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formerly Central European Journal of Physics

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Tachyonic field theory and neutrino mass running

1Department of Physics, Missouri University of Science and Technology, Rolla, Missouri, 65409-0640, USA

2Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, 69120, Heidelberg, Germany

© 2012 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)

Citation Information: Open Physics. Volume 10, Issue 4, Pages 749–762, ISSN (Online) 2391-5471, DOI: 10.2478/s11534-012-0031-1, July 2012

Publication History

Published Online:
2012-07-17

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.

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

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