The Superluminal Neutrinos From Deformed Lorentz Invariance

Abstract

We study two superluminal neutrino scenarios where δv ≡ (v −c)/c is a constant. To be consistent with the OPERA, Borexino, and ICARUS experiments and with the SN1987a observations, we assume that δvν on the Earth is about three order larger than that on the interstellar scale. To explain the theoretical challenges from the Bremsstrahlung effects and pion decays, we consider the deformed Lorentz invariance, and show that the superluminal neutrino dispersion relations can be realized properly while the modifications to the dispersion relations of the other Standard Model particles can be negligible. In addition, we propose the deformed energy and momentum conservation laws for a generic physical process. In Scenario I the momentum conservation law is preserved while the energy conservation law is deformed. In Scenario II the energy conservation law is preserved while the momentum conservation law is deformed. We present the energy and momentum conservation laws in terms of neutrino momentum in Scenario I and in terms of neutrino energy in Scenario II. In such formats, the energy and momentum conservation laws are exactly the same as those in the traditional quantum field theory with Lorentz symmetry. Thus, all the above theoretical challenges can be automatically solved. We show explicitly that the Bremsstrahlung processes are forbidden and there is no problem for pion decays.

Violations of Lorentz invariance in the neutrino sector: an improved analysis of anomalous threshold constraints

“…Of course one can envisage non-EFT scenarios[14][15][16][17][18][19][20][21][22][23] but so far or these alternative models have not reached the theoretical maturity to be suitable for casting constrains or have to be finely designed in order to avoid constraints similar to the one s we shall discuss here, see e.g [24]…”

Particle-Dependent Deformations of Lorentz Symmetry

“…Discussions of possible non-universal departures from Lorentz symmetry naturally came under consideration [23][24][25][26][27][28] in contemplating the preliminary OPERA reports, since for photons of, say, about 20 GeV the agreement of the speed law with the special-relativistic prescription is confirmed at the level of 1 part in 10…”

Multiple Lorentz Groups—A Toy Model for Superluminal Muon Neutrinos

“…The current experimental values or bounds for the three neutrino mixing angles 12  , 23  , and 13  are …”

“…In [12] two models were investigated, where the first gave rise to deformed energy conservation laws and the second resulted in deformed momentum conservation laws. For these models the bounds of [9] are not applica-ble.…”