Finding the 3 neutrino masses using a one-phase $ν$ emission model for SN 1987A

This paper argues that the three neutrino masses can be precisely determined rather than merely bounded by reinterpreting SN 1987A neutrino data through a one-phase emission model that rejects three standard assumptions regarding the Mont Blanc signal, mass limits, and emission time spread, while leveraging recent negative sterile neutrino results from KATRIN to validate the method.

The Gist

The Big Idea: Solving a 40-Year-Old Mystery

Imagine the universe sent us a cosmic "text message" in 1987. It was a supernova (a dying star exploding) called SN 1987A. When it exploded, it sent out a flood of invisible particles called neutrinos.

For decades, physicists have been trying to figure out the mass (weight) of these neutrinos. They know there are three different "flavors" of neutrinos, but they've only been able to guess an upper limit (like saying "it weighs less than a feather"). They've never been able to pin down the exact weight.

This paper claims: We actually can find the exact weights of all three neutrinos using the data from that 1987 explosion. And the results are wild:

1. Two of them are heavy (much heavier than anyone thought).
2. One of them is a "tachyon"—a particle that is so weird it might travel faster than light and have "negative mass squared."

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The Detective Work: How Did He Do It?

To understand how the author solved this, let's use a Marathon Analogy.

1. The Race (The Supernova)

Imagine a giant race where 100 runners (neutrinos) start at the exact same moment from a star 168,000 light-years away. They are all running toward Earth.

• The Fast Runners: Some are very light and fast.
• The Slow Runners: Some are heavy and slow.
• The Ghost Runners: One runner is so weird they might be running backwards in time (the tachyon).

If they all started at the exact same second, the heavy ones would arrive later than the light ones. The heavier the runner, the later they show up.

2. The Problem (The Noise)

Usually, physicists think the runners didn't start at the same time. They think the star "shouted" the runners out over a long period (like 10 seconds). If the start times are messy, you can't tell if a runner is late because they are heavy or because they just started late. It's like trying to time a race where everyone starts at random times; you can't measure their speed.

Ehrlich's Twist: He argues that the star actually "shouted" all the runners out in a tiny, split-second burst (less than 1 second). If they started together, the arrival times tell us their exact weights.

3. The Graph (The Magic Line)

The author took the data from the 1987 detectors and plotted it on a graph.

• X-axis: When they arrived.
• Y-axis: How much energy they had.

If the runners started together, the data points should line up perfectly on straight lines.

• The Result: The data didn't look like a messy cloud. It looked like three distinct straight lines passing through the origin.
• The Meaning: This proves there are exactly three groups of neutrinos, and we can calculate their masses from the slope of those lines.

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The Three "Weird" Neutrinos

Based on the slopes of those lines, the author found three specific masses:

1. The Heavy Hitter: One neutrino weighs about 21.6 eV. (Think of this as a "heavy" particle in the subatomic world).
2. The Medium One: Another weighs about 2.7 eV.
3. The Time-Traveler (The Tachyon): The third one has a "negative mass squared." In physics terms, this suggests it travels faster than light.

Wait, isn't faster-than-light impossible?
The paper addresses this. Most physicists say "No way!" But the author argues that if a particle travels faster than light, it mathematically looks like it has "negative mass squared." He suggests that while this sounds crazy, the math works out, and it explains why we haven't seen it before.

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The "Ghost" Evidence: The LSD Burst

Here is the most controversial part of the story.

In 1987, there were four detectors. Three of them (Kamiokande, IMB, Baksan) saw the main burst of neutrinos at 7:35 PM.
But a fourth detector, called LSD (under Mont Blanc), saw five neutrinos about 5 hours earlier.

The Standard View: Physicists ignored this. They said, "It's just random noise. It happened 5 hours too early to be from the star."

Ehrlich's View: He says, "No, that's the Tachyon!"

• If the tachyon travels faster than light, it would arrive before the light (and before the slower neutrinos).
• The fact that these 5 neutrinos arrived 5 hours early fits perfectly with the math of a faster-than-light particle.
• The fact that they all had the same energy (monochromatic) is also a clue that they belong to a specific, unique group.

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The "Missing" Clue: The KATRIN Experiment

There is a famous experiment called KATRIN in Germany that tries to weigh neutrinos.

• What they found: They haven't found any "heavy" or "sterile" neutrinos. They only see an upper limit (very light).
• The Conflict: If Ehrlich is right and there are heavy neutrinos, why didn't KATRIN see them?

The Paper's Explanation:
KATRIN is looking for the wrong thing.

• KATRIN assumes the neutrinos are "normal" (slower than light).
• Ehrlich argues that because the three neutrinos mix together, their "combined weight" (effective mass) cancels out. One is heavy positive, one is heavy positive, and one is "negative" (tachyon).
• When you add them up, the total looks like it's almost zero.
• The Analogy: Imagine you have a scale. You put a 10kg weight on one side and a -10kg weight on the other. The scale reads "0 kg." KATRIN sees "0" and says, "No heavy neutrinos!" But Ehrlich says, "Look closer! There are heavy weights there, they just canceled each other out."

The paper suggests KATRIN needs to redo its math using these three specific weird masses. If they do, they might finally see the evidence.

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Why Should We Care?

This paper is a "Hail Mary" pass. It challenges the Standard Model of physics (the rulebook of the universe).

• If it's wrong: It's just a statistical fluke, and neutrinos are still tiny and mysterious.
• If it's right: It means we have found particles that break the speed of light, we have solved the mystery of dark matter (heavy sterile neutrinos could be dark matter), and we have rewritten the laws of physics.

The Bottom Line

The author is saying: "Stop guessing. Look at the 1987 data again. The lines are right there. We have three neutrinos: two heavy ones and one time-traveling tachyon. If you believe the math, the universe is much stranger than we thought."

He ends with a hopeful note: We might not see this confirmed in our lifetime, but if a new star explodes in our galaxy (like Betelgeuse), the next generation of detectors will catch thousands of neutrinos and finally prove if he was right or wrong.

Technical Summary

1. Problem Statement

The paper addresses the long-standing unsolved problem of determining the absolute values of the three neutrino mass eigenstates ($m_1, m_2, m_3$). Currently, experiments like KATRIN and cosmological observations only provide upper limits (e.g., $m_\nu < 0.45$ eV/c$^2$) or constraints on the sum of masses ($\sum m_\nu$). The prevailing consensus is that the neutrino masses are too small to be resolved using the time-of-flight data from Supernova 1987A (SN 1987A), as the spread in emission times is assumed to be too large to distinguish tiny mass-dependent velocity differences.

The author challenges three standard assumptions:

1. The 5-hour early neutrino burst detected by the LSD (Mont Blanc) detector is unrelated to SN 1987A (background noise).
2. Neutrino masses $m_k > 1$ eV/c$^2$ are incompatible with KATRIN's "effective mass" limits.
3. The spread in neutrino emission times from the supernova is too large to allow for mass determination.

2. Methodology

A. The One-Phase Emission Model

The author proposes a single-phase neutrino emission model for SN 1987A, rejecting the standard two-phase (accretion + cooling) models.

• Assumption: Neutrinos were emitted within a very narrow time window ($\Delta t \approx 0.5$ to $1.0$ seconds).
• Rationale: If emission is nearly simultaneous, the arrival time delay ($t$) of a neutrino relative to a photon is determined solely by its mass and energy via relativistic kinematics.
• Kinematic Derivation:
  For a neutrino with mass $m$, energy $E$, traveling distance $D$ (time $T = D/c$), the delay $t$ relative to a photon is:
  $$\frac{v}{c} = 1 - \frac{t}{T} \approx 1 - \frac{m^2 c^4}{2E^2}$$
  Rearranging yields a linear relationship:
  $$\frac{1}{E^2} = \left( \frac{2}{T m^2 c^4} \right) t \equiv M t$$
  Where $M$ is the slope. If neutrinos of a specific mass $m$ are emitted simultaneously, plotting $1/E^2$ vs. $t$ should yield a straight line through the origin with slope $M$.

B. Data Analysis and Fitting

• Dataset: The author analyzes 37 neutrino events from three detectors: Kamiokande II, IMB, and Baksan (standard bursts), plus the 5 events from the LSD detector (Mont Blanc) which arrived ~484 minutes earlier.
• Inclusion of "Extra" Data: The author includes 7 additional Kamiokande II events (time $13 < t < 25$ s) previously excluded by other analyses, arguing they are signal rather than background.
• Fitting Procedure: A least-squares fit is performed to force the 37 data points onto three straight lines passing through the origin ($t=0, 1/E^2=0$).
  • The horizontal error bars (uncertainty in emission time) are treated as a free parameter ($H$).
  • The fit seeks to minimize $\chi^2$ by adjusting the slopes ($M_1, M_2, M_3$) of the three lines.

C. Addressing the "Sterile" Neutrino Paradox

The paper reconciles the large masses found with KATRIN's null results for sterile neutrinos by proposing that the "missing" sterile neutrino signal is actually an active neutrino with a large mass that was misidentified in KATRIN's analysis due to incorrect model assumptions (specifically, assuming a zero-mass background component).

3. Key Contributions

1. Rejection of the "Background" Hypothesis for LSD: The author argues the LSD burst is genuine and associated with SN 1987A. The 5-hour early arrival is interpreted as evidence of tachyonic (superluminal) neutrinos ($m^2 < 0$).
2. One-Phase vs. Multi-Phase Models: The paper critiques the standard two-phase emission models (e.g., Bozza et al.) for using too many free parameters (9 parameters) and circular logic (assuming small masses to justify the emission profile). The author's one-phase model uses only two parameters (the two positive mass slopes) and fits the data better under the assumption of simultaneous emission.
3. Resolution of KATRIN Discrepancy: The paper explains why KATRIN failed to see the 2.70 eV/c$^2$ sterile neutrino (reported by Neutrino-4). It posits that KATRIN's search method was designed for sterile neutrinos (disappearance into a non-interacting state) but the 2.70 eV/c$^2$ particle is an active neutrino. Therefore, KATRIN's "zero-mass" background assumption was invalid.
4. Cosmological Mass Sum: The paper resolves the conflict between the large individual masses found and the tight cosmological limit on $\sum m_\nu$ ($< 0.12$ eV). It argues that the cosmological limit applies to the sum of flavor states, not mass eigenstates. If one mass eigenstate is tachyonic ($m^2 < 0$), the effective flavor masses can be near zero even if individual mass eigenstates are large.

4. Results

The least-squares fit of the 37 data points to three lines through the origin yields the following mass squared values:

• Line 1 (Positive Slope): $m_1^2 c^4 \approx (21.6 \text{ eV})^2 \implies m_1 \approx 21.6$ eV/c$^2$.
• Line 2 (Positive Slope): $m_2^2 c^4 \approx (2.70 \text{ eV})^2 \implies m_2 \approx 2.70$ eV/c$^2$.
• Line 3 (Negative Slope): $m_3^2 c^4 \approx -192,000 \text{ eV}^2 \implies m_3^2 < 0$ (Tachyon).
  • The negative slope corresponds to the LSD burst events arriving early ($t < 0$).
  • The magnitude implies a tachyonic mass parameter, consistent with the author's previous predictions.

Statistical Significance:

• The fit yields a $\chi^2$ of 29.9 with 34 degrees of freedom, corresponding to a p-value of 67%.
• If the horizontal error bar is increased to $\pm 1.0$ second (implying a 1-second emission window), the p-value rises to 91%.
• This indicates a statistically robust fit, far superior to random chance, provided the emission window was indeed short ($<1$ s).

5. Significance and Implications

• Discovery of Absolute Masses: The paper claims to have determined the specific values of the three neutrino mass eigenstates, moving beyond upper limits.
• Existence of Tachyons: The result provides strong evidence for the existence of a tachyonic neutrino ($m^2 < 0$), challenging the standard model's assumption that all particles travel at $v \le c$.
• Reinterpretation of Experimental Data: It suggests that the "null" results from KATRIN and the "positive" results from Neutrino-4 are not contradictory but are artifacts of analyzing the data with the wrong mass model (assuming sterile vs. active).
• Testability: The author proposes a definitive test: KATRIN should re-analyze its data using the three specific masses ($2.70, 21.6, \text{and tachyonic}$) as fixed parameters and fit for mixing weights. A concentrated region of high probability on the mixing parameter plane would confirm the hypothesis.
• Future Verification: The paper concludes that a future galactic supernova (e.g., Betelgeuse) with modern detectors could provide thousands of events, offering a definitive confirmation or rejection of these claims.

Conclusion:
The paper presents a radical reinterpretation of SN 1987A data, arguing that the observed time-energy distribution is best explained by three distinct neutrino masses (one tachyonic) emitted in a single, brief burst. This model successfully fits the data with high statistical probability and offers a unified explanation for seemingly conflicting results in neutrino mass experiments and cosmology.