Global fit of oscillation parameters

On this page we present the result of our global fit of neutrino oscillation parameters. The full text can be found in our paper. In the menu on the left hand side you can also obtain information on the experiments analyzed separately. There we also summarize all of the datasets included in our global fit.

In the following we present the numerical values of our analysis for each of the parameters. In our global fit of neutrino oscillation data we obtain preference for normal neutrino mass ordering with \chi^2(\text{IO})-\chi^2(\text{NO})=6.4 which corresponds to a preference of 2.5\sigma.

parameter best fit \pm 1\sigma 2\sigma range 3\sigma range
\Delta m^2_{21}: [10^{-5} eV^2] 7.50^{+0.22}_{-0.20} 7.11–7.93 6.94–8.14
|\Delta m^2_{31}|: [10^{-3} eV^2] (NO) 2.55^{+0.02}_{-0.03} 2.49–2.60 2.47–2.63
|\Delta m^2_{31}|: [10^{-3} eV^2] (IO) 2.45^{+0.02}_{-0.03} 2.39–2.50 2.37–2.53
\sin^2\theta_{12} / 10^{-1} 3.18\pm0.16 2.86–3.52 2.71–3.69
\sin^2\theta_{23} / 10^{-1} (NO) 5.74\pm0.14 5.41–5.99 4.34–6.10
\sin^2\theta_{23} / 10^{-1} (IO) 5.78^{+0.10}_{-0.17} 5.41–5.98 4.33–6.08
\sin^2\theta_{13} / 10^{-2} (NO) 2.200^{+0.069}_{-0.062} 2.069–2.337 2.000–2.405
\sin^2\theta_{13} / 10^{-2} (IO) 2.225^{+0.064}_{-0.070} 2.086–2.356 2.018–2.424
\delta_{\rm CP}/\pi (NO) 1.08^{+0.13}_{-0.12} 0.84–1.42 0.71–1.99
\delta_{\rm CP}/\pi (IO) 1.58^{+0.15}_{-0.16} 1.26–1.85 1.11–1.96

Those numbers have been extracted from the profiles in the following figure. The solid lines are plotted with respect to the global best fit value, while the dashed lines are plotted with respect to the best fit value in inverted ordering.
The \chi^2 profiles used for the plots are available here.

From the constraints on the oscillation parameters, one can obtain the bounds on the mixing matrix elements (real and imaginary part) and on the Jarlskog invariant.
The mixing matrix is written in the canonical form.
We use the definitions J_{\rm max}=\cos\theta_{12} \sin\theta_{12} \cos\theta_{23} \sin\theta_{23} \cos\theta_{13} ^ 2 \sin\theta_{13} and J=J_{\rm max}\,\sin\delta_{\rm CP}.

From these results, we obtain the following 3\sigma constraints on the Jarlskog invariant:

quantity NO IO
J_{\rm max} 0.0312–0.0354 0.0314–0.0355
J -0.0348–0.0263 -0.0357– -0.0047
\Delta m^2_{21}/\Delta m^2_{31} 0.0271–0.0321 0.0281–0.0334

Concerning the mixing matrix, we have for normal ordering:

while for inverted ordering: