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
© 2012 Versita Warsaw
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.
