### Abstract

In this paper three things are done. (i) We investigate the analogues of Cerenkov radiation for the decay of a superluminal neutrino and calculate the Cerenkov angles for the emission of a photon through a W loop, and for a collinear electron-positron pair, assuming the tachyonic dispersion relation for the superluminal neutrino. The decay rate of a freely propagating neutrino is found to depend on the shape of the assumed dispersion relation, and is found to decrease with decreasing tachyonic mass of the neutrino. (ii)We discuss a few properties of the tachyonic Dirac equation (symmetries and plane-wave solutions), which may be relevant for the description of superluminal neutrinos seen by the OPERA experiment, and discuss the calculation of the tachyonic propagator. (iii) In the absence of a commonly accepted tachyonic field theory, and in view of an apparent "running" of the observed neutrino mass with the energy, we write down a model Lagrangian, which describes a Yukawa-type interaction of a neutrino coupling to a scalar background field via a scalar-minus-pseudoscalar interaction. This constitutes an extension of the standard model. If the interaction is strong, then it leads to a substantial renormalization-group "running" of the neutrino mass and could potentially explain the experimental observations.

Original language | English |
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Pages (from-to) | 749-762 |

Number of pages | 14 |

Journal | Central European Journal of Physics |

Volume | 10 |

Issue number | 4 |

DOIs | |

Publication status | Published - Aug 2012 |

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### Keywords

- cosmic rays
- gauge field theories
- neutrino, muon, pion, and other elementary particles
- relativistic wave equations
- renormalization group methods
- theory of quantized fields

### ASJC Scopus subject areas

- Physics and Astronomy(all)