Majorana Neutrino Oscillations in Vacuum

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DOI: 10.4236/jmp.2012.38105    4,091 Downloads   6,543 Views   Citations


In the context of a type I seesaw scenario which leads to get light left-handed and heavy right-handed Majorana neutrinos, we obtain expressions for the transition probability densities between two flavor neutrinos in the cases of left-handed and right-handed neutrinos. We obtain these expressions in the context of an approach developed in the canonical formalism of Quantum Field Theory for neutrinos which are considered as superpositions of mass-eigenstate plane waves with specific momenta. The expressions obtained for the left-handed neutrino case after the ultra-relativistic limit is taking lead to the standard probability densities which describe light neutrino oscillations. For the right-handed neutrino case, the expressions describing heavy neutrino oscillations in the non-relativistic limit are different respect to the ones of the standard neutrino oscillations. However, the right-handed neutrino oscillations are phenomenologically restricted as is shown when the propagation of heavy neutrinos is considered as superpositions of mass-eigenstate wave packets.

Cite this paper

Y. Perez and C. Quimbay, "Majorana Neutrino Oscillations in Vacuum," Journal of Modern Physics, Vol. 3 No. 8, 2012, pp. 803-814. doi: 10.4236/jmp.2012.38105.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] E. Majorana, “Teoria simmetrica dell’elettrone e del positrone,” Nuovo Cimento, Vol. 14, 1937, p. 171.
[2] P. B. Pal and R. N. Mohapatra, “Masive Neutrinos in Physics and Astrophysics,” World Scientific Publishing, Singapore, 2004.
[3] C. Giunti and Ch. Kim, “Fundamental of Neutrinos in Physics and Astrophysics,” Oxford University Press, New York, 2007.
[4] K. Nakamura, et al., “Particle Data Group, the Review of Particle Physics,” Journal of Physics G, Vol. 37, 2010, Article ID: 075021.
[5] A. Bottino, C. W. Kim, H. Nishiura and W. K. Sze, “Mod- el for Lepton Mixing Angles and Majorana Neutrino Masses,” Physical Review D, Vol. 34, No. 3, 1986, pp. 862-867. doi:10.1103/PhysRevD.34.862
[6] B. Pontecorvo, “Neutrino Experiments and the Problem of Conservation of Leptonic Charge,” Soviet Physics— JETP, Vol. 26, 1968, p. 984.
[7] S. M. Bilenky and B. Pontecorvo, “Lepton Mixing and Neutrino Oscillations,” Physics Reports, Vol. 41, No. 4, 1978, pp. 225-261. doi:10.1016/0370-1573(78)90095-9
[8] B. Kayser, “On the Quantum Mechanics of Neutrino Os- cillation,” Physical Review D, Vol. 24, No. 1, 1981, pp. 110-116. doi:10.1103/PhysRevD.24.110
[9] C. Giunti, C. W. Kim and U. W. Lee, “When Do Neutri- nos Really Oscillate? Quantum Mechanics of Neutrino Oscillations,” Physical Review D, Vol. 44, No. 11, 1991, pp. 3635-3640. doi:10.1103/PhysRevD.44.3635
[10] J. Rich, “The Quantum Mechanics of Neutrino Oscilla- tions,” Physical Review D, Vol. 48, No. 9, 1993, pp. 4318- 4325. doi:10.1103/PhysRevD.48.4318
[11] M. Zralec, “From Kaons to Neutrinos: Quantum Mechan- ics of Particle Oscillations,” Acta Physica Polonica B, Vol. 29, 1998, pp. 3925-3956.
[12] E. Sassarolli, “Neutrino Oscillations: A Relativistic Ex- ample of a Two-Level System,” American Journal of Physics, Vol. 67, No. 10, 1999, pp. 869-875. doi:10.1119/1.19140
[13] M. Blasone and G. Vitiello, “Quantum Field Theory of Fermion Mixing,” Annals of Physics, Vol. 244, No. 2, 1995, pp. 283-311. doi:10.1006/aphy.1995.1115
[14] E. Alfinito, M. Blasone, A. Iorio and G. Vitiello, “Squeezed Neutrino Oscillations in Quantum Field Theory,” Physics Letters B, Vol. 362, No. 1-4, 1995, pp. 91-96. doi:10.1016/0370-2693(95)01171-L
[15] C. Y. Cardall, “Coherence of Neutrino Flavor Mixing in Quantum Field Theory,” Physical Review D, Vol. 61, No. 7, 2000, Article ID: 073006. doi:10.1103/PhysRevD.61.073006
[16] A. D. Dolgov, “Neutrinos in Cosmology,” Physics Reports, Vol. 370, No. 405, 2002, pp. 333-535. doi:10.1016/S0370-1573(02)00139-4
[17] M. Beuthe, “Oscillations of Neutrinos and Mesons in Quantum Field Theory,” Physics Reports, Vol. 375, No. 2-3, 2003, pp. 105-218. doi:10.1016/S0370-1573(02)00538-0
[18] Y. F. Li and Q. Y. Liu, “A Paradox on Quantum Field Theory of Neutrino Mixing and Oscillations,” Journal of High Energy Physics, Vol. 2006, 2006, Article ID: 048. doi:10.1088/1126-6708/2006/10/048
[19] M. Dvornikov and J. Maalampi, “Oscillations of Dirac and Majorana neutrinos in Matter and Magnetic Field,” Physical Review D, Vol. 79, No. 11, 2009, Article ID: 113015. doi:10.1103/PhysRevD.79.113015
[20] E. Kh. Akhmedova and J. Kopp, “Neutrino Oscillations: Quantum Mechanics vs. Quantum Field Theory,” Journal of High Energy Physics, Vol. 2010, No. 4, 2010, p. 8. doi:10.1007/JHEP04(2010)008
[21] E. Sassaroli, “Flavor Oscillations in Field Theory,”
[22] E. Sassaroli, “Neutrino Flavor Mixing and Oscillations in Field Theory,”
[23] E. Sassaroli, “Two Component Theory of Neutrino Flavor Mixing,”
[24] C. Giunti, C. W. Kim and U. W. Lee, “Remarks on the Weak States of Neutrinos,” Physical Review D, Vol. 45, No. 7, 1992, pp. 2414-2420. doi:10.1103/PhysRevD.45.2414
[25] C. W. Kim, C. Giunti and U. W. Lee, “Oscillations of Non-Relativistic Neutrinos,” Nuclear Physics B—Pro- ceedings Supplements, Vol. 28, No. 1, 1992, pp. 172-175. doi:10.1016/0920-5632(92)90167-Q
[26] K. M. Case, “Reformulation of the Majorana Theory of Neutrino,” Physical Review, Vol. 107, No. 1, 1957, pp. 307-316. doi:10.1103/PhysRev.107.307
[27] P. B. Pal, “Dirac, Majorana and Weyl Fermions,” American Journal of Physics, Vol. 79, No. 5, 2011, p. 485. doi:10.1119/1.3549729
[28] E. Marsch, “The Two-Component Majorana Equation-Novel Derivations and Known Symmetries,” J. Mod. Phys, Vol. 2, No. 10, 2011, pp. 1109-1114. doi:10.4236/jmp.2011.210137
[29] S. M. Bilenky and S. T. Petcov, “Massive Neutrinos and Neutrino Oscillations,” Reviews of Modern Physics, Vol. 59, No. 3, 1987, pp. 671-754. doi:10.1103/RevModPhys.59.671
[30] Ch. W. Kim and A. Pevsner, “Neutrinos in Physics and Astrophysics,” Harwood Academic Publishers, Basel, 1993.
[31] S. S. Gershtein, E. P. Kuznetsov and V. A. Ryabov, “Reformulation of the Majorana Theory of Neutrino,” Physics-Uspekhi, Vol. 40, No. 8, 1997, p. 773. doi:10.1070/PU1997v040n08ABEH000272
[32] E. K. Akhmedov, V. A. Rubakov and A. Yu. Smirnov, “Baryogenesis via Neutrino Oscillations,” Physical Re- view Letters, Vol. 81, No. 7, 1998, pp. 1359-1362. doi:10.1103/PhysRevLett.81.1359
[33] R. R. Volkas, “Neutrinos in Cosmology, with Some Sig- nificant Digressions,” Particle Physics and Cosmology: Third Tropical Workshop on Particle Physics and Cosmology—Neutrinos, Branes, and Cosmology, San Juan, 19-23 August 2002, pp. 220-239. doi:10.1063/1.1543502
[34] A. D. Dolgov, “CP Violation in Cosmology,”
[35] Y. F. Pérez and C. J. Quimbay, “Temporal Dispersion Effects of Majorana’s Wave Packets for Neutrino Oscilla- tions in Vacuum,” Reprinted in Preparation.

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