Robert Ehrlich

The possibility of neutrinos moving at faster-than-light speeds can be modeled using terms in the Lagrangian that violate Lorentz symmetry, but the question of whether $m^2<0$ and $v>c$ tachyonic neutrinos exist is an empirical question. It remains unresolved despite evidence from cosmic ray and other data that the electron neutrino has an effective $m_{\nu }^2\approx -0.25{\mathrm{eV}}^2,$ which would require that one or more mass states is also tachyonic. In 2013, the $3+3$ model of the neutrino masses, which includes one tachyonic mass state, was proposed based on supernova SN 1987A neutrino data. Here, we update evidence for tachyonic electron neutrinos and the $3+3$ model and discuss one test which could prove conclusive. The update of earlier evidence includes many new elements, including new data which make the earlier cosmic ray evidence more robust, new results on cosmic ray composition, the ankle of the spectrum, leptonic cosmic ray data, and the statistical significance of finding the three large neutrino masses stipulated in the $3+3$ model. Barring a galactic supernova, which occur only around twice a century, a decisive test of the $3+3$ model could involve observing an extragalactic supernova neutrino burst, that is, a cluster of neutrinos in a specific time window well beyond what chance would predict. Even though existing searches for such bursts have yielded only upper limits on the extragalactic supernova frequency within a certain distance, it is shown that the choice of a one-day window for possible neutrino clusters in time might be far more sensitive. A search using a one-day time window could be conducted using existing data, and if a signal is found it would confirm the $3+3$ model. Of course, the absence of any day-long neutrino burst would not disprove the model, since it could mean only that the nearest supernova during the period when detectors were active was simply too far to be detected. Finally, apart from testing the $3+3$ model, an alternative type of search is suggested using existing hadronic cosmic ray data (from the IceCube Collaboration) that might verify the tachyonic neutrino hypothesis.

The question of whether some neutrinos are tachyons remains unresolved although various evidence from cosmic ray and other data exists that the electron neutrino has an effective $m_\nu^2\approx -0.25 eV^2,$ which would require that one or more mass states is also tachyonic. In 2013 the $3+3$ model of the neutrino masses, which includes one tachyonic mass state, was proposed based on supernova SN 1987A neutrino data. Here we update evidence for tachyonic electron neutrinos and the $3+3$ model and discuss one test which could prove conclusive. The update of earlier evidence includes many new elements, including new data which makes the earlier cosmic ray evidence more robust, new results on cosmic ray composition, the ankle of the spectrum, leptonic cosmic ray data, and the statistical significance of finding the three large neutrino masses stipulated in the $3+3$ model. Barring a galactic supernova, which occur only around twice a century, a decisive test of the $3+3$ model could involve observing an extragalactic supernova neutrino burst, that is a cluster of neutrinos in a specific time window well beyond what chance would predict. Even though existing searches for such bursts have yielded only upper limits on the extragalactic supernova frequency within a certain distance, it is shown that the choice of a one-day window for possible neutrino clusters in time might be far more sensitive. A search using a one day time window could be done using existing data, and if a signal is found it would confirm the $3+3$ model. Of course, the absence of any day-long neutrino burst would not disprove the model, since it could mean only that the nearest supernova during the period when detectors were active was simply too far to be detected. Finally, apart from testing the 3 + 3 model, an alternative type of search is suggested using existing hadronic cosmic ray data (from the IceCube Collaboration) that might verify the tachyonic neutrino hypothesis.

Here, we review searches for empirical evidence for the existence of tachyons, superluminal particles having $m^2<0.$ The review considers searches for new particles that might be tachyons, as well as evidence that neutrinos are tachyons from data that may have been gathered for other purposes. Much of the second half of the paper is devoted to the $3+3$ neutrino model including a tachyonic mass state, which has empirical support from a variety of areas. Although this is primarily a review article, it contains several newly identified results.