Neutrino oscillations in low density medium

Abstract

For the case of small matter effects: $V\ll \Delta m^2/2E$, where $V$ is the matter potential, we develop the perturbation theory using $\epsilon \equiv 2VE/\Delta m^2$ as the expansion parameter. We derive simple and physically transparent formulas for the oscillation probabilities in the lowest order in $\epsilon$ which are valid for arbitrary density profile. The formulas can be applied for propagation of the solar and supernova neutrinos in matter of the Earth, substantially simplifying numerical calculations. Using these formulas we study sensitivity of the oscillation effects to structures of the density profile situated at different distances from the detector $d$. We show that for the mass-to-flavor state transitions, {\it e.g.}, ${\nu }_2\to {\nu }_e$, the sensitivity is suppressed for remote structures: $d>l_{\nu }E/\Delta E$, where $l_{\nu }$ is the oscillation length and $\Delta E/E$ is the energy resolution of detector.

discussion simplified, clarifications added

References in corpus (16)

• Identifying the neutrino mass spectrum from a supernova neutrino burst
• Getting the most from the statistical analysis of solar neutrino oscillations
• Precise Measurement of the Solar Neutrino Day/Night and Seasonal Variation in Super-Kamiokande-I
• Parametric resonance of neutrino oscillations and passage of solar and atmospheric neutrinos through the earth
• Earth regeneration effect in solar neutrino oscillations: an analytic approach
• Identifying Earth matter effects on supernova neutrinos at a single detector
• Signatures of supernova neutrino oscillations in the Earth mantle and core
• Toward precision measurements in solar neutrinos
• Does the Sun Appear Brighter at Night in Neutrinos?
• Earth effects on supernova neutrinos and their implications for neutrino parameters
• Day-night effect in solar neutrino oscillations with three flavors
• Tomography of the Earth's Core Using Supernova Neutrinos
• Zenith angle distributions at Super-Kamiokande and SNO and the solution of the solar neutrino problem
• Solar Neutrino Zenith Angle Distribution and Uncertainty in Earth Matter Density
• Earth Regeneration of Solar Neutrinos at SNO and Super-Kamiokande
• Enhancing the Seasonal Variation Effect in the Case of the Vacuum Oscillation Solution of the Solar Neutrino Problem

Cited by in corpus (41)

• Where Are We With Light Sterile Neutrinos?
• Neutrino flavour transformation in supernovae
• Solar neutrinos and neutrino physics
• Oscillation Effects and Time Variation of the Supernova Neutrino Signal
• The MSW effect and Matter Effects in Neutrino Oscillations
• Neutrino Mass and New Physics
• Neutrino tomography - Learning about the Earth's interior using the propagation of neutrinos
• A precise analytical description of the Earth matter effect on oscillations of low energy neutrinos
• Solar neutrinos and 1-3 leptonic mixing
• Three Flavor Neutrino Oscillations in Matter: Flavor Diagonal Potentials, the Adiabatic Basis and the CP phase
• Probing the absolute density of the Earth's core using a vertical neutrino beam
• Monte Carlo Neutrino Oscillations
• Solar neutrino physics
• Oscillation tomography of the Earth with solar neutrinos and future experiments
• Geotomography with solar and supernova neutrinos
• Scanning the Earth with solar neutrinos and DUNE
• Perturbative exponential expansion and matter neutrino oscillations
• Precise Formulation of Neutrino Oscillation in the Earth
• Day-Night Asymmetries in Active-Sterile Solar Neutrino Oscillations
• Describing neutrino oscillations in matter with Magnus expansion
• Locating the Core-Mantle Boundary using Oscillations of Atmospheric Neutrinos
• Oscillations of the ${}^7$Be solar neutrinos inside the Earth
• Realistic Earth matter effects and a method to acquire information about small θ_{13} in the detection of supernova neutrinos
• Fourier Analysis of the Parametric Resonance in Neutrino Oscillations
• Earth tomography with supernova neutrinos at future neutrino detectors
• Attenuation effect and neutrino oscillation tomography
• Analytical treatment of long-term observations of the day-night asymmetry for solar neutrinos
• Does the Borexino experiment have enough resolution to detect the neutrino flavor day-night asymmetry?
• An accurate analytic description of neutrino oscillations in matter
• Earth Matter Effects in Detection of Supernova Neutrinos
• Acquire information about neutrino parameters by detecting supernova neutrinos
• Detection of supernova neutrinos at spallation neutron sources
• Earthquake Forecast via Neutrino Tomography
• Detection of supernova neutrinos on the Earth for large theta13
• From ray to spray: augmenting amplitudes and taming fast oscillations in fully numerical neutrino codes
• Density profiles of supernova matter and determination of neutrino parameters
• Tomography by neutrino pair beam
• Shedding light on the $\Delta m_{21}^2$ tension with supernova neutrinos
• Neutrino oscillations: theory and phenomenology
• Resonant flavor conversion of supernova neutrinos and neutrino parameters
• An approximate solution for solar and supernova neutrino oscillation in matter