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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)
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:
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. https://doi.org/10.1007/JHEP06(2016)051.
Denton, Peter B., Minakata, Hisakazu, & Parke, Stephen J. Compact perturbative expressions for neutrino oscillations in matter. United States. https://doi.org/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. https://doi.org/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 = {2016},
month = {6}
}

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    Analytical solutions to renormalization-group equations of effective neutrino masses and mixing parameters in matter
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    • Denton, Peter B.; Parke, Stephen J.
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    • DOI: 10.1007/jhep11(2018)063

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    Sensitivities and synergies of DUNE and T2HK
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    Rotations versus perturbative expansions for calculating neutrino oscillation probabilities in matter
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    Sub-GeV Atmospheric Neutrinos and C P Violation in DUNE
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    Decoherence in neutrino propagation through matter, and bounds from IceCube/DeepCore
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