1. Hunting the tachyon How faster-than-light particles
test
Hunting the tachyon
How faster-than-light particles
stayed hidden for over a century
Robert Ehrlich
George Mason University
mason.gmu.edu/~rehrlich
26 March, 2020
Interactive plot

2. Tachyons: a tale of good and evil particles having m2 < 0
“Good” variety:
An instability in a quantum field with imaginary mass (Higgs)
Spontaneous decay or “condensation” to ground state
No v > c or m2 < 0 particles observed
“Evil” variety:
Observable v > c or m2 < 0 particles
Violate Lorentz invariance & causality
Instability of the vacuum?
Banished from string theory (SUSY)
Neutrinos the only candidates
Many previous false sightings
(Thank you OPERA!)

3. How tachyons allow v > c
“rest mass”
E/m
m is imaginary!
v = c is a 2-way barrier
Bilaniuk, O.-M. P.; Deshpande, V. K.; Sudarshan, E. C. G. "'Meta' Relativity". American Journal of Physics (1962).

4. Conventional view of 3 neutrino mass states no sterile light neutrinos
Absolute scale unknown
=2.32 x 10-3 eV2
=7.59 x 10-5 eV2 ?

5. Origin of 3 + 3 Model 3 mass doublets – one being a tachyon based on neutrinos from SN 1987A
R. Ehrlich, Astropart. Phys., 35, (2012)
& R. Ehrlich, Astropart. Phys., 41 , 16 (2013)
First noted in 1987 (Huzita) & (Cowsik)

6. 12 event neutrino burst as seen in Kamiokande detector on Feb 24, 1987
publication included 7 other such plots from the same day
# Hits
Evis = 8 MeV
Time (minutes)

7. Two approaches to find the neutrino mass from SN 1987A
Emission time distribution
Arisaka, K. et al. Astropart.Phys. 36 (2012)
arXiv:
Standard analyses:
Assume: Spread in arrival times mainly reflects spread in emission times
Data can only give an upper limit m > 5.7 eV.1 based on standard model
Unconventional Analysis2:
Assume
Most SN 1987A neutrinos have small spread in emission times dt = s
Individual neutrinos might belong to distinguishable mass states.
1Loredo and Lamb, Phys. Rev. D65 (2002)
2 R. Cowsik, Phys. Rev. D 37, (1988);
R. Ehrlich, Astropart. Phys., 35, (2012)

8. Finding neutrino mass for simultaneous emissions
Slope
t is neutrino travel time
T is light travel time
Leads light
Lags light

9. 25 Neutrinos from SN 1987A fits 2 m’s (Ignore 5 from Mont Blanc for now)
m1 = eV
m2 = eV
Kam
IMB
Bak
R. Ehrlich, Evidence for two neutrino mass eigenstates from SN 1987A and the possibility
of superluminal neutrinos, Robert Ehrlich, Astroparticle Physics 35 , 625–628 (2012)

10. 3 + 3 Model: 3 L,R doublets Identical fractional splitting
A 3rd doublet having m2 < 0 is needed to keep the flavor state masses small so as to conform to cosmological constraints on the sum of the flavor state masses
Value chosen so all three doublets have the same fractional splitting

11. Pre-KATRIN evidence supporting the 3 + 3 neutrino model Evidence
Evidence
Comment
Ref 1
25 SN 1987A neutrinos in 3 detectors fit one of two masses (4 eV & 21 eV) & only 1 fits both.
Assumes the spread in emission times << spread in travel times
E(2012) 2
These two masses yield identical fractional Splittings, in the model; 3rd mass needs to be a tachyon with m2 = keV2
Assumes that the splittings are given by the solar and atmospheric dm2
E(2013) 3
The 21 eV neutrino mass in the model yields a good fit to the dark matter distribution in the Milky Way Galaxy
The tachyonic mass in would be associated with dark energy not dark matter.
C(2014) 4
The 4 eV neutrino mass in the model yields a good fit to the dark matter distribution in four galaxy clusters
The smaller mass would be expected for the larger structure. 5
The three best tritium beta decay experiments fit the model masses better than they do an effective mass m < 2 eV.
These fits are all made using published data of the spectra for Troitsk, Mainz and Livermore data.
E(2016) 6
The weights assigned to the 3 masses in doing these fits are the same in those 3 experiments and correspond to an effective m near zero.
The most prominent feature seen in these experiments is the kink in the spectrum at 21 eV. 7
Six different observations suggest a consistent value of m2 = eV2 for the electron neutrino effective mass.
A tachyonic mass in the model requires that at least one flavor state mass be tachyonic
E(2015) 8
The 5 Mont Blanc neutrinos are consistent
With all having the same energy ~8 MeV
No other model besides explains this observed constancy.
E(2018) 9
The computed tachyonic mass for the Mont
Blanc neutrinos is the same as that in model
A tachyonic mass for the Mont Blanc
Neutrinos requires an 8 MeV neutrino line From SN 1987A 10
The 16.7 MeV Z’ Boson provides the basis for a supernova model with 8 MeV cold dark matter particles yielding an 8 MeV neutrino line
This boson has been identified as a mediator between standard model matter particles and dark matter. 11
The spectrum of gamma rays from the galactic center is consistent with the annihilation of 8 MeV dark matter particles.
Aside from the next galactic supernova the galactic center is the best place to check the dark matter model. 12
The temperature and angular size of the source of gamma rays from the galactic center equal those found from the dark matter model.
The calculated temperature is model-dependent – this temperature is based on the low temperature solution. 13
The Kamiokande II data in the hours before and after the main burst yield an 8 MeV neutrino line above background (~30 sigma).
The background was obtained by another data set for K-II taken by the detector months later 14
The observed 8 MeV neutrino line is broadened by 25% energy resolution as expected.
The line was well hidden given the similar shapes of the background & line

12. Where to find evidence for the 3 + 3 model masses?

13. Evidence for dark matter in galaxies
Expected Observed

14. Fitting the observed DM profile Treat Ts as a free parameter
(1) Deduce ``observed” dark matter halo profile from rotation curve (2) Derive Equation of state for slightly degenerate neutrinos (3) Set neutrino mass density n(r) at r = 0 to ``observed” value & integrate outward using Eq. for hydrostatic equilibrium in order to find M(r): (4) Find v(r) = (2GM(r)/r)1/2
Chan, M .H. and Ehrlich, R., Astrophys. and Space Sci., 3, 49, (1), , (2014)

15. Observed and fitted rotation curve for Milky Way with m = 21. 4 + 1
Observed and fitted rotation curve for Milky Way with m = eV neutrinos
“Observed”
& smoothed
Fitted curve
& + 1 sigma

16. Use Virial Theorem to find mass M(r) that lies inside a radius, r
Clusters of galaxies
Use Virial Theorem to find mass M(r) that lies inside a radius, r
2<K>= - <U>
Properties:
The largest known gravitationally-bound structures
containing 100 to 1,000 galaxies (only 1% of total mass)
the rest: hot gas (9%) and dark matter (90%)
Dark matter fits:
Can infer DM profile from v of individual galaxies using the Virial Theorem
Only measure v along line of sight

17. Observed and fitted mass profiles for 4 clusters of galaxies with m = 4.0 + 0.5 eV neutrinos
Observed uncertainty (Error bars ) due to limited numbers of galaxies in cluster
Uncertainty in fitted profiles (Dotted curves) for +/- 1 sigma in neutrino mass

18. Pre-KATRIN evidence supporting the 3 + 3 neutrino model Evidence
Evidence
Comment
Ref 1
25 SN 1987A neutrinos in 3 detectors fit one of two masses (4 eV & 21 eV) & only 1 fits both.
Assumes the spread in emission times << spread in travel times
E(2012) 2
These two masses yield identical fractional Splittings, in the model;
3rd mass needs to be a tachyon with m2 = keV2
Assumes that the splittings are given by the solar and atmospheric dm2
E(2013) 3
The 21 eV neutrino mass in the model yields a good fit to the dark matter distribution in the Milky Way Galaxy
The tachyonic mass in would be associated with dark energy not dark matter.
C(2014) 4
The 4 eV neutrino mass in the model yields a good fit to the dark matter distribution in four galaxy clusters
The smaller mass would be expected for the larger structure. 5
The three best tritium beta decay experiments fit the model masses better than they do an effective mass m < 2 eV.
These fits are all made using published data of the spectra for Troitsk, Mainz and Livermore data.
E(2016) 6
The weights assigned to the 3 masses in doing these fits are the same in those 3 experiments and correspond to an effective m near zero.
The most prominent feature seen in these experiments is the kink in the spectrum at 21 eV. 7
Six different observations suggest a consistent value of m2 = eV2 for the electron neutrino effective mass.
A tachyonic mass in the model requires that at least one flavor state mass be tachyonic
E(2015) 8
The 5 Mont Blanc neutrinos are consistent
With all having the same energy ~8 MeV
No other model besides explains this observed constancy.
E(2018) 9
The computed tachyonic mass for the Mont
Blanc neutrinos is the same as that in model
A tachyonic mass for the Mont Blanc
Neutrinos requires an 8 MeV neutrino line From SN 1987A 10
The 16.7 MeV Z’ Boson provides the basis for a supernova model with 8 MeV cold dark matter particles yielding an 8 MeV neutrino line
This boson has been identified as a mediator between standard model matter particles and dark matter. 11
The spectrum of gamma rays from the galactic center is consistent with the annihilation of 8 MeV dark matter particles.
Aside from the next galactic supernova the galactic center is the best place to check the dark matter model. 12
The temperature and angular size of the source of gamma rays from the galactic center equal those found from the dark matter model.
The calculated temperature is model-dependent – this temperature is based on the low temperature solution. 13
The Kamiokande II data in the hours before and after the main burst yield an 8 MeV neutrino line above background (~30 sigma).
The background was obtained by another data set for K-II taken by the detector months later 14
The observed 8 MeV neutrino line is broadened by 25% energy resolution as expected.
The line was well hidden given the similar shapes of the background & line

19. Tritium beta decay and the neutrino mass

20. Fitting beta spectrum to 3 + 3 model
Fit to a single effective mass
NO!
Fit to 3 known masses
YES
If expression under square root is negative replace by zero Essentially the weighted sum of separate spectra with weights U2ej A one parameter fit to spectrum if we assume that the ve effective mass is very close to zero. The one free parameter is the spectral weight of the 21.4 eV mass.

21. Kinks located 21.4 eV and 4.0 eV before E0 & then a linear decline
3+3 model predicts 3 features in spectrum
Kinks located 21.4 eV and 4.0 eV before E0 & then a linear decline
Kink visibility depends on weight of 21.4 eV mass.
0.2
0.5
0.8
2nd Kink 4.0 eV from endpoint not visible in pre-KATRIN data E0

22. 3 + 3 model fitted data to 3 pre-KATRIN experiments Ehrlich (2015)
Based on roughly equal weights for the two m2 > 0 masses with just enough of the 3rd mass to give an effective mass close to zero.
Regrettably fits ignored final state distributions & it was shown to be incorrect by KATRIN’s first results
However, these earlier 3 experiments do not rule out the model when contribution from the 21.4 eV mass is small

23. Pre-KATRIN evidence supporting the 3 + 3 neutrino model Evidence
Evidence
Comment
Ref 1
25 SN 1987A neutrinos in 3 detectors fit one of two masses (4 eV & 21 eV) & only 1 fits both.
Assumes the spread in emission times << spread in travel times
E(2012) 2
These two masses yield identical fractional Splittings, in the model
Assumes that the splittings are given by the solar and atmospheric dm2
E(2013) 3
The 21 eV neutrino mass in the model yields a good fit to the dark matter distribution in the Milky Way Galaxy
The tachyonic mass in would be associated with dark energy not dark matter.
C(2014) 4
The 4 eV neutrino mass in the model yields a good fit to the dark matter distribution in four galaxy clusters
The smaller mass would be expected for the larger structure. 5
The three best tritium beta decay experiments fit the model masses better than they do an effective mass m < 2 eV.
These fits are all made using published data of the spectra for Troitsk, Mainz and Livermore data.
E(2016) 6
The weights assigned to the 3 masses in doing these fits are the same in those 3 experiments and correspond to an effective m near zero.
The most prominent feature seen in these experiments is the kink in the spectrum at 21 eV. 7
Six different observations suggest a consistent value of m2 = eV2 for the electron neutrino effective mass.
A tachyonic mass in the model requires that at least one flavor state mass be tachyonic
E(2015) 8
The 5 Mont Blanc neutrinos are consistent
With all having the same energy ~8 MeV
No other model besides explains this observed constancy.
E(2018) 9
The computed tachyonic mass for the Mont
Blanc neutrinos is the same as that in model
A tachyonic mass for the Mont Blanc
Neutrinos requires an 8 MeV neutrino line From SN 1987A 10
The 16.7 MeV Z’ Boson provides the basis for a supernova model with 8 MeV cold dark matter particles yielding an 8 MeV neutrino line
This boson has been identified as a mediator between standard model matter particles and dark matter. 11
The spectrum of gamma rays from the galactic center is consistent with the annihilation of 8 MeV dark matter particles.
Aside from the next galactic supernova the galactic center is the best place to check the dark matter model. 12
The temperature and angular size of the source of gamma rays from the galactic center equal those found from the dark matter model.
The calculated temperature is model-dependent – this temperature is based on the low temperature solution. 13
The Kamiokande II data in the hours before and after the main burst yield an 8 MeV neutrino line above background (~30 sigma).
The background was obtained by another data set for K-II taken by the detector months later 14
The observed 8 MeV neutrino line is broadened by 25% energy resolution as expected.
The line was well hidden given the similar shapes of the background & line

24. Evidence for an electron neutrino effective mass
Ehrlich(2015)
At least one tachyonic flavor required if one of the mass states has m2 < 0
|m|

25. Forbidden decays e P  n +e +v n Emitted v
time n
Emitted v
Energetically forbidden in proton rest frame P
distance

26. e n
Absorbed v
P  n +e +v
Energetically allowed for high energy proton
Appears like V + P  n +e P

27. Pre-KATRIN evidence supporting the 3 + 3 neutrino model Evidence
Evidence
Comment
Ref 1
25 SN 1987A neutrinos in 3 detectors fit one of two masses (4 eV & 21 eV) & only 1 fits both.
Assumes the spread in emission times << spread in travel times
E(2012) 2
These two masses yield identical fractional Splittings, in the model
Assumes that the splittings are given by the solar and atmospheric dm2
E(2013) 3
The 21 eV neutrino mass in the model yields a good fit to the dark matter distribution in the Milky Way Galaxy
The tachyonic mass in would be associated with dark energy not dark matter.
C(2014) 4
The 4 eV neutrino mass in the model yields a good fit to the dark matter distribution in four galaxy clusters
The smaller mass would be expected for the larger structure. 5
The three best tritium beta decay experiments fit the model masses better than they do an effective mass m < 2 eV.
These fits are all made using published data of the spectra for Troitsk, Mainz and Livermore data.
E(2016) 6
The weights assigned to the 3 masses in doing these fits are the same in those 3 experiments and correspond to an effective m near zero.
The most prominent feature seen in these experiments is the kink in the spectrum at 21 eV. 7
Six different observations suggest a consistent value of m2 = eV2 for the electron neutrino effective mass.
A tachyonic mass in the model requires that at least one flavor state mass be tachyonic
E(2015) 8
The 5 Mont Blanc neutrinos are consistent
With all having the same energy ~8 MeV
No other model besides explains this observed constancy.
E(2018) 9
The computed tachyonic mass for the Mont
Blanc neutrinos is the same as that in model
A tachyonic mass for the Mont Blanc
Neutrinos requires an 8 MeV neutrino line From SN 1987A 10
The 16.7 MeV Z’ Boson provides the basis for a supernova model with 8 MeV cold dark matter particles yielding an 8 MeV neutrino line
This boson has been identified as a mediator between standard model matter particles and dark matter. 11
The spectrum of gamma rays from the galactic center is consistent with the annihilation of 8 MeV dark matter particles.
Aside from the next galactic supernova the galactic center is the best place to check the dark matter model. 12
The temperature and angular size of the source of gamma rays from the galactic center equal those found from the dark matter model.
The calculated temperature is model-dependent – this temperature is based on the low temperature solution. 13
The Kamiokande II data in the hours before and after the main burst yield an 8 MeV neutrino line above background (~30 sigma).
The background was obtained by another data set for K-II taken by the detector months later 14
The observed 8 MeV neutrino line is broadened by 25% energy resolution as expected.
The line was well hidden given the similar shapes of the background & line

28. Evidence for a m2 < 0 mass in SN 1987A
Evidence for a m2 < 0 mass in SN 1987A? Suppose there were 5 neutrinos with that mass
1/E2
1/E2
Just solve for m2

29. Could 5 Mont Blanc neutrinos have m2 < 0?
An 8 MeV spectral line??? Δ𝐸
1/E2
The good news:
Within a factor of two of the mass value. Also 5 neutrinos consistent with having the same energy
5 h 7s

30. Pre-KATRIN evidence supporting the 3 + 3 neutrino model Evidence
Evidence
Comment
Ref 1
25 SN 1987A neutrinos in 3 detectors fit one of two masses (4 eV & 21 eV) & only 1 fits both.
Assumes the spread in emission times << spread in travel times
E(2012) 2
These two masses yield identical fractional Splittings, in the model
Assumes that the splittings are given by the solar and atmospheric dm2
E(2013) 3
The 21 eV neutrino mass in the model yields a good fit to the dark matter distribution in the Milky Way Galaxy
The tachyonic mass in would be associated with dark energy not dark matter.
C(2014) 4
The 4 eV neutrino mass in the model yields a good fit to the dark matter distribution in four galaxy clusters
The smaller mass would be expected for the larger structure. 5
The three best tritium beta decay experiments fit the model masses better than they do an effective mass m < 2 eV.
These fits are all made using published data of the spectra for Troitsk, Mainz and Livermore data.
E(2016) 6
The weights assigned to the 3 masses in doing these fits are the same in those 3 experiments and correspond to an effective m near zero.
The most prominent feature seen in these experiments is the kink in the spectrum at 21 eV. 7
Six different observations suggest a consistent value of m2 = eV2 for the electron neutrino effective mass.
A tachyonic mass in the model requires that at least one flavor state mass be tachyonic
E(2015) 8
The 5 Mont Blanc neutrinos are consistent
With all having the same energy ~8 MeV
No other model besides explains this observed constancy.
E(2018) 9
The computed tachyonic mass for the Mont
Blanc neutrinos is the same as that in model
A tachyonic mass for the Mont Blanc
Neutrinos requires an 8 MeV neutrino line From SN 1987A 10
The 16.7 MeV Z’ Boson provides the basis for a supernova model with 8 MeV cold dark matter particles yielding an 8 MeV neutrino line
This boson has been identified as a mediator between standard model matter particles and dark matter. 11
The spectrum of gamma rays from the galactic center is consistent with the annihilation of 8 MeV dark matter particles.
Aside from the next galactic supernova the galactic center is the best place to check the dark matter model. 12
The temperature and angular size of the source of gamma rays from the galactic center equal those found from the dark matter model.
The calculated temperature is model-dependent – this temperature is based on the low temperature solution. 13
The Kamiokande II data in the hours before and after the main burst yield an 8 MeV neutrino line above background (~30 sigma).
The background was obtained by another data set for K-II taken by the detector months later 14
The observed 8 MeV neutrino line is broadened by 25% energy resolution as expected.
The line was well hidden given the similar shapes of the background & line

31. How to get monochromatic 8 MeV SN neutrinos?
Z’ mediated reaction
e or v X
New Z’ = MeV boson
Krasznahorkay (2016)
X = COLD dark matter particles of mass 8.4 MeV
Yields monochromatic ~8 MeV neutrinos & e+ e- pairs Z’
Low T
High T
e or v X
Test of the model: Galactic center gamma rays

32. Spectrum of galactic center gamma rays
Enhancement above bkgd due to Z’ mediated reaction & subsequent e+ e -annihilation
100% e+ KE lost
0% e+ KE lost
50% e+ KE lost
Gamma ray flux MX
Background
Energy of gamma ray
0.511 MeV

33. Gamma rays from galactic center
Enhancements above a power law are shown for 3 dark matter masses
of 5, 10 & 50 MeV
= OSSE Data
MX = 10 MeV
Enhancement fitting data has MX = 10 +5/-2 MeV

34. Pre-KATRIN evidence supporting the 3 + 3 neutrino model Evidence
Evidence
Comment
Ref 1
25 SN 1987A neutrinos in 3 detectors fit one of two masses (4 eV & 21 eV) & only 1 fits both.
Assumes the spread in emission times << spread in travel times
E(2012) 2
These two masses yield identical fractional Splittings, in the model
Assumes that the splittings are given by the solar and atmospheric dm2
E(2013) 3
The 21 eV neutrino mass in the model yields a good fit to the dark matter distribution in the Milky Way Galaxy
The tachyonic mass in would be associated with dark energy not dark matter.
C(2014) 4
The 4 eV neutrino mass in the model yields a good fit to the dark matter distribution in four galaxy clusters
The smaller mass would be expected for the larger structure. 5
The three best tritium beta decay experiments fit the model masses better than they do an effective mass m < 2 eV.
These fits are all made using published data of the spectra for Troitsk, Mainz and Livermore data.
E(2016) 6
The weights assigned to the 3 masses in doing these fits are the same in those 3 experiments and correspond to an effective m near zero.
The most prominent feature seen in these experiments is the kink in the spectrum at 21 eV. 7
Six different observations suggest a consistent value of m2 = eV2 for the electron neutrino effective mass.
A tachyonic mass in the model requires that at least one flavor state mass be tachyonic
E(2015) 8
The 5 Mont Blanc neutrinos are consistent
With all having the same energy ~8 MeV
No other model besides explains this observed constancy.
E(2018) 9
The computed tachyonic mass for the Mont
Blanc neutrinos is the same as that in model
A tachyonic mass for the Mont Blanc
Neutrinos requires an 8 MeV neutrino line From SN 1987A 10
The 16.7 MeV Z’ Boson provides the basis for a supernova model with 8 MeV cold dark matter particles yielding an 8 MeV neutrino line
This boson has been identified as a mediator between standard model matter particles and dark matter. 11
The spectrum of gamma rays from the galactic center is consistent with the annihilation of 8 MeV dark matter particles.
Aside from the next galactic supernova the galactic center is the best place to check the dark matter model. 12
The temperature and angular size of the source of gamma rays from the galactic center equal those found from the dark matter model.
The calculated temperature is model-dependent – this temperature is based on the low temperature solution. 13
The Kamiokande II data in the hours before and after the main burst yield an 8 MeV neutrino line above background (~30 sigma).
The background was obtained by another data set for K-II taken by the detector months later 14
The observed 8 MeV neutrino line is broadened by 25% energy resolution as expected.
The line was well hidden given the similar shapes of the background & line

35. The final missing piece of the puzzle
Mont Blanc neutrinos were tachyons
An 8 MeV neutrino line from SN 1987A

36. Difficulty of spotting an 8 MeV neutrino line
Need a line many times taller to get this.
Much like spotting a hidden unicorn!
No neutrino lines ever actually seen from any source
Any neutrino line will be considerably broadened
Need large enough amplitude or it will fade into the background
Need to know background shape very accurately
The evidence for an 8 MeV neutrino line fell out of the heavens!
– thanks to the thoroughness of Dr. Hirata and colleagues

37. # Hits Spotting the hidden unicorn! ~ 30 sigma excess # Events
Kamiokande data on day of SN 1987A – total of 136 min
Bkgd is from a search for solar neutrinos some months later
Solid: assumes same bkgd, dashed: corrected for different triggers
Ehrlich (2018)
~ 30 sigma excess
Great camouflage!
# Hits
MeV

38. Pre-KATRIN evidence supporting the 3 + 3 neutrino model Evidence
Evidence
Comment
Ref 1
25 SN 1987A neutrinos in 3 detectors fit one of two masses (4 eV & 21 eV) & only 1 fits both.
Assumes the spread in emission times << spread in travel times
E(2012) 2
These two masses yield identical fractional Splittings, in the model
Assumes that the splittings are given by the solar and atmospheric dm2
E(2013) 3
The 21 eV neutrino mass in the model yields a good fit to the dark matter distribution in the Milky Way Galaxy
The tachyonic mass in would be associated with dark energy not dark matter.
C(2014) 4
The 4 eV neutrino mass in the model yields a good fit to the dark matter distribution in four galaxy clusters
The smaller mass would be expected for the larger structure. 5
The three best tritium beta decay experiments fit the model masses better than they do an effective mass m < 2 eV.
These fits are all made using published data of the spectra for Troitsk, Mainz and Livermore data.
E(2016) 6
The weights assigned to the 3 masses in doing these fits are the same in those 3 experiments and correspond to an effective m near zero.
The most prominent feature seen in these experiments is the kink in the spectrum at 21 eV. 7
Six different observations suggest a consistent value of m2 = eV2 for the electron neutrino effective mass.
A tachyonic mass in the model requires that at least one flavor state mass be tachyonic
E(2015) 8
The 5 Mont Blanc neutrinos are consistent
With all having the same energy ~8 MeV
No other model besides explains this observed constancy.
E(2018) 9
The computed tachyonic mass for the Mont
Blanc neutrinos is the same as that in model
A tachyonic mass for the Mont Blanc
Neutrinos requires an 8 MeV neutrino line From SN 1987A 10
The 16.7 MeV Z’ Boson provides the basis for a supernova model with 8 MeV cold dark matter particles yielding an 8 MeV neutrino line
This boson has been identified as a mediator between standard model matter particles and dark matter. 11
The spectrum of gamma rays from the galactic center is consistent with the annihilation of 8 MeV dark matter particles.
Aside from the next galactic supernova the galactic center is the best place to check the dark matter model. 12
The temperature and angular size of the source of gamma rays from the galactic center equal those found from the dark matter model.
The calculated temperature is model-dependent – this temperature is based on the low temperature solution. 13
The Kamiokande II data in the hours before and after the main burst yield an 8 MeV neutrino line above background (~30 sigma).
The background was obtained by another data set for K-II taken by the detector months later 14
The observed 8 MeV neutrino line is broadened by 25% energy resolution as expected.
The line was well hidden given the similar shapes of the background & line

39. Maybe FTL particles OK if mass imaginary (1962)
  Summary of talk
No FTL particles (1905)
Maybe FTL particles OK if mass imaginary (1962)
Neutrinos are the only candidates (1985)
3+3 model of neutrino masses with one imaginary (2013)
14 separate data sets support the 3+3 model (2018/19)
1st  KATRIN results (2019) --  neutrino mass < 1 eV 
          3+3 model ALSO fits first results
          After 1 yr of data model will be proven or dead. 
          If model is proven the tachyon had great camouflage!

40. Tardy-
centrism
“Subtle is the Lord, but malicious He is not.” ― Albert Einstein Ehrlich.physics.gmu.edu