Abstract
We reformulate perturbation theory for neutrino oscillations in matter with an expansion parameter related to the ratio of the solar to the atmospheric Δm 2 scales. Unlike previous works, we use a renormalized basis in which certain first-order effects are taken into account in the zeroth-order Hamiltonian. We show that the new framework has an exceptional feature that leads to the neutrino oscillation probability in matter with the same structure as in vacuum to first order in the expansion parameter. It facilitates immediate physical interpretation of the formulas, and makes the expressions for the neutrino oscillation probabilities extremely simple and compact. We find, for example, that the ν e disappearance probability at this order is of a simple two-flavor form with an appropriately identified mixing angle and Δm 2. More generally, all the oscillation probabilities can be written in the universal form with the channel-discrimination coefficient of 0, ± 1 or simple functions of θ 23. Despite their simple forms they include all order effects of θ 13 and all order effects of the matter potential, to first order in our expansion parameter.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
L. Wolfenstein, Neutrino oscillations in matter, Phys. Rev. D 17 (1978) 2369 [INSPIRE].
V.D. Barger, K. Whisnant, S. Pakvasa and R.J.N. Phillips, Matter effects on three-neutrino oscillations, Phys. Rev. D 22 (1980) 2718 [INSPIRE].
H.W. Zaglauer and K.H. Schwarzer, The mixing angles in matter for three generations of neutrinos and the MSW mechanism, Z. Phys. C 40 (1988) 273 [INSPIRE].
K. Kimura, A. Takamura and H. Yokomakura, Exact formulas and simple CP dependence of neutrino oscillation probabilities in matter with constant density, Phys. Rev. D 66 (2002) 073005 [hep-ph/0205295] [INSPIRE].
M. Blennow and A. Yu. Smirnov, Neutrino propagation in matter, Adv. High Energy Phys. 2013 (2013) 972485 [arXiv:1306.2903] [INSPIRE].
J. Arafune, M. Koike and J. Sato, CP violation and matter effect in long baseline neutrino oscillation experiments, Phys. Rev. D 56 (1997) 3093 [Erratum ibid. D 60 (1999) 119905] [hep-ph/9703351] [INSPIRE].
A. Cervera et al., Golden measurements at a neutrino factory, Nucl. Phys. B 579 (2000) 17 [Erratum ibid. B 593 (2001) 731] [hep-ph/0002108] [INSPIRE].
J. Arafune and J. Sato, CP and T violation test in neutrino oscillation, Phys. Rev. D 55 (1997) 1653 [hep-ph/9607437] [INSPIRE].
M. Freund, Analytic approximations for three neutrino oscillation parameters and probabilities in matter, Phys. Rev. D 64 (2001) 053003 [hep-ph/0103300] [INSPIRE].
E.K. Akhmedov, R. Johansson, M. Lindner, T. Ohlsson and T. Schwetz, Series expansions for three flavor neutrino oscillation probabilities in matter, JHEP 04 (2004) 078 [hep-ph/0402175] [INSPIRE].
S.P. Mikheev and A. Yu. Smirnov, Resonance amplification of oscillations in matter and spectroscopy of solar neutrinos, Sov. J. Nucl. Phys. 42 (1985) 913 [Yad. Fiz. 42 (1985) 1441] [INSPIRE].
H. Nunokawa, S.J. Parke and R. Zukanovich Funchal, Another possible way to determine the neutrino mass hierarchy, Phys. Rev. D 72 (2005) 013009 [hep-ph/0503283] [INSPIRE].
Daya Bay collaboration, F.P. An et al., Spectral measurement of electron antineutrino oscillation amplitude and frequency at Daya Bay, Phys. Rev. Lett. 112 (2014) 061801 [arXiv:1310.6732] [INSPIRE].
Daya Bay collaboration, F.P. An et al., New measurement of antineutrino oscillation with the full detector configuration at Daya Bay, Phys. Rev. Lett. 115 (2015) 111802 [arXiv:1505.03456] [INSPIRE].
RENO collaboration, J.H. Choi et al., Observation of energy and baseline dependent reactor antineutrino disappearance in the RENO experiment, arXiv:1511.05849 [INSPIRE].
C. Jarlskog, Commutator of the quark mass matrices in the standard electroweak model and a measure of maximal CP-violation, Phys. Rev. Lett. 55 (1985) 1039 [INSPIRE].
V.A. Naumov, Three neutrino oscillations in matter, CP-violation and topological phases, Int. J. Mod. Phys. D 1 (1992) 379 [INSPIRE].
P.F. Harrison and W.G. Scott, CP and T violation in neutrino oscillations and invariance of Jarlskog’s determinant to matter effects, Phys. Lett. B 476 (2000) 349 [hep-ph/9912435] [INSPIRE].
K. Asano and H. Minakata, Large-θ 13 perturbation theory of neutrino oscillation for long-baseline experiments, JHEP 06 (2011) 022 [arXiv:1103.4387] [INSPIRE].
H. Minakata and H. Nunokawa, CP violation versus matter effect in long baseline neutrino oscillation experiments, Phys. Rev. D 57 (1998) 4403 [hep-ph/9705208] [INSPIRE].
S.K. Agarwalla, Y. Kao and T. Takeuchi, Analytical approximation of the neutrino oscillation matter effects at large θ 13, JHEP 04 (2014) 047 [arXiv:1302.6773] [INSPIRE].
T.-K. Kuo and J.T. Pantaleone, Neutrino oscillations in matter, Rev. Mod. Phys. 61 (1989) 937 [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1505.01826
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Minakata, H., Parke, S.J. Simple and compact expressions for neutrino oscillation probabilities in matter. J. High Energ. Phys. 2016, 180 (2016). https://doi.org/10.1007/JHEP01(2016)180
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2016)180