Neutrino mixing in matter

Chiu, Shao-Hsuan; Kuo, T. K.; Liu, Lu-Xin

doi:10.1016/j.physletb.2010.03.035

Cited by 19 publications

(30 citation statements)

References 21 publications

(9 reference statements)

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“…From Eqs. (5) and (6), one can observe that the evolution of θ 23 and δ will be suppressed by both sin θ 13 and ∆ 21 /∆ 31 , at least in the region of small A c . Therefore, θ 23 ≈ θ 23 and δ ≈ δ can serve as the zeroth-order solutions.…”

Section: θ 23 and δmentioning

confidence: 86%

“…However, if we simply substitute the analytical expressions into the RGEs of θ 23 and δ in Eqs. (5) and (6), it will be too complicated to find any analytical and useful results. For this reason, we have to make some reasonable approximations.…”

Section: θ 23 and δmentioning

confidence: 99%

“…Recently, it has been shown in Refs. [5][6][7] that the elements of the effective neutrino mixing matrix V αi (for α = e, µ, τ and i = 1, 2, 3) and the effective neutrino mass-squared differences ∆ ij ≡ m 2 i − m 2 j (for ij = 21, 31, 32) satisfy a complete set of differential equations with respect to the matter parameter a. Making an analogy with the renormalization-group equations (RGEs) and adopting the standard parametrization for the effective mixing matrix V in matter, the authors of Ref.…”

Section: Introductionmentioning

confidence: 99%

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Analytical solutions to renormalization-group equations of effective neutrino masses and mixing parameters in matter

Wang

Zhou

2019

J. High Energ. Phys.

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Neutrino oscillations in matter can be fully described by six effective parameters, namely, three neutrino mixing angles { θ 12 , θ 13 , θ 23 }, one Dirac-type CP-violating phase δ, and two neutrino mass-squared differences ∆ 21 ≡ m 2 2 − m 2 1 and ∆ 31 ≡ m 2 3 − m 2 1 . Recently, a complete set of differential equations for these effective parameters have been derived to characterize their evolution with respect to the ordinary matter term a ≡ 2 √ 2G F N e E, in analogy with the renormalization-group equations (RGEs) for running parameters. Via series expansion in terms of the small ratio α c ≡ ∆ 21 /∆ c with ∆ c ≡ ∆ 31 cos 2 θ 12 +∆ 32 sin 2 θ 12 , we obtain approximate analytical solutions to the RGEs of the effective neutrino parameters and make several interesting observations. First, at the leading order, θ 12 and θ 13 are given by the simple formulas in the two-flavor mixing limit, while θ 23 ≈ θ 23 and δ ≈ δ are not changed by matter effects. Second, the ratio of the matter-corrected Jarlskog invariant J to its counterpart in vacuum J approximates to J /J ≈ 1/( C 12 C 13 ), where C 12 ≡ 1 − 2A * cos 2θ 12 + A 2 * with A * ≡ a/∆ 21 and C 13 ≡ 1 − 2A c cos 2θ 13 + A 2 c with A c ≡ a/∆ c have been defined. Finally, after taking higher-order corrections into account, we find compact and simple expressions of all the effective parameters, which turn out to be in perfect agreement with the exact numerical results. *

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Section: θ 23 and δmentioning

confidence: 86%

Section: θ 23 and δmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Analytical solutions to renormalization-group equations of effective neutrino masses and mixing parameters in matter

Wang

Zhou

2019

J. High Energ. Phys.

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“…where the effective neutrino massesm i (for i = 1, 2, 3) and flavor mixing matrixṼ in mater have been defined. Given a constant matter profile, the exact analytical relations between {Ṽ ,m i } and {V , m i } have been established in many works using different approaches [9,16,[25][26][27][28][29][30]. And the neutrino oscillation probabilities in matter can be written in the same way as those in vacuum by simply replacing V αi and ∆m 2 ji with the corresponding effective parametersṼ αi and ∆m 2 ji .…”

Section: Ters In the Matter-dominated Casementioning

confidence: 99%

Neutrino oscillation in dense matter

Luo

2020

Phys. Rev. D

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As the increasing of neutrino energy or matter density, the neutrino oscillation in matter may undergo "vacuum-dominated", "resonance" and "matter-dominated" three different stages successively. Neutrinos endure very different matter effects, and therefore present very different oscillation behaviors in these three different cases. In this paper, we focus on the less discussed matter-dominated case (i.e., |A CC | |∆m 2 31 |), study the effective neutrino mass and mixing parameters as well as neutrino oscillation probabilities in dense matter using the perturbation theory. We find that as the matter parameter |A CC | growing larger, the effective mixing matrix in matterṼ evolves approaching a fixed 3 × 3 constant real matrix which is free of CP violation and can be described using only one simple mixing angleθ which is independent of A CC . As for the neutrino oscillation behavior, ν e decoupled in the matter-dominated case due to its intense charged-current interaction with electrons while a two-flavor oscillation are still presented between ν µ and ν τ . Numerical analysis are carried on to help understanding the salient features of neutrino oscillation in matter as well as testing the validity of those concise approximate formulas we obtained. At the end of this paper, we make a very bold comparison of the oscillation behaviors between neutrinos passing through the Earth and passing through a typical white dwarf to give some embryo thoughts on under what circumstances these studies will be applied and put forward the interesting idea of possible "neutrino lensing" effect. A CC /|∆m 2 31 | J J = −0.0201 J f ixed = 0 J f ixed = 0 Inverted Mass Ordering neutrino (A CC > 0) anti-neutrino (A CC < 0) A CC /|∆m 2 31 | J J = −0.0331 J f ixed = 0 J f ixed = 0

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“…The relation between the branch cut singularities and level crossings will be discussed in detail and thus improve our understanding of the matter effect in neutrino oscillation [16][17][18][19][20][21][22][23][24][25][26][27][28][29]. As a byproduct of our analysis, a new approximate formula is derived in this paper, with better accuracy.…”

Section: Jhep10(2015)090mentioning

confidence: 99%

Why is the neutrino oscillation formula expanded in Δm 21 2 /Δm 31 2 still accurate near the solar resonance in matter?

Xu¹

2015

J. High Energ. Phys.

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Neutrino mixing in matter

Cited by 19 publications

References 21 publications

Analytical solutions to renormalization-group equations of effective neutrino masses and mixing parameters in matter

Analytical solutions to renormalization-group equations of effective neutrino masses and mixing parameters in matter

Neutrino oscillation in dense matter

Why is the neutrino oscillation formula expanded in Δm 21 2 /Δm 31 2 still accurate near the solar resonance in matter?

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