Constraints on $θ_{13}$ from A Three-Flavor Oscillation Analysis of Reactor Antineutrinos at KamLAND

TL;DR

The paper presents an updated three-flavor analysis of KamLAND reactor antineutrinos combined with solar-neutrino data to constrain $\Delta m^{2}_{21}$, $\theta_{12}$, and $\theta_{13}$ under CPT invariance. Using an unbinned maximum-likelihood approach, it finds KamLAND-alone best fits near $\Delta m^{2}_{21} \approx 7.5\times10^{-5}\,\text{eV}^{2}$ and a small but nonzero $\sin^{2}\theta_{13}$, with a more pronounced hint when solar data are included ($\sin^{2}\theta_{13} \approx 0.020^{+0.016}_{-0.016}$). A global combination with CHOOZ, atmospheric, and accelerator data yields $\sin^{2}\theta_{13}=0.009^{+0.013}_{-0.007}$, a modest indication but not yet conclusive. The results align with other measurements and underscore the need for future reactor/accelerator experiments to definitively determine $\theta_{13}$ and explore CP violation in the lepton sector.

Abstract

We present new constraints on the neutrino oscillation parameters $/textyen Delta m^{2}_{21}$, $/textyen theta_{12}$, and $/textyen theta_{13}$ from a three-flavor analysis of solar and KamLAND data. The KamLAND data set includes data acquired following a radiopurity upgrade and amounts to a total exposure of $3.49 \textyen times 10^{32}$ target-proton-year. Under the assumption of {\textyen it CPT} invariance, a two-flavor analysis (/textyen mbox{$\textyen theta_{13} = 0$}) of the KamLAND and solar data yields the best-fit values $\textyen tan^{2} \textyen theta_{12} = 0.444^{+0.036}_{-0.030}$ and $\textyen Delta m^{2}_{21} = 7.50^{+0.19}_{-0.20} \textyen times 10^{-5} ~ {\textyen rm eV}^{2}$; a three-flavor analysis with $\textyen theta_{13}$ as a free parameter yields the best-fit values $\textyen tan^{2} \textyen theta_{12} = 0.452^{+0.035}_{-0.033}$, $\textyen Delta m^{2}_{21} = 7.50^{+0.19}_{-0.20} \textyen times 10^{-5} ~ {\textyen rm eV}^{2}$, and $\textyen sin^{2} \textyen theta_{13} = 0.020^{+0.016}_{-0.016}$. This $\textyen theta_{13}$ interval is consistent with other recent work combining the CHOOZ, atmospheric and long-baseline accelerator experiments. We also present a new global $\textyen theta_{13}$ analysis, incorporating the CHOOZ, atmospheric and accelerator data, which indicates $\textyen sin^{2} \textyen theta_{13} = 0.009^{+0.013}_{-0.007}$. A nonzero value is suggested, but only at the 79\textyen% C.L.

Figures (6)

• Figure 1: Prompt energy spectrum of $\overline{\nu}_{e}$ candidate events above 0.9 MeV energy threshold (vertical dashed line). The data together with the background and reactor $\overline{\nu}_{e}$ contributions fitted from an unbinned maximum-likelihood three-flavor oscillation analysis are shown in the main panel. The number of geo-$\overline{\nu}_{e}$'s is unconstrained in the fit. The shaded background histograms are cumulative. The top panel shows the energy-dependent selection efficiency; each point is the weighted average over the five time periods described in the text.
• Figure 2: Allowed regions projected in the ($\tan^{2} \theta_{12}$, $\Delta m^{2}_{21}$) plane, for solar and KamLAND data from (a) the two-flavor oscillation analysis ($\theta_{13}=0$) and (b) the three-flavor oscillation analysis, where $\theta_{13}$ is a free parameter. The shaded regions are from the combined analysis of the solar and KamLAND data. The side panels show the $\Delta \chi^{2}$ profiles projected onto the $\tan^{2} \theta_{12}$ and $\Delta m^{2}_{21}$ axes.
• Figure 3: Allowed regions from the solar and KamLAND data projected in the ($\tan^{2} \theta_{12}$, $\sin^{2} \theta_{13}$) plane for the three-flavor analysis.
• Figure 4: $\Delta \chi^{2}$-profiles projected onto the $\sin^{2} \theta_{13}$ axis for different combinations of the oscillation data floating the undisplayed parameters ($\tan^{2} \theta_{12}$, $\Delta m^{2}_{21}$).
• Figure 5: Ratio of the observed $\overline{\nu}_{e}$ spectrum to the expectation for no-oscillation versus $L_{0}/E$ for the KamLAND data. $L_{0} = 180~{\rm km}$ is the flux-weighted average reactor baseline. The 2-$\nu$ and 3-$\nu$ histograms are the expected distributions based on the best-fit parameter values from the two- and three-flavor unbinned maximum-likelihood analyses of the KamLAND data.