This paper reports a new phenomenological analysis of the neutrino burst detected from SN 1987 A, and it reveals the presence of two mass eigenstates. The heavier mass eigenstate has $m_H=21.4 \pm 1.2 eV/c^2$, while the lighter one has $m_L=4.0 \pm0.5 eV/c^2 $. It is not the first paper to make such a claim, but it expands on a 1988 conditional analysis by Cowsik, and it attempts to make the evidence more robust through an improved statistical analysis, and through providing reasons why alternative explanations are unlikely. It also shows how the result can be made consistent with existing smaller electron neutrino mass limits with the existence of a third tachyonic (superluminal) mass eigenstate.
The neutrinos from SN 1987A have been the subject of hundreds of papers, both theoretical and phenomenological. [1] Some of these papers analyze the data to infer an upper limit on the neutrino mass, which ranges typically from 12 to 16 eV /c 2 . [2,3]. It is expected however that neutrinos from a supernova should include all three active neutrino mass eigenstates, therefore such a limit must represent some sort of average over whichever eigenstates are represented in the neutrino events recorded. There have in fact been at least three analyses of the SN 1987A neutrino data that have given evidence for a bifurcation into two groupings. [4][5][6]. The analysis by Loredo was based on Baysian statistics, [5] and it gave no physical interpretation to the two classes of events. The Roos paper based the bifurcation on neutrino mass, but he attributed the different mass values to the events recorded in the two detectors, rather than to two mass eigenstates. Finally, the Cowsik paper did suggest a bifurcation associated with two mass eigenstates whose masses he found based on the relation between neutrino arrival times and their measured energies. Cowsik reported these eigenstates as 24 ± 7eV /c 2 and 4 ± 1eV /c 2 . We here extend his analysis to include the possibility of observed regularity arising in part from chance, or variations in their emission times at the source, since his conclusion was conditional on there being near instantaneous emissions.
Additionally, we show how the result can be made consistent with existing electron neutrino mass limits, and other experiments. As with most SN 1987A analyses, we include neutrino events recorded in the Kamioka, and IMB detectors, but exclude the 5 events seen in the Mont Blanc detector since they occured 5 hours before those detected by the other three detectors. Additionally, given its size and sensitivity that detector should have only seen 1 neutrino from the supernova not 5. We also exclude 5 events seen in the Baksan detector because there are substantial reasons to believe that perhaps 2 or 3 of them may have been due to background.
As noted in the paper on the Baksan neutrinos from SN 1987A. [7] • The 5 event burst they saw over a 10 s period was only slightly above their background, since there have been past instances when the Baksan detector recorded 3 “random” events in 10 seconds
• The timing of the Baksan burst occurred 30 s after those seen in the IMB and Kamioka detectors • The 5 Baksan events were spread evenly over the entire 10 s period, not bunched strongly near the start of the 1987A burst as with the other detectors. Thus, there is considerable uncertainty over the true t = 0 time for these events relative to the other two detectors.
The basic idea of the analysis is straightforward. A neutrino of mass m and energy E that is emitted at a time t em and observed in a detector at time t will take a time to reach Earth given by
where the approximation requires that |m 2 | be small compared to E 2 and where t 0 is the light travel time from SN 1987A or 168,000 years. Eq. 1 allows us to calculate a mass m k for the kth neutrino event observed at a time t k whose energy is E k , assuming the neutrino was emitted at time t em,k , and travelled a distance ct 0,k to reach Earth. Note that t 0,k can vary from one event to another depending on the collapsing core radius at the time that neutrino was emitted. On solving for the mass attributed to a given event, we have:
but clearly eq. 2 can only be used to find m k when t em,k and t 0,k are both nearly eventindependent, which requires near-simultaneous emissions.
The evidence for near simultaneous emissions comes from supernova core collapse models and their calculated neutrino fluxes as a function of time, specifically:
brief “burst” of ν e The literature on electron neutrinos and antineutrinos emitted during a core collapse consistently shows that both fluxes rise and fall over a very short time interval. Typically, this initial burst is found to rise and fall by almost an order of magnitude over a time interval of 0.3 seconds, [1,8] while some models show this “burst” of electron neutrinos and antineutrinos being as short as about 0.02 seconds. [9] 2. greater ν e than ν µ flux during burst These core collapse simulations find that the drop in emitted muon and tau neutrinos following its peak is much more gradual and extends over 10 -15sec, but the initial ν e flux during its short “burst” is found to be about an order of magnitude greater than the ν µ flux for t > 1s, [9] and in any case, the SN 1987A neutrinos observed are unlikely to be these flavors -certainly not for the IMB detector whose threshold was below muon neutrino detection.
possibility of brief burst for ν µ Although some core collapse simulations find that the drop in emitted muon and tau neutrino fluxes following its peak is much more gradual than ν e , other authors suggest that a similar rapid rise and fall applies to th
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