An analysis of atmospheric neutrino data from all four run periods of Super-Kamiokande optimized for sensitivity to the neutrino mass hierarchy is presented. Confidence intervals for Δ m 32 2, sin 2 θ 23, sin 2 θ 13 and δ C P are presented for normal neutrino mass hierarchy and inverted neutrino mass hierarchy hypotheses, based on atmospheric neutrino data alone. Additional constraints from reactor data on θ 13 and from published binned T2K data on muon neutrino disappearance and electron neutrino appearance are added to the atmospheric neutrino fit to give enhanced constraints on the above parameters. Over the range of parameters allowed at 90% confidence level, the normal mass hierarchy is favored by between 91.9% and 94.5% based on the combined Super-Kamiokande plus T2K result.
Umumta'lim fanlar bo`yicha 2018-o`quv yili 'Bilimlar bellashuvi' 7-sinf ixtisoslashgan maktablar uchun o`zbek va rus tillarida fizika fanidan yozma ish variantlari.
Figure 2Oscillation probabilities for neutrinos (upper panels) and antineutrinos (lower panels) as a function of energy and zenith angle assuming a normal mass hierarchy. Matter effects in the Earth produce the distortions in the neutrino figures between two and ten GeV, which are not present in the antineutrino figures. Distortions in the ν μ survival probability and enhancements in the ν e appearance probability occur primarily in angular regions corresponding to neutrino propagation across both the outer core and mantle regions (cosine zenith. Figure 5Data and MC comparisons for the entire Super-K data divided into 19 analysis samples. Samples with more than one zenith angle bin (cf. Table ) are shown as zenith angle distributions (second through fifth column) and other samples are shown as reconstructed momentum distributions (first column). Lines denote the best fit MC assuming the normal hierarchy.
Narrow panels below each distribution show the ratio of the data to this MC. In all panels the error bars represent the statistical uncertainty. In this projection each bin contains events of all energies, which obscures the difference between the hierarchies. If the inverted hierarchy MC were also drawn it would lie on top of the normal hierarchy line and for this reason it is not shown here. Figure provides a better projection for comparing the hierarchies. Figure 10Upward- ( cos θ 0.4) event ratio as a function of energy. The error bars are statistical.
For the single-ring samples the energy is taken to be the visible energy assuming the light-producing particle was an electron. For the multi-ring samples the total energy is used after accounting for the particle type (electron or muon) of each reconstructed ring. The cyan line denotes the best fit from the normal hierarchy hypothesis, and the orange dashed line the best fit from the inverted hierarchy hypothesis. The error on the prediction is dominated by the uncertainty in the ν τ cross section and is not more than 3% (absolute) in any bin of the figure. Figure 17Constraints on neutrino oscillation contours from a combined fit of Super-K atmospheric neutrino data and a model of the T2K experiment. The left figure shows 90% C.L.
Constraints from the atmospheric neutrino data (dotted), the T2K model (dashed), and their combination (solid) for the normal hierarchy. The right figure shows the same for the inverted hierarchy fit. In each contour sin 2 θ 13 is constrained to be 0.0219 ± 0.0012.
Normal and inverted hierarchy contours for each analysis are drawn relative the best fit among the two. Figure 18Distributions of the difference in best fit χ 2 values between normal- and inverted-hierarchy fits to pseudo data sets used in the generation of the CL s value for the SK θ 13 constrained analysis. In the cyan (orange) histogram the pseudo data have been generated assuming the normal (inverted) hierarchy at the analysis best fit shown in Table.
Shaded portions of the histograms denote the fraction of pseudo data sets with more extreme values than that observed in the data, Δ χ data 2 = − 4.33. Reuse & PermissionsIt is not necessary to obtain permission to reuse thisarticle or its components as it is available under the terms ofthe license.This license permits unrestricted use, distribution, andreproduction in any medium, provided attribution to the author(s) andthe published article's title, journal citation, and DOI aremaintained. Please note that some figures may have been included withpermission from other third parties. It is your responsibility toobtain the proper permission from the rights holder directly forthese figures.