Status of three-neutrino oscillation parameters, circa 2013

TL;DR

The paper performs a comprehensive global fit of the three-neutrino oscillation framework using data from solar, atmospheric, accelerator, and reactor experiments to update the allowed ranges of the known parameters ($\delta m^2$, $\Delta m^2$, $\theta_{12}$, $\theta_{13}$, $\theta_{23}$) and to assess the status of unknowns (mass hierarchy, $\theta_{23}$ octant, and CP phase $\delta$). By progressively adding SBL reactor data, then atmospheric data, the analysis reduces $\sin^2\theta_{13}$ uncertainty, refines covariances, and reveals a mild preference for $\theta_{23}<\pi/4$ in NH and a CP-violating phase near $\delta\sim 1.4$–$1.5\pi$ with $\sin\delta<0$, though none of these hints are beyond $2\sigma$. The hierarchy remains inconclusive, with $igDelta \chi^2_{I-N}\big$ not yet significant enough to distinguish NH from IH; the work highlights parameter covariances as data sets evolve and emphasizes the need for continued combined analyses to resolve remaining ambiguities.

Abstract

The standard three-neutrino (3nu) oscillation framework is being increasingly refined by results coming from different sets of experiments, using neutrinos from solar, atmospheric, accelerator and reactor sources. At present, each of the known oscillation parameters [the two squared mass gaps (delta m^2, Delta m^2) and the three mixing angles (theta_12}, theta_13, theta_23)] is dominantly determined by a single class of experiments. Conversely, the unknown parameters [the mass hierarchy, the theta_23 octant and the CP-violating phase delta] can be currently constrained only through a combined analysis of various (eventually all) classes of experiments. In the light of recent new results coming from reactor and accelerator experiments, and of their interplay with solar and atmospheric data, we update the estimated N-sigma ranges of the known 3nu parameters, and revisit the status of the unknown ones. Concerning the hierarchy, no significant difference emerges between normal and inverted mass ordering. A slight overall preference is found for theta_23 in the first octant and for nonzero CP violation with sin delta < 0; however, for both parameters, such preference exceeds 1 sigma only for normal hierarchy. We also discuss the correlations and stability of the oscillation parameters within different combinations of data sets.

Figures (7)

• Figure 1: Combined $3\nu$ analysis of LBL Acc. + Solar + KL data: Bounds on the oscillation parameters in terms of standard deviations $N\sigma$ from the best fit. Solid (dashed) lines refer to NH (IH). The horizontal dotted lines mark the $1\sigma$, $2\sigma$ and $3\sigma$ levels for each parameter (all the others being marginalized away). See the text for details.
• Figure 2: As in Fig. 1, but adding SBL reactor data.
• Figure 3: As in Fig. 2, but adding SK atmospheric data in a global $3\nu$ analysis of all data.
• Figure 4: Results of the analysis in the plane charted by ($\sin^2\theta_{23},\,\Delta m^2$), all other parameters being marginalized away. From left to right, the regions allowed at 1, 2 and $3\sigma$ refer to increasingly rich datasets: LBL accelerator + solar + KamLAND data (left panels), plus SBL reactor data (middle panels), plus SK atmospheric data (right panels). Best fits are marked by dots. The three upper (lower) panels refer to normal (inverted) hierarchy.
• Figure 5: As in Fig. 4, but in the plane ($\sin^2\theta_{23},\,\sin^2\theta_{13}$).