Abstract
If a sterile neutrino ν s with an eV-scale mass and a sizeable mixing to the electron neutrino exists, as indicated by the reactor and gallium neutrino anomalies, a strong resonance enhancement of ν e -ν s oscillations of atmospheric neutrinos should occur in the TeV energy range. At these energies neutrino flavour transitions in the 3+1 scheme depend on just one neutrino mass squared difference and are fully described within a 3-flavour oscillation framework. We demonstrate that the flavour transitions of atmospheric ν e can actually be very accurately described in a 2-flavour framework, with neutrino flavour evolution governed by an inhomogeneous Schrödinger-like equation. Evolution equations of this type have not been previously considered in the theory of neutrino oscillations.
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References
LSND collaboration, C. Athanassopoulos et al., Candidate events in a search for \( {\overline{\nu}}_{\mu}\to {\overline{\nu}}_e \) oscillations, Phys. Rev. Lett. 75 (1995) 2650 [nucl-ex/9504002] [INSPIRE].
LSND collaboration, A.A. Aguilar-Arevalo et al., Evidence for neutrino oscillations from the observation of \( {\overline{\nu}}_e \) appearance in a \( {\overline{\nu}}_{\mu } \) beam, Phys. Rev. D 64 (2001) 112007 [hep-ex/0104049] [INSPIRE].
MiniBooNE collaboration, A.A. Aguilar-Arevalo et al., Improved Search for \( {\overline{\nu}}_{\mu}\to {\overline{\nu}}_e \) Oscillations in the MiniBooNE Experiment, Phys. Rev. Lett. 110 (2013) 161801 [arXiv:1207.4809] [arXiv:1303.2588] [INSPIRE].
G. Mention et al., The Reactor Antineutrino Anomaly, Phys. Rev. D 83 (2011) 073006 [arXiv:1101.2755] [INSPIRE].
T.A. Mueller et al., Improved Predictions of Reactor Antineutrino Spectra, Phys. Rev. C 83 (2011) 054615 [arXiv:1101.2663] [INSPIRE].
P. Huber, On the determination of anti-neutrino spectra from nuclear reactors, Phys. Rev. C 84 (2011) 024617 [Erratum ibid. C 85 (2012) 029901] [arXiv:1106.0687] [INSPIRE].
J.N. Abdurashitov et al., Measurement of the response of a Ga solar neutrino experiment to neutrinos from an 37 Ar source, Phys. Rev. C 73 (2006) 045805 [nucl-ex/0512041] [INSPIRE].
M. Laveder, Unbound neutrino roadmaps, Nucl. Phys. Proc. Suppl. 168 (2007) 344 [INSPIRE].
C. Giunti and M. Laveder, Short-Baseline Active-Sterile Neutrino Oscillations?, Mod. Phys. Lett. A 22 (2007) 2499 [hep-ph/0610352] [INSPIRE].
M.A. Acero, C. Giunti and M. Laveder, Limits on ν e and \( {\overline{\nu}}_e \) disappearance from Gallium and reactor experiments, Phys. Rev. D 78 (2008) 073009 [arXiv:0711.4222] [INSPIRE].
F. Kaether, W. Hampel, G. Heusser, J. Kiko and T. Kirsten, Reanalysis of the GALLEX solar neutrino flux and source experiments, Phys. Lett. B 685 (2010) 47 [arXiv:1001.2731] [INSPIRE].
C. Giunti, M. Laveder, Y.F. Li, Q.Y. Liu and H.W. Long, Update of Short-Baseline Electron Neutrino and Antineutrino Disappearance, Phys. Rev. D 86 (2012) 113014 [arXiv:1210.5715] [INSPIRE].
K.N. Abazajian et al., Light Sterile Neutrinos: A White Paper, arXiv:1204.5379 [INSPIRE].
A. Palazzo, Phenomenology of light sterile neutrinos: a brief review, Mod. Phys. Lett. A 28 (2013) 1330004 [arXiv:1302.1102] [INSPIRE].
J. Kopp, P.A.N. Machado, M. Maltoni and T. Schwetz, Sterile Neutrino Oscillations: The Global Picture, JHEP 05 (2013) 050 [arXiv:1303.3011] [INSPIRE].
S. Gariazzo, C. Giunti, M. Laveder, Y.F. Li and E.M. Zavanin, Light sterile neutrinos, J. Phys. G 43 (2016) 033001 [arXiv:1507.08204] [INSPIRE].
C. Giunti, Light Sterile Neutrinos: Status and Perspectives, Nucl. Phys. B 908 (2016) 336 [arXiv:1512.04758] [INSPIRE].
E. Akhmedov, P. Lipari and M. Lusignoli, Matter effects in atmospheric neutrino oscillations, Phys. Lett. B 300 (1993) 128 [hep-ph/9211320] [INSPIRE].
R. Foot, R.R. Volkas and O. Yasuda, Up-down atmospheric neutrino flux asymmetry predictions for various neutrino oscillation scenarios, Phys. Lett. B 421 (1998) 245 [hep-ph/9710403] [INSPIRE].
F. Vissani and A.Y. Smirnov, Neutral to charged current events ratio in atmospheric neutrinos and neutrino oscillations, Phys. Lett. B 432 (1998) 376 [hep-ph/9710565] [INSPIRE].
Q.Y. Liu and A.Y. Smirnov, Neutrino mass spectrum with ν μ → ν s oscillations of atmospheric neutrinos, Nucl. Phys. B 524 (1998) 505 [hep-ph/9712493] [INSPIRE].
R. Foot, R.R. Volkas and O. Yasuda, Comparing and contrasting the ν μ → ν τ and ν μ → ν s solutions to the atmospheric neutrino problem with Super-Kamiokande data, Phys. Rev. D 58 (1998) 013006 [hep-ph/9801431] [INSPIRE].
Q.Y. Liu, S.P. Mikheyev and A.Y. Smirnov, Parametric resonance in oscillations of atmospheric neutrinos?, Phys. Lett. B 440 (1998) 319 [hep-ph/9803415] [INSPIRE].
P. Lipari and M. Lusignoli, Comparison of ν μ ↔ ν τ and ν μ ↔ ν s oscillations as solutions of the atmospheric neutrino problem, Phys. Rev. D 58 (1998) 073005 [hep-ph/9803440] [INSPIRE].
J.G. Learned, S. Pakvasa and J.L. Stone, Up-down asymmetry of neutral current events as a diagnostic for ν μ − ν st versus ν μ − ν τ oscillations, Phys. Lett. B 435 (1998) 131 [hep-ph/9805343] [INSPIRE].
V.D. Barger, S. Pakvasa, T.J. Weiler and K. Whisnant, Variations on four neutrino oscillations, Phys. Rev. D 58 (1998) 093016 [hep-ph/9806328] [INSPIRE].
M.C. Gonzalez-Garcia, H. Nunokawa, O.L.G. Peres and J.W.F. Valle, Active-active and active-sterile neutrino oscillation solutions to the atmospheric neutrino anomaly, Nucl. Phys. B 543 (1999) 3 [hep-ph/9807305] [INSPIRE].
D. Dooling, C. Giunti, K. Kang and C.W. Kim, Matter effects in four neutrino mixing, Phys. Rev. D 61 (2000) 073011 [hep-ph/9908513] [INSPIRE].
Super-Kamiokande collaboration, S. Fukuda et al., Tau neutrinos favored over sterile neutrinos in atmospheric muon-neutrino oscillations, Phys. Rev. Lett. 85 (2000) 3999 [hep-ex/0009001] [INSPIRE].
G.L. Fogli, E. Lisi and A. Marrone, Four neutrino oscillation solutions of the atmospheric neutrino anomaly, Phys. Rev. D 63 (2001) 053008 [hep-ph/0009299] [INSPIRE].
O.L.G. Peres and A.Y. Smirnov, (3 + 1) spectrum of neutrino masses: A Chance for LSND?, Nucl. Phys. B 599 (2001) 3 [hep-ph/0011054] [INSPIRE].
M.C. Gonzalez-Garcia, M. Maltoni and C. Pena-Garay, Solar and atmospheric four neutrino oscillations, Phys. Rev. D 64 (2001) 093001 [hep-ph/0105269] [INSPIRE].
MACRO collaboration, M. Ambrosio et al., Matter effects in upward going muons and sterile neutrino oscillations, Phys. Lett. B 517 (2001) 59 [hep-ex/0106049] [INSPIRE].
H. Nunokawa, O.L.G. Peres and R. Zukanovich Funchal, Probing the LSND mass scale and four neutrino scenarios with a neutrino telescope, Phys. Lett. B 562 (2003) 279 [hep-ph/0302039] [INSPIRE].
M. Maltoni and T. Schwetz, Sterile neutrino oscillations after first MiniBooNE results, Phys. Rev. D 76 (2007) 093005 [arXiv:0705.0107] [INSPIRE].
S. Choubey, Signature of sterile species in atmospheric neutrino data at neutrino telescopes, JHEP 12 (2007) 014 [arXiv:0709.1937] [INSPIRE].
G. Karagiorgi, Z. Djurcic, J.M. Conrad, M.H. Shaevitz and M. Sorel, Viability of Δm 2 ∼ 1 eV 2 sterile neutrino mixing models in light of MiniBooNE electron neutrino and antineutrino data from the Booster and NuMI beamlines, Phys. Rev. D 80 (2009) 073001 [Erratum ibid. D 81 (2010) 039902] [arXiv:0906.1997] [INSPIRE].
S. Razzaque and A.Y. Smirnov, Searching for sterile neutrinos in ice, JHEP 07 (2011) 084 [arXiv:1104.1390] [INSPIRE].
R. Gandhi and P. Ghoshal, Atmospheric neutrinos as a probe of eV 2 -scale active-sterile oscillations, Phys. Rev. D 86 (2012) 037301 [arXiv:1108.4360] [INSPIRE].
S. Razzaque and A.Y. Smirnov, Searches for sterile neutrinos with IceCube DeepCore, Phys. Rev. D 85 (2012) 093010 [arXiv:1203.5406] [INSPIRE].
A. Esmaili, F. Halzen and O.L.G. Peres, Constraining Sterile Neutrinos with AMANDA and IceCube Atmospheric Neutrino Data, JCAP 11 (2012) 041 [arXiv:1206.6903] [INSPIRE].
A. Esmaili, F. Halzen and O.L.G. Peres, Exploring ν τ − ν s mixing with cascade events in DeepCore, JCAP 07 (2013) 048 [arXiv:1303.3294] [INSPIRE].
A. Esmaili and A.Y. Smirnov, Restricting the LSND and MiniBooNE sterile neutrinos with the IceCube atmospheric neutrino data, JHEP 12 (2013) 014 [arXiv:1307.6824] [INSPIRE].
M. Lindner, W. Rodejohann and X.-J. Xu, Sterile neutrinos in the light of IceCube, JHEP 01 (2016) 124 [arXiv:1510.00666] [INSPIRE].
IceCube collaboration, M.G. Aartsen et al., Searches for Sterile Neutrinos with the IceCube Detector, arXiv:1605.01990 [INSPIRE].
S.P. Behera, A. Ghosh, S. Choubey, V.M. Datar, D.K. Mishra and A.K. Mohanty, Search for the sterile neutrino mixing with the ICAL detector at INO, arXiv:1605.08607 [INSPIRE].
E.K. Akhmedov, Parametric resonance of neutrino oscillations and passage of solar and atmospheric neutrinos through the earth, Nucl. Phys. B 538 (1999) 25 [hep-ph/9805272] [INSPIRE].
E.K. Akhmedov, M. Maltoni and A.Y. Smirnov, 1-3 leptonic mixing and the neutrino oscillograms of the Earth, JHEP 05 (2007) 077 [hep-ph/0612285] [INSPIRE].
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Akhmedov, E. Atmospheric neutrinos, ν e-ν s oscillations and a novel neutrino evolution equation. J. High Energ. Phys. 2016, 153 (2016). https://doi.org/10.1007/JHEP08(2016)153
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DOI: https://doi.org/10.1007/JHEP08(2016)153