Global analysis of neutrino masses, mixings, and phases: Entering the era of leptonic $CP$ violation searches

We perform a global analysis of neutrino oscillation data, including high-precision measurements of the neutrino mixing angle ${\theta }_{13}$ at reactor experiments, which have confirmed previous indications in favor of ${\theta }_{13}>0$. Recent data presented at the Neutrino 2012 conference are also included. We focus on the correlations between ${\theta }_{13}$ and the mixing angle ${\theta }_{23}$, as well as between ${\theta }_{13}$ and the neutrino $CP$-violation phase $\delta$. We find interesting indications for ${\theta }_{23}<\pi /4$ and possible hints for $\delta \sim \pi$, with no significant difference between normal and inverted mass hierarchy.

Figure 1

Results of the analysis in the plane charted by $({sin}^2{\theta }_{13},{sin}^2{\theta }_{23})$, all other parameters being marginalized away. From left to right, the regions allowed at 1, 2 and $3\sigma$ refer to increasingly rich data sets: $\mathrm{LBL}+\mathrm{\text{solar}}+\mathrm{\text{KamLAND}}$ data (left panels), plus SBL reactor data (middle panels), plus SK atmospheric data (right panels). Best fits are marked by dots. A preference emerges for ${\theta }_{23}$ in the first octant in both normal hierarchy (NH, upper panels) and inverted hierarchy (IH, lower panels).

Figure 2

Results of the analysis in the plane charted by $({sin}^2{\theta }_{13},\delta )$, all other parameters being marginalized away. From left to right, the regions allowed at 1, 2 and $3\sigma$ refer to increasingly rich data sets: $\mathrm{LBL}+\mathrm{\text{solar}}+\mathrm{\text{KamLAND}}$ data (left panels), plus SBL reactor data (middle panels), plus SK atmospheric data (right panels). A preference emerges for $\delta$ values around $\pi$ in both normal hierarchy (NH, upper panels) and inverted hierarchy (IH, lower panels).

Figure 3

Results of the global analysis in terms of $N\sigma$ bounds on the six parameters governing $3\nu$ oscillations. Blue (solid) and red (dashed) curves refer to NH and IH, respectively.

Figure 4

Constraints induced by oscillation data (at $2\sigma$ level) in the planes charted by any two among the absolute mass observables $m_{\beta }$ (effective electron neutrino mass), $m_{\beta \beta }$ (effective Majorana mass), and $\Sigma$ (sum of neutrino masses). Blue (red) bands refer to normal (inverted) hierarchy.