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Can the 3 neutrino masses really be found using SN 1987A data?

Robert Ehrlich

TL;DR

The work investigates whether SN 1987A neutrino data can determine the three neutrino mass eigenvalues, including a tachyonic state, by exploiting a near-simultaneous emission assumption and fitting a $1/E^2$ versus time pattern to yield three lines through the origin and corresponding masses. The core method derives $M = \frac{2}{T m^2 c^4}$ with $1/E^2 = M t$, enabling a direct extraction of $m_j^2$ from slopes, and incorporates the LSD Mont Blanc data to support a three-mass scenario with one tachyonic state $m_3^2<0$. The paper argues that a lack of sterile neutrino signals in KATRIN can be reconciled within this framework (the so-called dog that didn't bark) and discusses implications for cosmology and IceCube, while proposing concrete reanalysis strategies and a future galactic supernova as a definitive test. If validated, this approach would redefine neutrino mass measurements, imply a nonzero (and even negative) $m^2$ for one state, and motivate coordinated analyses across KATRIN, IceCube, and oscillation data to confirm or falsify the SN-based masses and the possible tachyonic neutrino. The study also emphasizes the need for multi-mass fits in sterile neutrino searches and links the inferred masses to dark-matter halo structures, highlighting broad implications for particle physics and cosmology.

Abstract

Neutrino masses remain a significant unsolved problem in physics and their nonzero value proves the Standard Model is incomplete. Currently, the values of the three masses only have upper limits from cosmology and experiments like KATRIN. This paper shows that the SN 1987A neutrino data can remarkably yield values for the three neutrino masses, and not merely upper limits. Although this seemingly preposterous idea was suggested a dozen years ago by the author, here it is demonstrated in a much more convincing manner with many new elements, including a stronger statistical treatment, and a thorough explanation of why the method used to find the three masses from supernova SN 1987A neutrino data really works. The key to finding the three neutrino masses is realizing why three normally accepted assumptions are unjustified, The three rejected assumptions are:(a) the 5-hr early LSD (Mont Blanc) neutrinos are unrelated to SN 1987A, (b) any neutrino masses $m_k>1 eV/c^2$ cannot be reconciled with upper limits on the ``effective mass" from KATRIN and other data, and (c) the spread in neutrino emission times from SN 1987A data is too great for the method to work. A particularly crucial piece of evidence supporting the claim made in the paper's title involves a recent negative KATRIN result finding an absence of sterile neutrinos. This absence of a sterile neutrino signal leads to two tests of the claim based on existing data: one for KATRIN and one for IceCube.

Can the 3 neutrino masses really be found using SN 1987A data?

TL;DR

The work investigates whether SN 1987A neutrino data can determine the three neutrino mass eigenvalues, including a tachyonic state, by exploiting a near-simultaneous emission assumption and fitting a versus time pattern to yield three lines through the origin and corresponding masses. The core method derives with , enabling a direct extraction of from slopes, and incorporates the LSD Mont Blanc data to support a three-mass scenario with one tachyonic state . The paper argues that a lack of sterile neutrino signals in KATRIN can be reconciled within this framework (the so-called dog that didn't bark) and discusses implications for cosmology and IceCube, while proposing concrete reanalysis strategies and a future galactic supernova as a definitive test. If validated, this approach would redefine neutrino mass measurements, imply a nonzero (and even negative) for one state, and motivate coordinated analyses across KATRIN, IceCube, and oscillation data to confirm or falsify the SN-based masses and the possible tachyonic neutrino. The study also emphasizes the need for multi-mass fits in sterile neutrino searches and links the inferred masses to dark-matter halo structures, highlighting broad implications for particle physics and cosmology.

Abstract

Neutrino masses remain a significant unsolved problem in physics and their nonzero value proves the Standard Model is incomplete. Currently, the values of the three masses only have upper limits from cosmology and experiments like KATRIN. This paper shows that the SN 1987A neutrino data can remarkably yield values for the three neutrino masses, and not merely upper limits. Although this seemingly preposterous idea was suggested a dozen years ago by the author, here it is demonstrated in a much more convincing manner with many new elements, including a stronger statistical treatment, and a thorough explanation of why the method used to find the three masses from supernova SN 1987A neutrino data really works. The key to finding the three neutrino masses is realizing why three normally accepted assumptions are unjustified, The three rejected assumptions are:(a) the 5-hr early LSD (Mont Blanc) neutrinos are unrelated to SN 1987A, (b) any neutrino masses cannot be reconciled with upper limits on the ``effective mass" from KATRIN and other data, and (c) the spread in neutrino emission times from SN 1987A data is too great for the method to work. A particularly crucial piece of evidence supporting the claim made in the paper's title involves a recent negative KATRIN result finding an absence of sterile neutrinos. This absence of a sterile neutrino signal leads to two tests of the claim based on existing data: one for KATRIN and one for IceCube.

Paper Structure

This paper contains 24 sections, 7 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Are $m^2<0,$ and $v>c$ Tachyons "unphysical"?
  3. Do negative searches make tachyons less likely?
  4. KATRIN and circumventing upper limits on $m_\nu.$
  5. Supernova SN 1987A neutrinos
  6. The 5 hour early LSD neutrino burst
  7. Finding $m^2$ of SN 1987A neutrinos
  8. Fitting 30 data points to 3 lines
  9. Fixing a limitation of sterile neutrino searches
  10. More evidence for the two $m^2>0$ masses
  11. Discussion
  12. Why not exclude the LSD data?
  13. Why are the LSD data so bunched in time?
  14. Why do the LSD neutrinos have the same E?
  15. Alternate explanations for the LSD neutrinos?
  16. ...and 9 more sections

Figures (5)

  • Figure 1: Best fit of 30 data points $(t,1/E^2),$ one for each neutrino to one of three straight lines that pass through the origin. Error bars in both horizontal and vertical are included in the fit. The fit has $\chi^2=25.4$ for 27 dof, which yields $p=55\%$. The three best fit masses $m_j$ are obtained from the three best fit slopes according to Eq. 5. Note the different scales used for $t>0$ and $t<0$ The five LSD data points at $t=-17 ksec$ have been slightly separated from each other for clarity.
  • Figure 2: The probability from the least squares fit to three straight lines through the origin versus the size of the horizontal error bars, assumed to be the same for all 30 data points. Note that there is no "best" fit to three straight lines unless one first fixes the size of the horizontal error bars because for $H>>5$ sec error bars the fit probability $p\approx100\%$
  • Figure 3: $3+3$ neutrino mass squared diagram postulated by the author in 2013, with updated $m_1$ and $m_2$ values. There are 3 active-sterile doublets (solid and dotted lines) split by three $\Delta m^2$ The three $\Delta m^2$ are for solar, atmospheric and short baseline (sbl) oscillations. Diagram is not to scale. The "haunted" area is for $m^2<0$ neutrinos. Many physicists regard $m^2<0$ tachyons as ghost particles. Illustration of a ghostly nightmare is from Shutterstock.
  • Figure 4: Computed temporal electron antineutrino luminosity L in units of $10^{53}erg/s$ for SN 1987A neutrinos from Bozza et al. Bozza2025. Note the time scale change at $t=1$ seconds. The fraction of the integrated luminosity for $t<1$ seconds is only a bit more than half because of that scale change. Figure is used under creative commons license https://creativecommons.org/licenses/by/4.0
  • Figure 5: How 50 neutrinos might appear on a $1/E^2$ versus t plot if their mass $m<< 1 eV/c^2$ and they were emitted during a time window of 2 seconds. No congregation of the points about specific lines would be observed, completely unlike the real SN 1987A data which clearly clusters along three straight lines. Essentially, each of the 50 points lies on its own different vertical line somewhere within the 2 second time window and no two points lie on the same line.