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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access July 17, 2012

Tachyonic field theory and neutrino mass running

Ulrich Jentschura
From the journal Open Physics

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.

[1] E. Recami, J. Phys. Conf. Ser. 196, 012020 (2009) http://dx.doi.org/10.1088/1742-6596/196/1/01202010.1088/1742-6596/196/1/012020Search in Google Scholar

[2] V. L. Dadykin et al., JETP 45, 593 (1987) Search in Google Scholar

[3] P. Adamson et al., Phys. Rev. D 76, 072005 (2007) http://dx.doi.org/10.1103/PhysRevD.76.07200510.1103/PhysRevD.76.072005Search in Google Scholar

[4] G. R. Kalbfleisch, N. Baggett, E. C. Fowler, J. Alspector, Phys. Rev. Lett. 43, 1361 (1979) http://dx.doi.org/10.1103/PhysRevLett.43.136110.1103/PhysRevLett.43.1361Search in Google Scholar

[5] T. Adam et al. (OPERA Collaboration), arXiv:1109.4897v2 Search in Google Scholar

[6] R. G. H. Robertson, T. J. Bowles, G. J. Stephenson, D. L. Wark, J. F. Wilkerson, D. A. Knapp, Phys. Rev. Lett. 67, 957 (1991) http://dx.doi.org/10.1103/PhysRevLett.67.95710.1103/PhysRevLett.67.957Search in Google Scholar

[7] K. Assamagan et al., Phys. Lett. B 335, 231 (1994) http://dx.doi.org/10.1016/0370-2693(94)91419-210.1016/0370-2693(94)91419-2Search in Google Scholar

[8] W. Stoeffl, D. J. Decman, Phys. Rev. Lett. 75, 3237 (1995) http://dx.doi.org/10.1103/PhysRevLett.75.323710.1103/PhysRevLett.75.3237Search in Google Scholar

[9] K. Assamagan et al., Phys. Rev. D 53, 6065 (1996) http://dx.doi.org/10.1103/PhysRevD.53.606510.1103/PhysRevD.53.6065Search in Google Scholar

[10] C. Weinheimer et al., Phys. Lett. B 460, 219 (1999) http://dx.doi.org/10.1016/S0370-2693(99)00780-710.1016/S0370-2693(99)00780-7Search in Google Scholar

[11] V. M. Lobashev et al., Phys. Lett. B 460, 227 (1999) http://dx.doi.org/10.1016/S0370-2693(99)00781-910.1016/S0370-2693(99)00781-9Search in Google Scholar

[12] A. I. Belesev et al., Phys. At. Nucl. 71, 449 (2008) http://dx.doi.org/10.1134/S106377880803004610.1134/S1063778808030046Search in Google Scholar

[13] A. Chodos, A. I. Hauser, V. A. Kostelecky, Phys. Lett. B 150, 431 (1985) http://dx.doi.org/10.1016/0370-2693(85)90460-510.1016/0370-2693(85)90460-5Search in Google Scholar

[14] T. Chang, arXiv:hep-th/0011087 Search in Google Scholar

[15] T. Chang, Nucl. Sci. Technol. 13, 129 (2002) 10.1088/0957-0233/13/3/316Search in Google Scholar

[16] U. D. Jentschura, B. J. Wundt, arXiv:1110.4171 [hepph] Search in Google Scholar

[17] A. Sommerfeld, Zur Elektronentheorie. III. Ue-ber Lichtgeschwindigkeits- und Ueberlichtgeschwindigkeitselektronen, Nachr. k. Ges. Wiss. Göttingen, Heft 3, 201–235 (1905) Search in Google Scholar

[18] G. Feinberg, Phys. Rev. 159, 1089 (1967) http://dx.doi.org/10.1103/PhysRev.159.108910.1103/PhysRev.159.1089Search in Google Scholar

[19] O. M. P. Bilaniuk, V. K. Deshpande, E. C. G. Sudarshan, Am. J. Phys. 30, 718 (1962) http://dx.doi.org/10.1119/1.194177310.1119/1.1941773Search in Google Scholar

[20] J. Bandukwala, D. Shay, Phys. Rev. D 9, 889 (1974) http://dx.doi.org/10.1103/PhysRevD.9.88910.1103/PhysRevD.9.889Search in Google Scholar

[21] H. van Dam, Y. J. Ng, L. C. Biedenharn, Phys. Lett. B 158, 227 (1985) http://dx.doi.org/10.1016/0370-2693(85)90961-X10.1016/0370-2693(85)90961-XSearch in Google Scholar

[22] L. Xinzhou, L. Jizong, J. Phys. A 20, 6113 (1987) http://dx.doi.org/10.1088/0305-4470/20/17/04310.1088/0305-4470/20/17/043Search in Google Scholar

[23] O. M. Bilaniuk, J. Phys. Conf. Ser. 196, 012021 (2009) http://dx.doi.org/10.1088/1742-6596/196/1/01202110.1088/1742-6596/196/1/012021Search in Google Scholar

[24] S. K. Bose, J. Phys. Conf. Ser. 196, 012022 (2009) http://dx.doi.org/10.1088/1742-6596/196/1/01202210.1088/1742-6596/196/1/012022Search in Google Scholar

[25] P. Defraigne, G. Petit, Metrologia 40, 184 (2003) http://dx.doi.org/10.1088/0026-1394/40/4/30710.1088/0026-1394/40/4/307Search in Google Scholar

[26] J. Levine, Metrologia 45, 184 (2008) 10.1088/0026-1394/45/6/S04Search in Google Scholar

[27] A. G. Cohen, S. L. Glashow, Phys. Rev. Lett. 107, 181803 (2011) http://dx.doi.org/10.1103/PhysRevLett.107.18180310.1103/PhysRevLett.107.181803Search in Google Scholar PubMed

[28] G. Amelino-Camelia, arXiv:gr-qc/0012051 Search in Google Scholar

[29] G. Amelino-Camelia, Symmetry 2, 230 (2010) http://dx.doi.org/10.3390/sym201023010.3390/sym2010230Search in Google Scholar

[30] G. Amelino-Camelia et al. (OPERA Collaboration), arXiv:1109.5172 Search in Google Scholar

[31] G. Amelino-Camelia, L. Freidel, J. Kowalski-Glikman, L. Smolin (OPERA Collaboration), arXiv:1110.0521 Search in Google Scholar

[32] X.-J. Bi, P.-F. Yin, Z.-H. Yu, Q. Yuan, Phys. Rev. Lett. 107, 241802 (2011) http://dx.doi.org/10.1103/PhysRevLett.107.24180210.1103/PhysRevLett.107.241802Search in Google Scholar PubMed

[33] R. Cowsik, S. Nussinov, U. Sarkar, Phys. Rev. Lett. 107, 251801 (2011) http://dx.doi.org/10.1103/PhysRevLett.107.25180110.1103/PhysRevLett.107.251801Search in Google Scholar PubMed

[34] L. Gonzalez-Mestres, arXiv:1109.6630 Search in Google Scholar

[35] M. E. Arons, E. C. G. Saudarshan, Phys. Rev. 173, 1622 (1968) http://dx.doi.org/10.1103/PhysRev.173.162210.1103/PhysRev.173.1622Search in Google Scholar

[36] J. Dhar, E. C. G. Saudarshan, Phys. Rev. 174, 1808 (1968) http://dx.doi.org/10.1103/PhysRev.174.180810.1103/PhysRev.174.1808Search in Google Scholar

[37] R. I. Sutherland, J. R. Shepanski, Phys. Rev. D 33, 2896 (1986) http://dx.doi.org/10.1103/PhysRevD.33.289610.1103/PhysRevD.33.2896Search in Google Scholar

[38] S. Mohanty, S. Rao, arXiv:1111.2725 Search in Google Scholar

[39] M. Li, D. Liu, J. Meng, T. Wang, L. Zhou, arXiv:1111.3294 Search in Google Scholar

[40] U. D. Jentschura, Phys. Rev. A 64, 013403 (2001) http://dx.doi.org/10.1103/PhysRevA.64.01340310.1103/PhysRevA.64.013403Search in Google Scholar

[41] W. Pauli, Rev. Mod. Phys. 15, 175 (1943) http://dx.doi.org/10.1103/RevModPhys.15.17510.1103/RevModPhys.15.175Search in Google Scholar

[42] C. M. Bender, S. Boettcher, Phys. Rev. Lett. 80, 5243 (1998) http://dx.doi.org/10.1103/PhysRevLett.80.524310.1103/PhysRevLett.80.5243Search in Google Scholar

[43] C. M. Bender, G. V. Dunne, J. Math. Phys. 40, 4616 (1999) http://dx.doi.org/10.1063/1.53299110.1063/1.532991Search in Google Scholar

[44] C. M. Bender, S. Boettcher, P. N. Meisinger, J. Math. Phys. 40, 2201 (1999) http://dx.doi.org/10.1063/1.53286010.1063/1.532860Search in Google Scholar

[45] C. M. Bender, D. C. Brody, H. F. Jones, Phys. Rev. Lett. 89, 270401 (2002) http://dx.doi.org/10.1103/PhysRevLett.89.27040110.1103/PhysRevLett.89.270401Search in Google Scholar

[46] A. Mostafazadeh, J. Math. Phys. 43, 205 (2002) http://dx.doi.org/10.1063/1.141824610.1063/1.1418246Search in Google Scholar

[47] A. Mostafazadeh, J. Math. Phys. 43, 2814 (2002) http://dx.doi.org/10.1063/1.146142710.1063/1.1461427Search in Google Scholar

[48] A. Mostafazadeh, J. Math. Phys. 43, 3944 (2002) http://dx.doi.org/10.1063/1.148907210.1063/1.1489072Search in Google Scholar

[49] A. Mostafazadeh, J. Math. Phys. 44, 974 (2003) http://dx.doi.org/10.1063/1.153930410.1063/1.1539304Search in Google Scholar

[50] D. G. Boulware, Phys. Rev. D 1, 2426 (1970) http://dx.doi.org/10.1103/PhysRevD.1.242610.1103/PhysRevD.1.2426Search in Google Scholar

[51] N. Moiseyev, Phys. Rep. 302, 211 (1998) http://dx.doi.org/10.1016/S0370-1573(98)00002-710.1016/S0370-1573(98)00002-7Search in Google Scholar

[52] C. W. McCurdy, C. K. Stroud, Comput. Phys. Commun. 63, 323 (1991) http://dx.doi.org/10.1016/0010-4655(91)90259-N10.1016/0010-4655(91)90259-NSearch in Google Scholar

[53] U. D. Jentschura, A. Surzhykov, M. Lubasch, J. Zinn-Justin, J. Phys. A 41, 095302 (2008) http://dx.doi.org/10.1088/1751-8113/41/9/09530210.1088/1751-8113/41/9/095302Search in Google Scholar

[54] C. Itzykson, J. B. Zuber, Quantum Field Theory (McGraw-Hill, New York, 1980) Search in Google Scholar

[55] U. D. Jentschura, B. J. Wundt, arXiv:1201.0359 [hepph] Search in Google Scholar

[56] V. K. Oikonomou, arXiv:1109.6170 Search in Google Scholar

[57] I. M. Suslov, JETP 93, 1 (2001) http://dx.doi.org/10.1134/1.139151510.1134/1.1391515Search in Google Scholar

[58] I. M. Suslov, JETP Lett. 74, 191 (2001) http://dx.doi.org/10.1134/1.141354310.1134/1.1413543Search in Google Scholar

[59] I. M. Suslov, JETP Lett. 76, 327 (2002) http://dx.doi.org/10.1134/1.152503010.1134/1.1525030Search in Google Scholar

[60] O.-M. Bilaniuk, E. C. G. Sudarshan, Nature (London) 223, 386 (1969) http://dx.doi.org/10.1038/223386b010.1038/223386b0Search in Google Scholar

Published Online: 2012-7-17
Published in Print: 2012-8-1

© 2012 Versita Warsaw

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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