Multiple Lorentz Groups—A Toy Model for Superluminal Muon Neutrinos

Marco Schreck

Institute for Theoretical Physics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany.

DOI: 10.4236/jmp.2012.310177                

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 if— within 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.

Keywords

Special Relativity; Dispersion Relations; Neutrino Interactions; Non-Standard-Model Neutrinos

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	T. Adam, et al., “Measurement of the Neutrino Velocity with the OPERA Detector in the CNGS Beam,” arXiv:1109.4897.
[2]	C. R. Contaldi, “The OPERA Neutrino Velocity Result and the Synchronisation of Clocks,” arXiv:1109.6160.
[3]	O. Besida, “Three Errors in the Article: ‘The OPERA Neutrino Velocity Result and the Synchronisation of Clocks’,” arXiv:1110.2909.
[4]	R. A. J. van Elburg, “Measuring Time of Flight Using Satellite-Based Clocks,” arXiv:1110.2685.
[5]	R. Alicki, “A Possible Statistical Mechanism of Anomalous Neutrino Velocity in OPERA Experiment?” arXiv:1109.5727.
[6]	G. Henri, “A Simple Explanation of OPERA Results without Strange Physics,” arXiv:1110.0239.
[7]	B. Broda, “An OPERA Inspired Classical Model Reproducing Superluminal Velocities,” arXiv:1110.0644.
[8]	H. Davoudiasl and T. G. Rizzo, “Testing the OPERA Superluminal Neutrino Anomaly at the LHC,” Physical Review D, Vol. 84, No. 9, 2011, Article ID: 091903. doi:10.1103/PhysRevD.84.091903
[9]	A. G. Cohen and S. L. Glashow, “Pair Creation Constrains Superluminal Neutrino Propagation,” Physical Review Letters, Vol. 107, No. 18, 2011, Article ID: 181803. doi:10.1103/PhysRevLett.107.181803
[10]	S. Mohanty and S. Rao, “Constraint on Super-luminal Neutrinos from Vacuum Cerenkov Processes,” arXiv: 1111.2725.
[11]	L.-L. Zhou and B.-Q. Ma, “On the Rationality of the OPERA Experiment as a Signal of Lorentz Violation,” arXiv:1111.1574.
[12]	Y. Huo, T. Li, Y. Liao, D. V. Nanopoulos, Y. Qi and F. Wang, “The OPERA Superluminal Neutrinos from Deformed Lorentz Invariance,” arXiv:1111.4994.
[13]	X.-J. Bi, P.-F. Yin, Z.-H. Yu and Q. Yuan, “Constraints and Tests of the OPERA Superluminal Neutrinos,” Physical Review Letters, Vol. 107, No. 24, 2011, Article ID: 241802. doi:10.1103/PhysRevLett.107.241802
[14]	G. Cacciapaglia, A. Deandrea and L. Panizzi, “Superluminal Neutrinos in Long Baseline Experiments and SN1987a,” Journal of High Energy Physics, Vol. 2011, No. 11, 2011, Article ID: 137. doi:10.1007/JHEP11(2011)137
[15]	G. Amelino-Camelia, G. Gubitosi, N. Loret, F. Mercati, G. Rosati, and P. Lipari, “OPERA-Reassessing Data on the Energy Dependence of the Speed of Neutrinos,” International Journal of Modern Physics D, Vol. 20, No. 14, 2011, pp. 2623-2640.
[16]	N. Nakanishi, “An Interpretation of ‘Superluminal Neutrino’ Compatible with Relativity in the Framework of Standard Model,” arXiv:1111.1760.
[17]	S. Nojiri and S. D. Odintsov, “Could the Dynamical Lorentz Symmetry Breaking Induce the Superluminal Neutrinos?” The European Physical Journal C, Vol. 71, No. 11, 2011, Article ID: 1801. doi:10.1140/epjc/s10052-011-1801-4
[18]	G. E. Volovik, “Topology of Quantum Vacuum,” arXiv: 1111.4627.
[19]	F. R. Klinkhamer, “Superluminal Muon-Neutrino Velocity from a Fermi-Point-Splitting Model of Lorentz Violation,” arXiv:1109.5671.
[20]	G. Dvali and A. Vikman, “Price for Environmental Neutrino-Superluminality,” Journal of High Energy Physics, Vol. 2012, No. 2, 2012, Article ID: 134. doi:10.1007/JHEP02(2012)134
[21]	I. Oda and H. Taira, “Superluminal Neutrinos from Gauge Field,” Modern Physics Letters A, Vol. 26, No. 39, 2011, pp. 2917-2921. doi:10.1142/S0217732311037297
[22]	L. Iorio, “Constraints from Orbital Motions around the Earth of the Environmental Fifth-Force Hypothesis for the OPERA Superluminal Neutrino Phenomenology,” Journal of High Energy Physics, Vol. 2012, No. 5, 2012, Article ID: 73. doi:10.1007/JHEP05(2012)073
[23]	B. Allés, “Relativity Accommodates Superluminal Mean Velocities,” Physical Review D, Vol. 85, No. 4, 2012, Article ID: 047501.
[24]	E. N. Saridakis, “Superluminal Neutrinos in Horava-Lifshitz Gravity,” arXiv:1110.0697.
[25]	F. R. Klinkhamer, “Spontaneously Broken Lorentz Invariance from the Dynamics of a Heavy Sterile Neutrino,” Letters to Journal of Experimental and Theoretical Physics, Vol. 95, No. 10, 2012, pp. 497-500. doi:10.1134/S0021364012100062
[26]	W. Winter, “Constraints on the Interpretation of the Superluminal Motion of Neutrinos at OPERA,” Physical Review D, Vol. 85, No. 1, 2012, Article ID: 017301. doi:10.1103/PhysRevD.85.017301
[27]	B. C. Lacki, “Olber’s Paradox for Superluminal Neutrinos: Constraining Extreme Neutrino Speeds at TeV-ZeV Energies with the Diffuse Neutrino Background,” Journal of Cosmology and Astroparticle Physics, Vol. 2012, No. 1, 2012, Article ID: 054. doi:10.1088/1475-7516/2012/01/054
[28]	S. Liberati, S. Sonego and M. Visser, “Faster-than-c Signals, Special Relativity, and Causality,” Annals of Physics, Vol. 298, No. 1, 2002, pp. 167-184. doi:10.1006/aphy.2002.6233
[29]	A. A. Michelson and E. W. Morley, “On the Relative Motion of the Earth and the Luminiferous Ether,” American Journal of Science, Vol. 34, No. 203, 1887, pp. 333- 345.
[30]	R. J. Kennedy and E. M. Thorndike, “Experimental Establishment of the Relativity of Time,” Physical Review, Vol. 42, No. 3, 1932, pp. 400-418. doi:10.1103/PhysRev.42.400
[31]	H. E. Ives and G. R. Stilwell, “An Experimental Study of the Rate of a Moving Atomic Clock,” Journal of the Optical Society of America, Vol. 28, No. 7, 1938, pp. 215- 219. doi:10.1364/JOSA.28.000215
[32]	L. Brillouin, “Wave Propagation and Group Velocity,” Academic, New York, 1960.
[33]	T. Cheng and L. Li, “Gauge Theory of Elementary Particle Physics,” Clarendon Press, Oxford, 1984.
[34]	D. Colladay and V. A. Kostelecky, “Lorentz-Violating Extension of the Standard Model,” Physical Review D, Vol. 58, No. 11, 1998, Article ID: 116002. doi:10.1103/PhysRevD.58.116002
[35]	V. A. Kostelecky and M. Mewes, “Lorentz and CPT Violation in Neutrinos,” Physical Review D, Vol. 69, No. 1, 2004, Article ID: 016005.
[36]	Q. G. Bailey and V. A. Kostelecky, “Lorentz-Violating Electrostatics and Magnetostatics,” Physical Review D, Vol. 70, No. 7, 2004, Article ID: 076006. doi:10.1103/PhysRevD.70.076006
[37]	B. Altschul, “Vacuum Cerenkov Radiation in Lorentz-Violating Theories without CPT Violation,” Physical Review Letters, Vol. 98, No. 4, 2007, Article ID: 041603. doi:10.1103/PhysRevLett.98.041603
[38]	K. Nakamura, et al., “The Review of Particle Physics,” Journal of Physics G, Vol. 37, No. 7A, 2010, Article ID: 075021. doi:10.1088/0954-3899/37/7A/075021
[39]	E. W. Otten and C. Weinheimer, “Neutrino Mass Limit from Tritium Beta Decay,” Reports on Progress in Physics, Vol. 71, No. 8, 2008, Article ID: 086201. doi:10.1088/0034-4885/71/8/086201
[40]	K. Hirata, et al., “Observation of a Neutrino Burst from the Supernova SN 1987a,” Physical Review Letters, Vol. 58, No. 14, 1987, pp. 1490-1493. doi:10.1103/PhysRevLett.58.1490
[41]	M. J. Longo, “Tests of Relativity from SN 1987a,” Physical Review D, Vol. 36, No. 10, 1987, pp. 3276-3277. doi:10.1103/PhysRevD.36.3276
[42]	E. Komatsu, et al., “Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation,” The Astrophysical Journal Supplement Series, Vol. 180, No. 2, 2009, pp. 330-376. doi:10.1088/0067-0049/180/2/330
[43]	F. R. Klinkhamer, “Superluminal Neutrino, Flavor, and Relativity,” Physical Review D, Vol. 85, No. 1, 2012, Article ID: 016011.
[44]	D. Marfatia, H. P?s, S. Pakvasa and T. J. Weiler, “A Model of Superluminal Neutrinos,” Physics Letters B, Vol. 707, No. 5, 2012, pp. 553-557. doi:10.1016/j.physletb.2012.01.028