On Resonances and Mixing Angles in Three Neutrino Oscillations in Matter

Bellandi, J.; Guzzo, M. M.; Aquino, V. M.

doi:10.1590/s0103-97331997000300008

Cited by 6 publications

(3 citation statements)

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“…The Toshev [86] and Kimura, Takamura and Yokomakura [87] identities are no longer valid when V Þ 0. Other than a rearrangement of the ordering of the eigenvalues and some notational changes the expressions for tan 2 12 and sin 2 13 are the same as those one may find in Bellandi et al [88]; our expression for tan 2 23 differs from Bellandi et al because we allow the possibility of Þ 0 and do not set ¼ 0. When performing numerical calculations, the expressions (16a)-(16f) become increasingly difficult to use when the densities become large.…”

Section: The Matter Basismentioning

confidence: 91%

Three flavor neutrino oscillations in matter: Flavor diagonal potentials, the adiabatic basis, and theCPphase

Kneller

McLaughlin

2009

Phys. Rev. D

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We discuss the three neutrino flavor evolution problem with general, flavor-diagonal, matter potentials and a fully parametrized mixing matrix that includes CP violation, and derive expressions for the eigenvalues, mixing angles, and phases. We demonstrate that, in the limit that the mu and tau potentials are equal, the eigenvalues and matter mixing angles 12 and 13 are independent of the CP phase, although 23 does have CP dependence. Since we are interested in developing a framework that can be used for S matrix calculations of neutrino flavor transformation, it is useful to work in a basis that contains only offdiagonal entries in the Hamiltonian. We derive the ''nonadiabaticity'' parameters that appear in the Hamiltonian in this basis. We then introduce the neutrino S matrix, derive its evolution equation and the integral solution. We find that this new Hamiltonian, and therefore the S matrix, in the limit that the and neutrino potentials are the same, is independent of both 23 and the CP violating phase. In this limit, any CP violation in the flavor basis can only be introduced via the rotation matrices, and so effects which derive from the CP phase are then straightforward to determine. We then show explicitly that the electron neutrino and electron antineutrino survival probability is independent of the CP phase in this limit. Conversely, if the CP phase is nonzero and mu and tau matter potentials are not equal, then the electron neutrino survival probability cannot be independent of the CP phase.

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Section: The Matter Basismentioning

confidence: 91%

Three flavor neutrino oscillations in matter: Flavor diagonal potentials, the adiabatic basis, and theCPphase

Kneller

McLaughlin

2009

Phys. Rev. D

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“…Even the solution for constant density is not easily known, understandable the physical meaning. A solution is given by references [113,114] 6 uses the eigenvalues and eigenvectors of the 3 × 3 matrix that is not much illuminating. Other analytical solutions involve • a perturbative approach of full oscillation probability such as (I) small θ 13 perturbative expansion [106] (II) large θ 13 expansion [30,107].…”

Section: Perturbative Approaches and The Neutrino Time-evolutionmentioning

confidence: 99%

Improvements on perturbative oscillation formulas including non-standard neutrino interactions

Chaves

Gratieri

Peres

2020

J. Phys. G: Nucl. Part. Phys.

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We use perturbation theory to obtain neutrino oscillation probabilities, including the standard mass-mixing paradigm and non-standard neutrino interactions (NSI). The perturbation is made on the standard parameters Δ m 21 2 / Δ m 31 2 and sin2(θ 13) and on the non-diagonal NSI parameters, but keeps diagonal NSI parameters non-perturbated. We perform the calculation for the channels ν μ → ν e and ν μ → ν μ . The resulting oscillation formulas are compact and present functional structure similar to the standard oscillation (SO) case. They apply to a wide range in the allowed NSI space of parameters and include the previous results from perturbative approaches as limit cases. Also, we use the compact formulas we found to explain the origin of the degeneracies in the neutrino probabilities in terms of the invariance of amplitude and phase of oscillations. Then we determine analytically the multiple sets of combinations of SO and NSI parameters that result in oscillation probabilities identical to the SO case.

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“…A solution given by Ref. [41,42] 1 use the eigenvalues and eigenvectors of the 3 × 3 matrix that is not much illuminating. Other analytical solutions involve • a perturbative approach of full oscillation probability such as (I) Cervera's expansion [37] (II) Improved θ 13 expansion [25],…”

Section: Perturbative Approaches and The Neutrino Time-evolutionmentioning

confidence: 99%

Improvements on perturbative oscillation formulas including non-standard neutrino Interactions

Chaves,

Gratieri,

Peres

2018

Preprint

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We present perturbative oscillation probabilities for electron and muon channels including non-standard interaction (NSI) effects. The perturbation was performed in standard parameters ∆m 2 21 /∆m 2 31 and sin 2 (θ 13 ) as in non-standard interaction couplings. Our goal is to match non-standard parameters with the standard ones. This leads to oscillation probabilities with NSI compact and with functional structure similar to the Standard Oscillation (SO) case. Such formalism allows us to recognize degeneracies between standard oscillation parameters and NSI parameters. In such scenario, we also have an educated guess about the origin of the reported behavior of long-baseline experiments degeneracies, which should be due to marginalization on standard oscillation parameters δ CP , θ 23 and NSI parameters.

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On Resonances and Mixing Angles in Three Neutrino Oscillations in Matter

Cited by 6 publications

References 0 publications

Three flavor neutrino oscillations in matter: Flavor diagonal potentials, the adiabatic basis, and theCPphase

Three flavor neutrino oscillations in matter: Flavor diagonal potentials, the adiabatic basis, and theCPphase

Improvements on perturbative oscillation formulas including non-standard neutrino interactions

Improvements on perturbative oscillation formulas including non-standard neutrino Interactions

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