Updated fit to three neutrino mixing: status of leptonic CP violation

TL;DR

<3-5 sentence high-level summary>

Abstract

We present a global analysis of solar, atmospheric, reactor and accelerator neutrino data in the framework of three-neutrino oscillations based on data available in summer 2014. We provide the allowed ranges of the six oscillation parameters and show that their determination is stable with respect to uncertainties related to reactor neutrino and solar neutrino flux predictions. We find that the maximal possible value of the Jarlskog invariant in the lepton sector is $0.0329 \pm 0.0009$ ($\pm 0.0027$) at the $1σ$ ($3σ$) level and we use leptonic unitarity triangles to illustrate the ability of global oscillation data to obtain information on CP violation. We discuss "tendencies and tensions" of the global fit related to the octant of $θ_{23}$ as well as the CP violating phase $δ_\mathrm{CP}$. The favored values of $δ_\mathrm{CP}$ are around $3π/2$ while values around $π/2$ are disfavored at about $Δχ^2 \simeq 6$. We comment on the non-trivial task to assign a confidence level to this $Δχ^2$ value by performing a Monte Carlo study of T2K data.

Figures (10)

• Figure 1: Global $3\nu$ oscillation analysis. Each panel shows a two-dimensional projection of the allowed six-dimensional region after minimization with respect to the undisplayed parameters. The different contours correspond to $1\sigma$, 90%, $2\sigma$, 99% and $3\sigma$ CL (2 dof). Full regions correspond to the analysis with free normalization of reactor fluxes and data from short-baseline (less than 100 m) reactor experiments included. For void regions short-baseline reactor data are not included but reactor fluxes as predicted in Huber:2011wv are assumed. Note that as atmospheric mass-squared splitting we use $\Delta m^2_{31}$ for NO and $\Delta m^2_{32}$ for IO. The regions in the lower 4 panels are based on a $\Delta\chi^2$ minimized with respect to NO and IO.
• Figure 2: Global $3\nu$ oscillation analysis. The red (blue) curves are for Normal (Inverted) Ordering. For solid curves the normalization of reactor fluxes is left free and data from short-baseline (less than 100 m) reactor experiments are included. For dashed curves short-baseline data are not included but reactor fluxes as predicted in Huber:2011wv are assumed. Note that as atmospheric mass-squared splitting we use $\Delta m^2_{31}$ for NO and $\Delta m^2_{32}$ for IO.
• Figure 3: Dependence of the global $\Delta\chi^2$ function on the Jarlskog invariant. The red (blue) curves are for NO (IO).
• Figure 4: Six leptonic unitarity triangles. After scaling and rotating each triangle so that two of its vertices always coincide with $(0,0)$ and $(1,0)$ (see text for details) we plot the $1\sigma$, 90%, $2\sigma$, 99%, $3\sigma$ CL (2 dof) allowed regions of the third vertex. Note that in the construction of the triangles the unitarity of the $U$ matrix is always explicitly imposed.
• Figure 5: Contours ($1\sigma$, 90%, $2\sigma$, 99%, $3\sigma$ CL for 2 dof) in the plane of $\theta_{13}$ and the reactor flux normalization $f_\text{flux}$. Full regions correspond to the combined analysis of all reactor neutrino experiments with the exception of KamLAND, but including the RSBL experiments. The green contours correspond to only the RSBL experiments and red contours include RSBL + medium-baseline reactors without a near detector (i.e. without including Daya Bay and RENO).