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Title: Compact perturbative expressions for neutrino oscillations in matter

Abstract

We further develop and extend a recent perturbative framework for neutrino oscillations in uniform matter density so that the resulting oscillation probabilities are accurate for the complete matter potential versus baseline divided by neutrino energy plane. This extension also gives the exact oscillation probabilities in vacuum for all values of baseline divided by neutrino energy. The expansion parameter used is related to the ratio of the solar to the atmospheric $$\Delta m^2$$ scales but with a unique choice of the atmospheric $$\Delta m^2$$ such that certain first-order effects are taken into account in the zeroth-order Hamiltonian. Using a mixing matrix formulation, this framework has the exceptional feature that the neutrino oscillation probability in matter has the same structure as in vacuum, to all orders in the expansion parameter. It also contains all orders in the matter potential and $$\sin\theta_{13}$$. It facilitates immediate physical interpretation of the analytic results, and makes the expressions for the neutrino oscillation probabilities extremely compact and very accurate even at zeroth order in our perturbative expansion. Furthermore, the first and second order results are also given which improve the precision by approximately two or more orders of magnitude per perturbative order.

Authors:
ORCiD logo [1];  [2]; ORCiD logo [3]
  1. Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States); Vanderbilt Univ., Nashville, TN (United States)
  2. Univ. de Sao Paulo, Sao Paulo (Brazil); Yachay Tech Univ., San Miguel de Urcuqui (Ecuador)
  3. Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
Publication Date:
Research Org.:
Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
OSTI Identifier:
1256704
Report Number(s):
FERMILAB-PUB-16-126-T; YACHAY-PUB-16-01-PN; arXiv:1604.08167
Journal ID: ISSN 1029-8479; 1452689
Grant/Contract Number:
AC02-07CH11359
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 6; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CP violation; neutrino physics

Citation Formats

Denton, Peter B., Minakata, Hisakazu, and Parke, Stephen J.. Compact perturbative expressions for neutrino oscillations in matter. United States: N. p., 2016. Web. doi:10.1007/JHEP06(2016)051.
Denton, Peter B., Minakata, Hisakazu, & Parke, Stephen J.. Compact perturbative expressions for neutrino oscillations in matter. United States. doi:10.1007/JHEP06(2016)051.
Denton, Peter B., Minakata, Hisakazu, and Parke, Stephen J.. Wed . "Compact perturbative expressions for neutrino oscillations in matter". United States. doi:10.1007/JHEP06(2016)051. https://www.osti.gov/servlets/purl/1256704.
@article{osti_1256704,
title = {Compact perturbative expressions for neutrino oscillations in matter},
author = {Denton, Peter B. and Minakata, Hisakazu and Parke, Stephen J.},
abstractNote = {We further develop and extend a recent perturbative framework for neutrino oscillations in uniform matter density so that the resulting oscillation probabilities are accurate for the complete matter potential versus baseline divided by neutrino energy plane. This extension also gives the exact oscillation probabilities in vacuum for all values of baseline divided by neutrino energy. The expansion parameter used is related to the ratio of the solar to the atmospheric $\Delta m^2$ scales but with a unique choice of the atmospheric $\Delta m^2$ such that certain first-order effects are taken into account in the zeroth-order Hamiltonian. Using a mixing matrix formulation, this framework has the exceptional feature that the neutrino oscillation probability in matter has the same structure as in vacuum, to all orders in the expansion parameter. It also contains all orders in the matter potential and $\sin\theta_{13}$. It facilitates immediate physical interpretation of the analytic results, and makes the expressions for the neutrino oscillation probabilities extremely compact and very accurate even at zeroth order in our perturbative expansion. Furthermore, the first and second order results are also given which improve the precision by approximately two or more orders of magnitude per perturbative order.},
doi = {10.1007/JHEP06(2016)051},
journal = {Journal of High Energy Physics (Online)},
number = 6,
volume = 2016,
place = {United States},
year = {Wed Jun 08 00:00:00 EDT 2016},
month = {Wed Jun 08 00:00:00 EDT 2016}
}

Journal Article:
Free Publicly Available Full Text
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Cited by: 3works
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  • In this paper we rewrite the neutrino mixing angles and mass squared differences in matter given, in our original paper, in a notation that is more conventional for the reader. Replacing the usual neutrino mixing angles and mass squared differences in the expressions for the vacuum oscillation probabilities with these matter mixing angles and mass squared differences gives an excellent approximation to the oscillation probabilities in matter. Comparisons for T2K, NOvA, T2HKK and DUNE are also given for neutrinos and anti-neutrinos, disappearance and appearance channels, normal ordering and inverted ordering.
  • 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, use a renormalized basis in which certain first-order effects are taken into account in the zeroth-order Hamiltonian. Using this perturbation theory we derive extremely compact expressions for the neutrino oscillations probabilities in matter. 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. Furthermore, despite exceptional simplicity in their forms they accommodatemore » all order effects θ 13 and the matter potential.« less
  • We derive an analytical description of neutrino oscillations in matter based on the Magnus exponential representation of the time evolution operator. Our approach is valid in a wide range of the neutrino energies and properly accounts for the modifications that the respective probability transitions suffer when neutrinos originated in different sources traverse the Earth. The present approximation considerably improves over other perturbative treatments existing in the current literature. Furthermore, the analytical expressions derived inside the Magnus framework are remarkably simple, which facilitates their practical use. When applied to the calculation of the day-night asymmetry in the solar neutrino flux ourmore » result reproduces the numerical calculation with an accuracy better than 1% for the first-order approximation. When the approximation is extended to the second order, the accuracy of the method is further improved by almost 1 order of magnitude, and it is still better than 5% even for neutrino energies as large as 100 MeV. In the GeV regime characteristic of atmospheric and accelerator neutrinos this accuracy is complemented by a good reproduction of the position of the maxima in the flavor transition probabilities.« less
  • The effects of perturbative Lorentz and CPT violation on neutrino oscillations are studied. Features include neutrino-antineutrino oscillations, direction dependence, and unconventional energy behavior. Leading-order corrections arising from renormalizable operators are derived in the general three-flavor effective field theory. The results are applied to neutrino-beam experiments with long baselines, which offer excellent sensitivity to the accompanying effects. Key signatures of Lorentz and CPT violation using neutrino beams include sidereal variations in the oscillation probabilities arising from the breakdown of rotational symmetry, and CPT asymmetries comparing neutrino and antineutrino modes. Attainable sensitivities to coefficients for Lorentz violation are estimated for several existingmore » and future experiments.« less
  • Proceeding in analogy to the Mikheyev-Smirnov enhancement of matter effects on neutrino oscillations the authors consider the limit wherein the effects of the medium on K/sup 0/ - K-bar/sup 0/ oscillations are maximized. In this limit it is found that the ratio of the strangeness-oscillation probability in matter to that in vacuum cannot exceed unity.