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Exact Formulas and Simple CP dependence of Neutrino Oscillation Probabilities in Matter with Constant Density

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arxiv hep-ph/0205295 v4 pith:MWY3NK2Z submitted 2002-05-26 hep-ph

classification hep-ph
keywords deltaprobabilitymatterexactformidentityneutrinochannel
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We investigate neutrino oscillations in constant matter within the context of the standard three neutrino scenario. We derive an exact and simple formula for the oscillation probability applicable to all channels. In the standard parametrization, the probability for $\nu_e$ $\to$ $\nu_{\mu}$ transition can be written in the form $P(\nu_e \to \nu_{\mu})=A_{e\mu}\cos\delta+B_{e\mu}\sin\delta+C_{e\mu}$ without any approximation using CP phase $\delta$. For $\nu_{\mu}$ $\to$ $\nu_{\tau}$ transition, the linear term of $\cos 2\delta$ is added and the probability can be written in the form $P(\nu_{\mu} \to \nu_{\tau})=A_{\mu\tau}\cos\delta+B_{\mu\tau} \sin\delta+C_{\mu\tau}+D_{\mu\tau}\cos 2\delta$. We give the CP dependences of the probability for other channels. We show that the probability for each channel in matter has the same form with respect to $\delta$ as in vacuum. It means that matter effects just modify the coefficients $A$, $B$, $C$ and $D$. We also give the exact expression of the coefficients for each channel. Furthermore, we show that our results with respect to CP dependences are reproduced from the effective mixing angles and the effective CP phase calculated by Zaglauer and Schwarzer. Through the calculation, a new identity is obtained by dividing the Naumov-Harrison-Scott identity by the Toshev identity.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Analytic formulae for T violation in neutrino oscillations

    hep-ph 2025-02 conditional novelty 6.0 of 10

    Analytic expressions for T violation are derived for standard neutrino oscillations, nonstandard interactions, and unitarity violation, with different energy dependences that could distinguish new physics.

  2. Impact of matter effects on the unitarity test of lepton mixing

    hep-ph 2026-05 unverdicted novelty 5.0 of 10

    The authors examine extraction of lepton mixing matrix elements from spectral data in neutrino oscillation experiments including matter effects and test unitarity via a vanishing quantity in a four-generation model.

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