Constraints on ${\theta }_{13}$ from a three-flavor oscillation analysis of reactor antineutrinos at KamLAND

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

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 $({tan}^2{\theta }_{12},\Delta m_{21}^2)$ 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 $\Delta m_{21}^2$ 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 $({tan}^2{\theta }_{12},\Delta m_{21}^2)$.

Figure 5

Ratio of the observed ${\overline{\nu }}_e$ spectrum to the expectation for no-oscillation versus $L_0/E$ for the KamLAND data. $L_0=180\mathrm{km}$ 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.

Figure 6

Survival probability of reactor ${\overline{\nu }}_e$ versus $x\equiv ⟨{sin}^{2}2{\widehat{\theta }}_{12M}{sin}^2(1.27\Delta {\widehat{m}}_{21M}^{2}L/E)⟩/{sin}^{2}2{\widehat{\theta }}_{12}$. The angle bracket indicates the weighted average over reactor baseline ($L_i$) and original neutrino energies ($E$). The points are the survival probability for the KamLAND data. The 3-$\nu$ line and $1\sigma$ C.L. region are calculated using the unbinned maximum-likelihood fit to the KamLAND data. The 2-$\nu$ line is calculated from the two-flavor unbinned maximum-likelihood KamLAND analysis. The $1\sigma$ C.L. band for the 2-$\nu$ case is not shown but is similar in magnitude to the no-oscillation case shown at $P=1.0$.