Series expansions for three-flavor neutrino oscillation probabilities in matter
By E. Akhmedov, R. Johansson, Manfred Lindner, T. Ohlsson, T. Schwetz. 2004
306 citations recorded by the source corpus.
We present a number of complete sets of series expansion formulas for neutrino oscillation probabilities in matter of constant density for three flavors. In particular, we study expansions in the mass hierarchy parameter α≡Δm212/Δm312 and mixing parameter s13≡sin θ13 up to second order and expansions only in α and only in s13 up to first order. For each type of expansion we also present the corresponding formulas for neutrino oscillations in vacuum. We perform a detailed analysis of the accuracy of the different sets of series expansion formulas and investigate which type of expansion is most accurate in different regions of the parameter space spanned by the neutrino energy E, the baseline length L, and the expansion parameters α and s13. We also present the formulas for series expansions in α and in s13 up to first order for the case of arbitrary matter density profiles. Furthermore, it is shown that in general all the 18 neutrino and antineutrino oscillation probabilities can be expressed through just two independent probabilities.
Subfields: Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/f60087179df4dc8f00036303d61c9c56398f5466
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In Nuclear and High Energy Physics
Citations in the corpus
- On the description of nonunitary neutrino mixing (2015, unknown): “Pμe = (α11α22) (2)P 3×3 μe + α 2 11α22|α21|P I μe + α(2) 11|α21|(2), (21) where we have denoted the standard three-neutrino conversion probability P 3×3 μe as [2, 53, 54] P 3×3 μe = 4 [ cos(2) θ12 cos 2 θ23 sin 2 θ12 sin 2 ( ∆m(2)21L 4Eν )”
- Updated fit to three neutrino mixing: status of leptonic CP violation (2014, unknown): “This can be understood from the relevant νe appearance probability at T2K and MINOS, which, at the second order in the small parameters sin θ13 and α ≡ ∆m21/∆m31 and assuming a constant matter density, takes the form [70–72]: Pνμ→νe ≈ 4 sin θ13 sin θ23 sin ∆(1−A) (1−A)2 + α sin 2θ12 cos 2 θ23 sinA∆ ”
- Global fit to three neutrino mixing: critical look at present precision (2012, background): “Expanding to second order in the small parameters sin θ13 and α ≡ ∆m21/∆m31 and assuming a constant matter density one finds [74–76]:”
- Invited review: Physics potential of the ICAL detector at the India-based Neutrino Observatory (INO) (2015, background): “To understand the results presented in this Report, the probability expressions obtained under the following two approximations are mostly relevant: • the one mass scale dominance (OMSD) approximation which assumes ∆m(2)21 = 0, and • the double expansion in terms of small parameters α = ∆m(2)21/∆m(2”