Global analysis of three-flavour neutrino oscillations: synergies and tensions in the determination of theta_23, delta_CP, and the mass ordering

TL;DR

This work performs a comprehensive global fit of three-flavor neutrino oscillations using data up to fall 2018, comparing analyses with and without Super-Kamiokande atmospheric data. It finds a preference for normal mass ordering, a second octant for θ23, and a CP-violating phase near 215°, with CP conservation still allowed at modest Δχ^2. The study also highlights persistent tensions between solar and KamLAND determinations of Δm^2_21 and θ12 and examines synergies among LBL, MBL, and atmospheric datasets. It extends the impact of oscillation results to absolute mass observables mνe, mee, and Σ, providing projections valuable for beta decay, 0νββ searches, and cosmology. Overall, the analysis demonstrates how complementary datasets constrain the oscillation parameter space and informs expectations for future mass-scale measurements.

Abstract

We present the results of a global analysis of the neutrino oscillation data available as of fall 2018 in the framework of three massive mixed neutrinos with the goal at determining the ranges of allowed values for the six relevant parameters. We describe the complementarity and quantify the tensions among the results of the different data samples contributing to the determination of each parameter. We also show how those vary when combining our global likelihood with the chi^2 map provided by Super-Kamiokande for their atmospheric neutrino data analysis in the same framework. The best fit of the analysis is for the normal mass ordering with inverted ordering being disfavoured with a Delta_chi^2 = 4.7 (9.3) without (with) SK-atm. We find a preference for the second octant of theta_23, disfavouring the first octant with Delta_chi^2 = 4.4 (6.0) without (with) SK-atm. The best fit for the complex phase is Delta_CP = 215_deg with CP conservation being allowed at Delta_chi^2 = 1.5 (1.8). As a byproduct we quantify the correlated ranges for the laboratory observables sensitive to the absolute neutrino mass scale in beta decay, m_nu_e, and neutrino-less double beta decay, m_ee, and the total mass of the neutrinos, Sigma, which is most relevant in Cosmology.

Figures (14)

• Figure 1: Global $3\nu$ oscillation analysis. We show $\Delta\chi^2$ profiles minimized with respect to all undisplayed parameters. The red (blue) curves correspond to Normal (Inverted) Ordering. Solid (dashed) curves are without (with) adding the tabulated SK-atm $\Delta\chi^2$. Note that as atmospheric mass-squared splitting we use $\Delta m^2_{31}$ for NO and $\Delta m^2_{32}$ for IO.
• Figure 2: Global $3\nu$ oscillation analysis. Each panel shows the two-dimensional projection of the allowed six-dimensional region after minimization with respect to the undisplayed parameters. The regions in the four lower panels are obtained from $\Delta\chi^2$ minimized with respect to the mass ordering. The different contours correspond to $1\sigma$, 90%, $2\sigma$, 99%, $3\sigma$ CL (2 dof). Coloured regions (black contour curves) are without (with) adding the tabulated SK-atm $\Delta\chi^2$. 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). Solid (dashed) curves are without (with) adding the tabulated SK-atm $\Delta\chi^2$.
• Figure 4: Left: Allowed parameter regions (at 1$\sigma$, 90%, 2$\sigma$, 99%, and 3$\sigma$ CL for 2 dof) from the combined analysis of solar data for GS98 model (full regions with best fit marked by black star) and AGSS09 model (dashed void contours with best fit marked by a white dot), and for the analysis of KamLAND data (solid green contours with best fit marked by a green star) for fixed $\sin^2{\theta_{13}}=0.0224$ ($\theta_{13}=8.6$). We also show as orange contours the results of a global analysis for the GS98 model but without including the day-night information from SK. Right: $\Delta\chi^2$ dependence on $\Delta m^2_{21}$ for the same four analyses after marginalizing over $\theta_{12}$.
• Figure 5: Determination of $\Delta m^2_{3\ell}$ at $2\sigma$ (2 dof), where $\ell=1$ for NO (upper panels) and $\ell=2$ for IO (lower panels). The left panels show regions in the $(\theta_{23}, \Delta m^2_{3\ell})$ plane using both appearance and disappearance data from MINOS (green), T2K (red), NO$\nu$A (brown), as well as IceCube/DeepCore (orange), and SK-atm (from the table provided by the experiment, marron line) and the combination of them (blue coloured region). In the left panels the constraint on $\theta_{13}$ from the global fit (which is dominated by the reactor data) is imposed as a Gaussian bias. The right panels show regions in the $(\theta_{13}, \Delta m^2_{3\ell})$ plane using only Daya Bay (black), Reno (violet) and Double Chooz (magenta) reactor data, and their combination (blue coloured region). In all panels $\Delta m^2_{21}$, $\sin^2\theta_{12}$ are fixed to the global best fit values. Contours are defined with respect to the global minimum of the two orderings.