feature—is clearly stated. However, the headline claim that each mass state can be measured is not supported by the paper's own Table II for most benchmarks, and the new-physics scenario rests on an unexamined ansatz about the PMNS matrix. The central physics is sound and the shortcomings are addressable in revision.

major comments (4)

[Section VIII, Table II] The conclusion that 'a detection of a galactic SN can measure the mass of each neutrino state' is stronger than the numerical results in Table II. In the Oscs:NO and Planck:NO rows every entry is a one-sided upper limit; in the High mass row m1 is only bounded from above (m1 < 0.40 eV for QCD, m1 < 0.54 eV for black-hole formation, m1 < 0.80 eV for the neutronization burst), and none of these intervals excludes m1 = 0. Two-sided intervals for all three masses appear only in the KATRIN benchmark, and only for the QCD phase-transition feature. The abstract and conclusions should be reworded to state which scenarios yield measurements and which yield upper bounds; otherwise the central advertised capability is overstated.
[Section III.A, Section II] The new-physics benchmark in Table I and the associated conclusion that 'each separate mass state can be uniquely identified' rest on the ansatz stated after Eq. (9) that the PMNS matrix is unchanged when neutrino masses vary. This ansatz is not derived or tested. If neutrino masses are modified by a coupling to dark matter, as Section II motivates, the mass matrix—and hence the mixing angles in the galactic center—can also be modified; the paper's own statement in Section II that spatially varying masses during propagation are not modeled adds a further unquantified effect. Without either a concrete model in which the PMNS matrix is exactly environment-independent or a demonstration that the Table II intervals are robust to O(1) changes in |U_ei|^2, the claimed new-physics sensitivities are not established.
[Eq. (27), Section VI.B] The time-delay formula uses the ultra-relativistic approximation D (m_i/E)^2 / 2. For the High mass benchmark (Table I: m2 = 1.0 eV, m3 = 1.8 eV) and for the 5 eV illustrative cases in Figs. 5 and 10, the relevant low-energy events have m_i/E not much smaller than unity; at E = 5 MeV the exact delay D (1/sqrt(1 - (m_i/E)^2) - 1) differs from the approximation by about 10% for m_i = 1.8 eV and much more at lower energies. Since the sensitivity to masses is driven by low-energy events, the numerical implementation via Eq. (28) should either use the exact time delay or impose a validity cut. Otherwise the high-mass rows of Table II and the corresponding corner plots are biased.
[Section VI.B, Section III.C] The quantitative 1-sigma intervals in Table II are computed for one fiducial 27 solar-mass model from Ref. [21] and for fixed parameterized shapes of the QCD and black-hole features; the only systematic effect marginalized is the feature start time. The paper acknowledges in Sections III.C and IV that supernova models and feature details are uncertain, but it does not propagate these uncertainties. A robustness study varying the supernova model and the feature width, amplitude, and turn-off times is needed before the Table II intervals can be read as realistic predictions. As written, the numbers are conditional on the assumed feature and model.

minor comments (4)

[Section III.B.2] The statements that the relevant angle 'is probably θ13' and that 'the other factor is most likely' the given expression are vague; since the numerical conclusion depends on jump probabilities being negligible, these three-flavor mapping choices should be stated more definitively or explicitly verified.
[Eq. (18)] The symbol s is used for sin θ in Eq. (18), while s2ij is used for sin(2θij) elsewhere in the paper; this overloaded notation could confuse readers. Using sin θ in Eq. (18) would remove the ambiguity.
[Table I] The 'Heaviest by Planck' benchmark values are rounded to three decimals, so the implied squared-mass splittings are not exactly consistent with the quoted oscillation parameters; specifying the exact masses used in the simulation would improve reproducibility.
[Fig. 5 caption] The sentence 'some of the low-energy events are somewhat delayed due to m3 large, but the effect of the remaining events is smaller' is vague; it would be clearer to specify which mass state produces which visible delay feature in the panel.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the flux framework is a relabeled standard MSW result and the numerical sensitivities are forward-modeled closure tests, with the paper's limitations stated explicitly rather than hidden.

full rationale

Equations (11)-(14) are the standard adiabatic MSW flux formulas (1)-(8) rewritten without applying unitarity, with mass eigenstates relabeled H/M/L via eqs. (9)-(10); this is an explicit reorganizational step, not a circular reduction, because the individual-mass sensitivity comes from the separate kinematic time-delay insertion (27)-(28) applied to the PMNS-weighted terms. The numerical projections are forward-modeled sensitivity forecasts: events are simulated from assumed benchmark masses (Table I) with external SNEWPY and SNOwGLoBES, then fitted with a Poisson likelihood; recovering the injected masses in a closure test is the standard meaning of a sensitivity projection, not a fitted input renamed as a prediction. Self-citations [50,51,57] set the mass-state labeling convention and three-flavor jump-probability factors, but they are not load-bearing: the convention is stated in the text, the jump-probability suppression is verified numerically in Figs. 2-4, and the benchmarks come from external oscillation, Planck, and KATRIN constraints. The paper's own caveats - the Section III.A ansatz that the mixing matrix is unchanged for new-physics masses, the Section VII admission that the uniqueness statement rests on the PMNS matrix being determined, and the Table II high-mass benchmark showing only upper bounds on m1 - are limitations or overclaim risks, not circularity.

Assumptions & free parameters 9 free parameters · 7 assumptions · 0 invented entities

The central framework uses standard MSW/PMNS physics and the relativistic time-of-flight formula, which are external benchmarks from prior literature. The paper supplies a new decomposition of the flux into heavy/medium/light mass states (eqs. 11-14) and a closure-test sensitivity study. The quantitative forecasts rest on chosen benchmarks, one fiducial supernova model, an unchanged-PMNS ansatz, and the validity of Wilks' theorem in low-count bins. No new physical entities are postulated; the spatially varying neutrino mass scenario is borrowed from cited models and used as a benchmark.

free parameters (9)

Benchmark masses: lightest osc NO = m1=0.0, m2=0.009, m3=0.050 eV
Chosen as lightest masses consistent with normal ordering oscillations (Table I); sensitivities in Table II for this case are upper bounds only.
Benchmark masses: lightest osc IO = m1=0.050, m2=0.051, m3=0.0 eV
Lightest masses consistent with inverted ordering oscillations (Table I).
Benchmark masses: heaviest Planck NO = m1=0.075, m2=0.075, m3=0.090 eV
Maximum masses allowed by Planck-only sum constraint, normal ordering (Table I).
Benchmark masses: heaviest Planck IO = m1=0.085, m2=0.086, m3=0.069 eV
Maximum masses allowed by Planck-only sum constraint, inverted ordering (Table I).
Benchmark masses: KATRIN limit = m1=0.45, m2=0.45, m3=0.45 eV
Degenerate masses at the KATRIN upper limit (Table I); this is the standard benchmark where all three masses are individually constrained rather than only bounded.
Benchmark masses: new-physics high mass = m1=0.2, m2=1.0, m3=1.8 eV
Motivated by spatially varying neutrino masses via dark matter coupling (Section II, Table I).
Fiducial supernova model = 27 M_sun explosion (Mirizzi et al. 2016)
Sets the neutronization burst shape and overall statistics (Section III.C); all numerical results are conditional on this model.
Feature start time t0 = minimized over
The likelihood is minimized over the start time of each sharp feature, the largest assumed uncertainty (Section VI.B).
Feature integration windows = 1 s (neutronization), 40 ms (QCD and BH)
Timing windows around each feature used in the sensitivity calculation (Section IV); this affects the included statistics.

assumptions (7)

domain assumption Standard MSW matter effects and adiabatic flavor evolution in the supernova
Used to derive the Earth fluxes eqs. (11)-(14) from the source fluxes; Section III.A.
domain assumption Neutrino production occurs at densities above all MSW resonances for the mass range considered
Justified by the density estimate in Section III.A (rho_res up to about 10^7 g/cc versus decoupling at 10^11 to 10^12 g/cc). Load-bearing for the complete level-crossing formula.
standard math Jump probabilities are negligible for the relevant parameter space
Verified numerically in Section III.B.3 for known mixing angles and mass ranges, using two-flavor approximations for arbitrary masses.
ad hoc to paper The PMNS matrix elements are known and unchanged when neutrino masses vary, including spatially
Stated as an ansatz in Section III.A. Needed to map heavy/medium/light states to terrestrial mass states; the weakest premise for the new-physics benchmarks.
domain assumption The fiducial 27 solar mass supernova model from Mirizzi et al. (2016) provides a representative neutrino flux
Section III.C; no model uncertainty is propagated into the quoted sensitivities.
standard math Wilks' theorem provides valid confidence intervals for the Poisson log-likelihood ratio
Section VI.B; authors note this may be conservative but can fail in low-statistics bins, and they refer to refs. 16-17 for more careful treatments.
standard math Time delay formula Delta t = (D/2)(m_i/E)^2 applies in the ultra-relativistic limit m << E
Section IV, eq. (27); standard kinematics.

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Cite this review

Pith. "Pith review of Individual Neutrino Masses From a Supernova." pith.science (2026). https://pith.science/paper/PKBCZFXC

@misc{pith2026241113634,
  author       = {Pith},
  title        = {Pith review of: Individual Neutrino Masses From a Supernova},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PKBCZFXC}},
  note         = {Machine review of arXiv:2411.13634}
}

read the original abstract

A nearby supernova will carry an unprecedented wealth of information about astrophysics, nuclear physics, and particle physics. Because supernova are fundamentally neutrino driven phenomenon, our knowledge about neutrinos -- particles that remain quite elusive -- will increase dramatically with such a detection. One of the biggest open questions in particle physics is related to the masses of neutrinos. Here we show how a galactic supernova provides information about the masses of each of the three mass eigenstates \emph{individually}, at some precision, and is well probed at JUNO. This information comes from several effects including time delay and the MSW effect within the supernova. The time delay feature is strongest during a sharp change in the flux such as the neutronization burst; additional information may also come from a QCD phase transition in the supernova or if the supernova forms a black hole. We consider both standard cases as dictated by local oscillation experiments as well as new physics motivated scenarios where neutrino masses may differ across the galaxy.

Figures

Figures reproduced from arXiv: 2411.13634 by the authors.

**Figure 2.** FIG. 2. The regions in [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** FIG. 3. The same as fig [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (10 more)

**Figure 4.** Figure 4: FIG. 4. The jump probability for the two standard mass [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

**Figure 5.** Figure 5: FIG. 5. The expected event rates for a SN at 10 kpc detected by JUNO as a function of energy and time for three different [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

**Figure 6.** Figure 6: FIG. 6. The expected preferred regions given a detection of a SN at 10 kpc by JUNO under four different hypotheses about the [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]

**Figure 7.** Figure 7: FIG. 7. The same as fig [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]

**Figure 8.** Figure 8: FIG. 8. The same as fig [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]

**Figure 9.** Figure 9: FIG. 9. The same as fig [PITH_FULL_IMAGE:figures/full_fig_p013_9.png]

**Figure 10.** Figure 10: FIG. 10. The same as fig [PITH_FULL_IMAGE:figures/full_fig_p014_10.png]

**Figure 11.** Figure 11: FIG. 11. The same as fig [PITH_FULL_IMAGE:figures/full_fig_p015_11.png]

**Figure 12.** Figure 12: FIG. 12. The same as fig [PITH_FULL_IMAGE:figures/full_fig_p016_12.png]

**Figure 13.** Figure 13: FIG. 13. The same as fig [PITH_FULL_IMAGE:figures/full_fig_p017_13.png]

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Reference graph

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Basic Picture of Jump Probabilities For small angles we have Pj = exp − π 2 γ , (16) at the resonance, where the adiabaticity parameter 2 γ > 0 is γ = ∆m2 2E s2 2 c2 1 ˙ne/ne . (17) We also note that the mixing angles present in the PMNS matrix are not particularly small. For this and other reasons, a more complete expression for the jump probabilities is...

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Three-Flavor Picture We are in a three-flavor picture, however, which com- plicates things somewhat. Since the formulas are derived in a two-flavor picture and involve an integrand of the form p (a − ∆m2 cos 2θ)2 + (∆m2 sin 2θ)2 , (23) which is the the typical matter correction factor, we know how to best adjust these for a three-flavor picture, see [57],...

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Numerical Studies We now numerically verify that these jump probabil- ities are small, using the known mixing angles. First, we note that for θ = 8.5◦ and 34 ◦ we get f = 0.97 and 0.41, respectively, thus the f correction cannot be ig- nored. Second, we let the masses vary across a range of [0, 1] eV and highlight the regions with noticeable jump probabil...

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