Analytic approximations for three neutrino oscillation parameters and probabilities in matter
By M. Freund. 2001
254 citations recorded by the source corpus.
The corrections to neutrino mixing parameters in the presence of matter of constant density are calculated systematically as series expansions in terms of the mass hierarchy $\ensuremath{\Delta}{m}_{21}^{2}/\ensuremath{\Delta}{m}_{31}^{2}.$ The parameter mapping obtained is then used to find simple, but nevertheless accurate formulas for oscillation probabilities in matter including $\mathrm{CP}$ effects. Expressions with one to one correspondence to the vacuum case are derived, which are valid for neutrino energies above the solar resonance energy. Two applications are given to show that these results are a useful and powerful tool for analytical studies of neutrino beams passing through the Earth mantle or core: First, the ``disentanglement problem'' of matter and $\mathrm{CP}$ effects in $\mathrm{CP}$ asymmetry is discussed and second, estimations of the statistical sensitivity to the $\mathrm{CP}$ terms of the oscillation probabilities in neutrino factory experiments are presented.
Subfields: Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/8622b64e102ecbc2e6557262343dc1ab3f83cd35
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Citations in the corpus
- Status of three-neutrino oscillation parameters, circa 2013 (2013, unknown): “5π, since for sin δ ∼ −1 the CP-odd term in the νμ → νe appearance probability [35, 36] is maximized [17].”
- 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 )”
- 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”
- 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]:”
- 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∆ ”
- The Long-Baseline Neutrino Experiment: Exploring Fundamental Symmetries of the Universe (2013, unknown): “The oscillation probability of νμ,e → νe,μ through matter, in a constant density approximation, keeping terms up to second order in α ≡ |∆m(2)21|/|∆m(2)31| and sin2 θ13, is [77,55]: P (νμ → νe) ∼= P (νe → νμ) ∼= P0 + Psin δ } {{ } CP violating +Pcos δ + P3 (2.”
- Flavor structures of charged fermions and massive neutrinos (2019, background): “This commutative property allows one to derive an exact relationship between the effective parameters (̃θ23, δ̃ν) in matter and their genuine counterparts (θ23, δν) in vacuum [401, 405, 478] — the so-called Toshev relation [479], provided the matter-corrected PMNS matrix Ũ takes the same parametriza”