Multiple Lorentz Groups—A Toy Model for Superluminal Muon Neutrinos

Abstract

In this article an idea is presented, which allows for the explanation of superluminal muon neutrinos. It is based on the introduction of a new superluminal, massless gauge boson coupling to the neutrino only, but not to other standard model particles. The model is discussed with regard to the Supernova 1987 (SN 1987) velocity bound on electron antineutrinos and the Cohen-Glashow constraint on superluminal neutrino propagation. The latter can be circumvented ifwithin the framework of the model-a sterile neutrino mixing with the active neutrino mass eigenstates is introduced. The suggestion of a sterile neutrino accounting for superluminal neutrinos has already been proposed in several papers. It is possible to choose mixing angles with the sterile neutrino sector such that the model respects both the SN 1987 bound and the muon neutrino travels superluminally.

Analysis of the consistency of parity-odd nonbirefringent modified Maxwell theory

“…Especially in the case where Lorentz violation resides in the photon sector, it can lead to a variety of new effects, for example a birefringent vacuum [13], new particle decays 1 At the end of September 2011 this seemed to change with the publication of the result by the OPERA collaboration, which claimed to have discovered Lorentz violation in the neutrino sector [1]. A large number of theoretical models emerged trying to explain the observed anomaly, for example by Fermi point splitting [2], spontaneous symmetry breaking caused by the existence of a fermionic condensate [3], or a multiple Lorentz group structure [4]. However, the physics community remained sceptical and articles were published trying to explain the result by an error source that had not been taken into account [5][6][7].…”

Constraints from orbital motions around the Earth of the environmental fifth-force hypothesis for the OPERA superluminal neutrino phenomenology

“…= c 5 8πG = 2.43 × 10 18 GeV is the energy equivalent of the reduced Planck's mass, where is the reduced Planck constant, c is the speed of light in vacuum and G is the Newtonian constant of gravitation, and the scale M * sets the strength of the coupling of the putative new massive spin-2 degree of freedom to the neutrino [17]. For other investigations involving various aspects of gravitation, astrophysics and cosmology, see, e.g., [19,20,21,22,23,24,25,26,27,28,29,30,31]. According to Dvali [18], the range length λ should not be shorter then the terrestrial radius R e : see also [32], in which Earth-size extra dimensions were studies.…”

Neutrino processes with power law dispersion relations

“…2. Lorentz invariance violation as in Lifshitz type field theories [15,16,24,25,26], from a gauge singlet SUSY sector [27] or a hidden sector [28], environmental couplings [29,30,31,32,33,34,35], dynamical symmetry breaking [37,38], Fermi-point splitting [39], space-time fluctuations [40] and string theory [41].…”