Abstract
Neutrino oscillations in matter can exhibit a specific resonance enhancement — parametric resonance, which is different from the MSW resonance. Oscillations of atmospheric and solar neutrinos inside the earth can undergo parametric enhancement when neutrino trajectories cross the core of the earth. In this paper we review the parametric resonance of neutrino oscillations in matter. In particular, physical interpretation of the effect and the prospects of its experimental observation in oscillations of solar and atmospheric neutrinos in the earth are discussed.
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References
S P Mikheyev and A Yu Smirnov, Sov. J. Nucl. Phys. 42, 913 (1985)
L Wolfenstein, Phys. Rev. D17, 2369 (1978)
V K Ermilova, V A Tsarev, V A Chechin and Kr Soob, Fiz. Short Notices of the Lebedev Institute 5, 26 (1986)
E Kh Akhmedov, preprint IAE-4470/1 (1987); Yad. Fiz. 47, 475 (1988); Sov. J. Nucl. Phys. 47, 301 (1988)
Proceedings of the NATO Advanced Study Research Workshop Statistical Process in Physics and Biology, J. Stat. Phys. 70, N 1/2 (1993)
P I Krastev and A Yu Smirnov, Phys. Lett. B226, 341 (1989)
Q Y Liu and A Yu Smirnov, Nucl. Phys. B524, 505 (1998)
Q Y Liu, S P Mikheyev and A Yu Smirnov, Phys. Lett. B440, 319 (1998)
S T Petcov, Phys. Lett. B434, 321 (1998) (hep-ph/9805262)
In [9] a different name for this phenomenon was suggested — neutrino oscillation length resonance. We prefer to follow the original terminology of [3,4]
E Kh Akhmedov, Nucl. Phys. B538, 25 (1999) (hep-ph/9805272)
E Kh Akhmedov, A Dighe, P Lipari and A Yu Smirnov, Nucl. Phys. B542, 3 (1999) (hep-ph/9808270)
M Chizhov, M Maris and S T Petcov, hep-ph/9810501
E Kh Akhmedov, hep-ph/9903302
In refs [3,4,6] these conditions were derived for the particular case =, which, however, includes the most important principal resonance with = = 0.
For a geometric interpretation of the parametric resonance in terms of the spin precession in magnetic field, see [8, 17, 18]. The analogy with a pendulum with vertically oscillating point of support was discussed in [11]
A Yu Smirnov, Talk given at the 18th International Conference on Neutrino Physics and Astrophysics, Neutrino 98, Takayama, Japan, June 4–9, 1998, hep-ph/9809481
A Yu Smirnov, Talk given at the Symposium New Era in Neutrino Physics, Tokyo, Japan, June 11–12 1998, hep-ph/9811296
S P Mikheyev and A Yu Smirnov, in 1987 New and Exotic Phenomena, proceedings of the 7th Moriond Workshop edited by O Fackler and J Trân Thanh Vân (Editions Frontières, Gif-sur-Yvette, 1987) p. 405
A J Baltz and J Weneser, Phys. Rev. D35 528 (1987)
J N Bahcall, P I Krastev and A Yu Smirnov, Phys. Rev. D58, 096016 (1998)
F D Stacey, Physics of the Earth (John Wiley and Sons, New York, 1969)
For the parametric resonance to be a maximum of the transition probability, an additional condition has to be satisfied (two conditions in the case of v 2 ↔ v e oscillations[9]). For the oscillations between neutrinos of different flavor, this condition can be written as cos(2θ c 4θ m ) 0. For small vacuum mixing angles θ 0 it essentially reduces to δ V c , with a small region around δ = V m excluded
The parametric enhancement of neutrino oscillations in the earth for neutrinos that travel significant distances in the earth’s core was found numerically in a number of earlier papers [25]. However, in these papers the parametric nature of the effect has not been recognized
S P Mikheyev and A Yu Smirnov, in 1986 Massive Neutrinos in Astrophysics and in Particle Physics, Proceedings of the 6th Moriond Workshop edited by O Fackler and J Trân Thanh Vân (Editions Frontières, Gif-sur-Yvette, 1986) p. 355
E D Carlson, Phys. Rev. D34, 1454 (1986)
A J Baltz and J Weneser, ref. [20]
M Cribier, W Hampel, J Rich, and D Vignaud, Phys. Lett. B182, 89 (1986)
A Dar, A Mann, Y Melina and D Zajfman, Phys. Rev. D35, 3607 (1987)
G Auriemma, M Felcini, P Lipari and J L Stone, Phys. Rev. D37, 665 (1988)
A Nicolaidis, Phys. Lett. B200, 553 (1988)
J M LoSecco, Phys. Rev. D47, 2032 (1993)
J M Gelb, W-K Kwong and S P Rosen, Ref. [26]
Q Y Liu, M Maris and S T Petcov, Phys. Rev. D56, 5991 (1997)
M Maris and S T Petcov, Phys. Rev. D56, 7444 (1997)
M Maris and S T Petcov, Phys. Rev. D58, 113008 (1998)
J M Gelb, W-K Kwong and S P Rosen, Phys. Rev. Lett. 78, 2296 (1997)
P Lipari and M Lusignoli, Phys. Rev. D58, 073005 (1998)
In general, the parametric enhancement can take place even for ‘wrong sign’ δm 2, but in the case of neutrino oscillations in the earth these effects are small
E Kh Akhmedov, P Lipari, M Lusignoli and A Yu Smirnov, in progress
Super-Kamiokande Collaboration: Y Fukuda et al., Phys. Rev. Lett. 82, 1810 (1999)
K Inoue, talk given at the VIII International Workshop Neutrino Telescopes, Venice, Italy, February 23–26, 1999
J N Bahcall and P I Krastev, Phys. Rev. C56, 2839 (1997)
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On leave from National Research Centre, Kurchatov Institute, Moscow 123182, Russia
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Akhmedov, E.K. Parametric resonance in neutrino oscillations in matter. Pramana - J Phys 54, 47–63 (2000). https://doi.org/10.1007/s12043-000-0006-4
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DOI: https://doi.org/10.1007/s12043-000-0006-4