Atmospheric neutrino oscillation analysis with sub-leading effects in Super-Kamiokande I, II, and III

TL;DR

This work performs a comprehensive three-flavor analysis of atmospheric neutrino data from Super-Kamiokande I–III to probe sub-leading effects related to the mixing angle $\theta_{13}$ and the octant of $\theta_{23}$, under both normal and inverted mass hierarchies. By employing a pulled $\chi^{2}$ framework across 420 bins and 120 systematics, the study conducts two targeted analyses: a $\theta_{23}$ octant test and a $\theta_{13}$ appearance search using optimized event samples. The results show no evidence for $\theta_{13}>0$, with best-fit parameters at $\Delta m^{2} \approx 2.1 \times 10^{-3}~\text{eV}^2$ and $\sin^{2}\theta_{13} \approx 0$ (normal) or $0.006$ (inverted), and $\sin^{2}\theta_{23}$ near 0.5, along with a 90% C.L. limit of $\sin^{2}\theta_{13} < 0.04$ (normal) or $<0.09$ (inverted). The $\theta_{23}$ octant analysis finds no significant octant preference, yielding $0.407 \leq \sin^{2}\theta_{23} \leq 0.583$ at 90% C.L. The results are compatible with the Chooz constraint and contribute to narrowing the parameter space for leptonic mixing and the mass hierarchy.

Abstract

We present a search for non-zero theta_{13} and deviations of sin^2 theta_{23} from 0.5 in the oscillations of atmospheric neutrino data from Super-Kamiokande -I, -II, and -III. No distortions of the neutrino flux consistent with non-zero theta_{13} are found and both neutrino mass hierarchy hypotheses are in agreement with the data. The data are best fit at Delta m^2 = 2.1 x 10^-3 eV^2, sin^2 theta_{13} = 0.0, and sin^2 theta_{23} =0.5. In the normal (inverted) hierarchy theta_{13} and Delta m^2 are constrained at the one-dimensional 90% C.L. to sin^2 theta_{13} < 0.04 (0.09) and 1.9 (1.7) x 10^-3 < Delta m^2 < 2.6 (2.7) x 10^-3 eV^2. The atmospheric mixing angle is within 0.407 <= sin^2 theta_{23} <= 0.583 at 90% C.L.

Figures (11)

• Figure 1: (color online). The left side of the figure shows the calculated $\nu_e$ transition probability $P_{ex}$ for atmospheric neutrinos with an energy $E_\nu$ and neutrino zenith angle, cos$\Theta_{\nu}$, using $\Delta m^{2}_{12} = 7.7 \times 10^{-5} eV^{2} \hbox{sin}^{2}\theta_{12} = 0.3$Schwetz08, $\hbox{sin}^{2}\theta_{23} = 0.5, \hbox{sin}^{2}\theta_{13} = 0.0 \hbox{and} \Delta m^{2}_{23} = 2.1 \times 10^{-3} eV^{2}.$ Matter effects within the Earth are taken into account. Negative $\hbox{cos}\Theta_{\nu}$ corresponds to upward-going neutrinos and 0 is the horizon. The electron neutrino flux ratio $\Phi_{e}/\Phi_{e}^{0}$ is shown in the right side of the figure. An expected excess (deficit) for atmospheric mixing in the first (second) octant is shown in the upper (lower) panel. The island shapes are regions of probability driven by the solar oscillation parameters. The center panel shows no significant region of excess or deficit when $\hbox{sin}^{2} \theta_{23} = 0.5.$
• Figure 2: (color online). The three flavor oscillation probability $\nu_{\mu} \leftrightarrow \nu_{e}$ for $\theta_{13}$ at the Chooz limit for neutrinos under the normal hierarchy in the one mass scale dominant framework is shown at left. In the right panel the $\nu_{e}$ flux ratio $\Phi_{e}^{Chooz}/\Phi_{e}^{0} - 1$ for oscillations with $\theta_{13}$ at the Chooz limit relative to those at $\theta_{13} = 0.$ Large matter-induced resonances between 2-10 GeV appear for upward going neutrinos traversing the core ($\hbox{cos}\Theta_{\nu} < -0.84$) and mantle regions ($-0.84 < \hbox{cos}\Theta_{\nu} < -0.45$). Atmospheric mixing is assumed at $\Delta m^{2}_{23} = 2.1\times 10^{-3}~\hbox{eV}^{2}$ and $\hbox{sin}^{2} \theta_{23} = 0.5$.
• Figure 3: (color online). The distributions used in the $\pi^{0}$ selection for five momentum regions: (a)$P_e <$ 250 MeV/c, (b)250 MeV/c $\leq P_e <$ 400 MeV/c, (c)400 MeV/c $\leq P_e <$ 630 MeV/c, (d)630 MeV/c $\leq P_e <$ 1000 MeV/c and (e)1000 MeV/c $\leq P_e$. Solid (dashed) lines represent CCQE (NC) events in the FC sub-GeV single-ring $e$-like Monte Carlo. Events with an invariant mass above $100~\hbox{MeV/c}^2$ are selected as $\pi^0$-like. To separate $\pi^0$-like and electron-like more efficiently, an additional likelihood selection is applied for events with momentum above 250 MeV/c. The distributions of the three likelihood variables are shown: the fraction of energy carried by the second fitted ring ($E_2/(E_1+E_2)$), the $\pi^0$ mass and $\Delta$-likelihood (described in the text). All distributions have been normalized to unit area.
• Figure 4: (color online). Variables used in the likelihood definition to create the SK-I multi-GeV multi-ring $e$-like sample. The energy bins correspond to the the most energetic ring (MER) and the distributions have been scaled to the SK-I livetime. Signal events (CC $\nu_{e} + \bar{\nu}_{e}$) are shown as the solid line and background events (CC $\nu_{\mu} + \bar{\nu}_{\mu}$ and NC) are shown as the dashed line. The shapes of these distributions do not differ appreciably among SK-I, SK-II, and SK-III.
• Figure 5: (color online). $\chi^2$-$\chi^2_{min}$ distribution as a function of sin$^2\theta_{23}$ for oscillations without the 1-2 parameters (dotted line) and with the 1-2 parameters (solid line). For each sin$^2\theta_{23}$ point, $\Delta m^2_{23}$ is chosen so that $\chi^2$ is minimized. The horizontal line corresponds to the 68 %(90 %) confidence level which is located at $\chi^2_{min} + 1.0(2.7)$.