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

Xu, Xun-Jie

doi:10.1007/jhep10(2015)090

Cited by 13 publications

(17 citation statements)

References 43 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This is why one gets the divergence θ 12 → ∞ in the limit of A c → 0. For a small value A c α c , one can certainly find another suitable form of series expansion [23,24], which is however invalid for a larger value of A c . The main reason is that there may exist two resonances at A c = α c cos 2θ 12 and A c = cos 2θ 13 , and the level crossing of two relevant eigenvalues occurs at each resonance.…”

Section: Series Expansionmentioning

confidence: 99%

“…As was previously noticed in Refs. [21,23,24], it is inappropriate to expand the functions like A 2 c + α 2 c with respect to α c in the presence of a comparable or even smaller A c . It has also been demonstrated in Ref.…”

Section: θ 13 and θ 12mentioning

confidence: 99%

“…It has also been demonstrated in Ref. [24] that such a problem can be avoided when one makes use of the series expansion of m 2 2 + m 2 1 but not that of m 2 2 − m 2 1 . This is obviously the case for the solution to θ 13 in Eq.…”

Section: θ 13 and θ 12mentioning

confidence: 99%

See 2 more Smart Citations

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

Wang

Zhou

2019

J. High Energ. Phys.

View full text Add to dashboard Cite

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. *

show abstract

Section: Series Expansionmentioning

confidence: 99%

Section: θ 13 and θ 12mentioning

confidence: 99%

See 1 more Smart Citation

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

Wang

Zhou

2019

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…A lot of efforts have been made in the past decades to formulate matter effects on neutrino oscillations, and recently some interest has been shown in going beyond Freund's analytical approximations [7] to reformulate probabilities of neutrino oscillations with weak or strong terrestrial matter contamination (see, e.g., Refs. [8,9,10,11,12,13,14]), or in describing matter effects on neutrino mixing and CP violation with the help of a language similar to the renormalization-group equations (see, e.g., Refs. [15,16,17,18]).…”

Section: Introductionmentioning

confidence: 99%

Sum rules and asymptotic behaviors of neutrino mixing in dense matter

Zhang

Zhu

2019

Nuclear Physics B

View full text Add to dashboard Cite

It has proved convenient to define the effective lepton flavor mixing matrix U and neutrino mass-squared differences ∆ ji ≡ m 2 j − m 2 i (for i, j = 1, 2, 3) to describe the phenomena of neutrino mixing and flavor oscillations in a medium, but the prerequisite is to establish direct and transparent relations between these effective quantities and their fundamental counterparts in vacuum. With the help of two sets of sum rules for U and ∆ ji , we derive new and exact formulas for moduli of the nine elements of U and the sides of its three Dirac unitarity triangles in the complex plane. The asymptotic behaviors of | U αi | 2 and ∆ ji (for α = e, µ, τ and i, j = 1, 2, 3) in very dense matter (namely, allowing the matter parameter A = 2 √ 2 G F N e E to mathematically approach infinity) are analytically unraveled for the first time, and in this connection the confusion associated with the parameter redundancy of θ 12 , θ 13 , θ 23 and δ in the standard parametrization of U is clarified.

show abstract

“…[28,29,30] for early development along this direction, and Ref. [31,32,22,33,34,23,24] for recent progress.…”

mentioning

confidence: 99%

Symmetric formulation of neutrino oscillations in matter and its intrinsic connection to renormalization-group equations

Zhou¹

2017

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

View full text Add to dashboard Cite

In this article, we point out that the effective Hamiltonian for neutrino oscillations in matter is invariant under the transformation of the mixing angle θ 12 → θ 12 −π/2 and the exchange of first two neutrino masses m 1 ↔ m 2 , if the standard parametrization of lepton flavor mixing matrix is adopted. To maintain this symmetry in perturbative calculations, we present a symmetric formulation of the effective Hamiltonian by introducing an η-gauge neutrino mass-squared difference ∆ * ≡ η∆ 31 + (1 − η)∆ 32 for 0 ≤ η ≤ 1, where ∆ ji ≡ m 2 j − m 2 i for ji = 21, 31, 32, and show that only η = 1/2, η = cos 2 θ 12 or η = sin 2 θ 12 is allowed. Furthermore, we prove that η = cos 2 θ 12 is the best choice to derive more accurate and compact neutrino oscillation probabilities, by implementing the approach of renromalization-group equations. The validity of this approach becomes transparent when an analogy is made between the parameter η herein and the renormalization scale µ in relativistic quantum field theories.

show abstract

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

Cited by 13 publications

References 43 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

Sum rules and asymptotic behaviors of neutrino mixing in dense matter

Symmetric formulation of neutrino oscillations in matter and its intrinsic connection to renormalization-group equations

Contact Info

Product

Resources

About