Erratum: Three flavor long-wavelength vacuum oscillation solution to the solar neutrino problem [Phys. Rev. D63, 013005 (2001)]

Abstract

We investigate the current status of the long-wavelength vacuum oscillation solution to the solar neutrino problem and to what extent the presence of a third neutrino can affect and modify it. Assuming that the smaller mass squared difference that can induce such oscillations, ∆m 2 12 , is in the range 10 −11 − 10 −8 eV 2 and the larger one, ∆m 2 23 , in the range relevant to atmospheric neutrino observations, we analyze the most recent solar neutrino data coming from Homestake, SAGE, GALLEX, GNO and Super-Kamiokande experiments in the context of three neutrino generations. We include in our vacuum oscillation analysis the MSW effect in the Sun, which is relevant for some of the parameter space scrutinized. We have also performed, as an extreme exercise, the fit without Homestake data. While we found that the MSW effect basically does not affect the best fitted parameters, it significantly modifies the allowed parameter space for ∆m 2 12 larger than ∼ 3 × 10 −10 eV 2 , in good agreement with the result obtained by A. Friedland in the case of two generations. Although the presence of a third neutrino does not essentially improve the quality of the fit, the solar neutrino data alone can give an upper bound on θ 13 , which is constrained to be less than ∼ 60 • at 95 % C.L.

How Sensitive is a Neutrino Factory to the Angleθ13?

“…We note that the NU coefficient ǫ τ τ does not show up in leading order in the appearance probability [14]. Therefore, we will neglect it in our numerical studies and concentrate only on FCI.…”

“…Such non-standard interactions of neutrinos affect their propagation in matter, with implications for solar [7,8,9,10], atmospheric [11,12], and astrophysical neutrino sources [13]. The possibility to use a neutrino factory for probing NSI with the earth matter, which neutrinos have to cross necessarily in a longbaseline experiment, has been previously examined in the appearance channels (−) ν e → (−) ν τ [14] and [14,15]. In this letter we will consider the impact of NSI on the determination of neutrino mixing parameters assuming the standard setup of a neutrino factory.…”

“…In contrast to refs. [14,15] we need only to assume a muon detector, which seems more realistic than a tau detector. We treat NSI and neutrino oscillations in a common framework to investigate correlations between the corresponding parameters.…”

Violation of Equivalence Principle and Solar Neutrinos

“…We performed the same statistical analysis as we did for three flavor vaccum oscillation solution to the SNP in Ref. [14], which is slightly different from our analysis in Ref. [12].…”

How precisely can we reduce the three-flavor neutrino oscillation to the two-flavor one only fromδm122/δm13

“…II. This relation is often used in the analysis of the solar neutrino [12,13,14,15,16,17,18,19]. Although it is exact in the limit ∆ 12 /∆ 13 , A(x)/∆ 13 → 0, the actual hierarchy is not so good.…”