Effects of a neutrino-dark energy coupling on oscillations of high-energy neutrinos

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Effects of a neutrino-dark energy coupling on oscillations of high-energy neutrinos

Niki Klop and Shin’ichiro Ando

Phys. Rev. D 97, 063006 – Published 8 March 2018

Abstract

If dark energy (DE) is a dynamical field rather than a cosmological constant, an interaction between DE and the neutrino sector could exist, modifying the neutrino oscillation phenomenology and causing $C P$ and apparent Lorentz violating effects. The terms in the Hamiltonian for flavor propagation induced by the DE-neutrino coupling do not depend on the neutrino energy, while the ordinary components decrease as $Δ m^{2} / E_{ν}$ . Therefore, the DE-induced effects are absent at lower neutrino energies, but become significant at higher energies, allowing to be searched for by neutrino observatories. We explore the impact of the DE-neutrino coupling on the oscillation probability and the flavor transition in the three-flavor framework, and investigate the $C P$ -violating and apparent Lorentz violating effects. We find that DE-induced effects become observable for $E_{ν} m_{eff} \sim 10^{- 20} {GeV}^{2}$ , where $m_{eff}$ is the effective mass parameter in the DE-induced oscillation probability, and $C P$ is violated over a wide energy range. We also show that current and future experiments have the sensitivity to detect anomalous effects induced by a DE-neutrino coupling and probe the new mixing parameters. The DE-induced effects on neutrino oscillation can be distinguished from other new physics possibilities with similar effects, through the detection of the directional dependence of the interaction, which is specific to this interaction with DE. However, current experiments will not yet be able to measure the small changes of $\sim 0.03 %$ in the flavor composition due to this directional effect.

Received 8 January 2018

DOI:https://doi.org/10.1103/PhysRevD.97.063006

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Dark energy Neutrino interactions Neutrino oscillations

Gravitation, Cosmology & Astrophysics

Authors & Affiliations

Niki Klop^1,* and Shin’ichiro Ando^1,2

¹Gravitation Astroparticle Physics Amsterdam (GRAPPA), Institute for Theoretical Physics Amsterdam and Delta Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
²Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU, WPI), Todai Institutes for Advanced Study, University of Tokyo, Kashiwa, Chiba 277-8583, Japan

^*l.b.klop@uva.nl

Article Text

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Issue

Vol. 97, Iss. 6 — 15 March 2018

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Images

Figure 1
The possible ratios of $ν_{e} ∶ ν_{μ} ∶ ν_{τ}$ at Earth for different starting flavor ratios $ν_{e} ∶ ν_{μ} ∶ ν_{τ}$ at the source. The colored regions correspond to oscillation in the presence of DE-induced mixing, where we varied over all combinations of the values of the new mixing angles. The expected ratios for vacuum mixing (assuming normal hierarchy) are drawn in black. The solid grey contours show the allowed regions by IceCube at 68% and 95% confidence levels, while the grey cross represents their best-fit flavor ratio [42].
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Figure 2
The possible ratios of $ν_{e} ∶ ν_{μ} ∶ ν_{τ}$ at Earth for different proportions of $ν_{e}$ and $ν_{μ}$ at the source, and no $ν_{τ}$ at production. The magenta region corresponds to oscillation in the presence of DE-induced mixing, where all combinations of the values of the new mixing angles are varied. The cyan region corresponds to vacuum oscillation. The solid grey contours show the allowed regions by IceCube at 68% and 95% confidence levels, while the grey cross represents their best-fit flavor ratio [42].
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Figure 3
The flavor ratios as a function of neutrino energy for different sets of parameter values. The flavor composition at the source is set to $1 ∶ 2 ∶ 0$ . The effective mass parameters are set to $m_{{eff}_{21}} = \frac{1}{2} m_{{eff}_{31}} = 10^{- 26} GeV$ , and $δ_{CP} = 0$ . The values of the new mixing angles are set to (a) $θ_{12} = 0.25 π$ and $θ_{13}$ , $θ_{23} = 0$ ; (b) $θ_{13} = 0.25 π$ and $θ_{12}$ , $θ_{23} = 0$ ; (c) $θ_{23} = 0.25 π$ and $θ_{12}$ , $θ_{13} = 0$ (bottom left); and (d) $θ_{12}$ , $θ_{13}$ , $θ_{23} = 0.25 π$ (maximal mixing). The transition from the domination of vacuum oscillation to DE-induced domination takes place at $E_{ν} m_{eff} \sim 10^{- 20} {GeV}^{2}$ .
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Figure 4
The flavor ratios as a function of neutrino energy for different values of $δ_{DE}$ , for both neutrinos and antineutrinos. The values of the new mixing parameters are set to $θ_{12}$ , $θ_{13}$ , $θ_{23} = 0.25 π$ , $m_{{eff}_{21}} = \frac{1}{2} m_{{eff}_{31}} = 10^{- 26} GeV$ and the starting flavor ratio is set to $1 ∶ 2 ∶ 0$ . The usual $C P$ -violating phase $δ_{DE}$ is set to zero. The new DE-induced $C P$ -violating phase is set to (a) $0.25 π$ , (b) $0.5 π$ , and (c) 0. The effect in (c) comes solely from the sign difference of $m_{eff}$ in the oscillation probability for neutrinos and antineutrinos.
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Figure 5
The sensitivity for neutrino experiments capable of distinguishing muon neutrinos to probe for the value of $m_{eff}$ , in case of a detection of 100, 1000 and 10 000 events, for different neutrino energy ranges: (a) 0.1–100 PeV and (b) 0.1–100 EeV. When the genuine values of the parameters $m_{eff}$ and $θ_{12}$ lie above the colored lines, more $ν_{μ}$ than compatible with standard physics will be detected. In this example, the new mixing angles are set to $θ_{13}$ , $θ_{23} = 0$ . The flavor composition at the source is set to $1 ∶ 2 ∶ 0$ .
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Figure 6
The effect of the directional dependence on the flavor composition as a function of incoming azimuthal angle (a, c), polar angle (d) and the angle corresponding to the seasonal position of Earth (b). The DE-induced parameters are set to $θ_{12}$ , $θ_{13}$ , $θ_{23} = 0.25 π$ and $m_{{eff}_{21}} = \frac{1}{2} m_{{eff}_{31}} = 10^{- 26} GeV$ , and the flavor composition at the source is set to $1 ∶ 2 ∶ 0$ . The results are shown for a neutrino energy of $E_{ν} = 10^{5} GeV$ , which lies inside the transition range from vacuum domination towards DE-induced domination. For energies outside the transition phase, the effect is an order of magnitude smaller.
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