Status of neutrino oscillations 2018: first hint for normal mass ordering and improved CP sensitivity

We present a new global fit of neutrino oscillation parameters within the simplest three-neutrino picture, including new data which appeared since our previous analysis~\cite{Forero:2014bxa}. In this update we include new long-baseline neutrino data involving the antineutrino channel in T2K, as well as new data in the neutrino channel, data from NO$\nu$A, as well as new reactor data, such as the Daya Bay 1230 days electron antineutrino disappearance spectrum data and the 1500 live days prompt spectrum from RENO, as well as new Double Chooz data. We also include atmospheric neutrino data from the IceCube DeepCore and ANTARES neutrino telescopes and from Super-Kamiokande. Finally, we also update our solar oscillation analysis by including the 2055-day day/night spectrum from the fourth phase of the Super-Kamiokande experiment. With the new data we find a preference for the atmospheric angle in the upper octant for both neutrino mass orderings, with maximal mixing allowed at $\Delta\chi^2 = 1.6 \, (3.2)$ for normal (inverted) ordering. We also obtain a strong preference for values of the CP phase $\delta$ in the range $[\pi,2\pi]$, excluding values close to $\pi/2$ at more than 4$\sigma$. More remarkably, our global analysis shows for the first time hints in favour of the normal mass ordering over the inverted one at more than 3$\sigma$. We discuss in detail the origin of the mass ordering, CP violation and octant sensitivities, analyzing the interplay among the different neutrino data samples.

Similarly, neutrino magnetic moment interactions in turbulent convective-zone magnetic fields would induce an enhanced solar antineutrino flux, to which KamLAND observations are sensitive [12,13]. Likewise, radiative-zone random magnetic fields [45] would induce sizeable density fluctuations, capable of affecting neutrino propagation in a significant manner [46,47]. However, under the hypothesis of CPT conservation, KamLAND constrains the effect of potentially large density fluctuations on solar neutrino oscillations [48,49].
Here we reconsider the determination of neutrino oscillation parameters within the simplest three-neutrino picture, in the light of new data that appeared since our previous published global analysis [1]. These include new longbaseline disappearance and appearance data involving the antineutrino channel in T2K [50,51], an updated dataset in the neutrino mode [52], as well as disappearance and appearance neutrino data from NOνA [53][54][55]. Turning to reactors, we have included the electron antineutrino disappearance spectrum of Daya Bay corresponding to 1230 days of data [56], the 1500 live days prompt reactor spectra from RENO [57,58] as well as the Double Chooz event energy spectrum from the far-I and far-II data periods [59]. Concerning atmospheric neutrinos, we have included data from the IceCube DeepCore [60] and ANTARES [61] neutrino telescopes, properly taking into account the relevant matter effects in the neutrino propagation inside the Earth. Given the difficulties to analyze the most recent atmospheric neutrino data from Super-Kamiokande with the public information available, we directly include the χ 2tables provided by the Super-Kamiokande collaboration, corresponding to the combination of the four run periods of the experiment [62]. Finally, we have also updated our solar oscillation analysis by including the 2055-day day/night spectrum from the fourth phase of the Super-Kamiokande experiment [63].

II. NEW EXPERIMENTS
In this section we present a brief description of the NOνA long-baseline accelerator neutrino experiment as well as the neutrino telescopes ANTARES and IceCube DeepCore which were not included in the previous global fit [1].
The ANTARES neutrino telescope ANTARES is a deep sea neutrino telescope located at the Mediterranean Sea, near Toulon (France). It consists of 12 lines with 75 optical modules each, covering a height of 350m and anchored at the sea floor at a depth of about 2.5 km, with a separation of around 70 m between neighboring modules. The neutrino detection is based on the Cherenkov light emitted when the charged leptons produced by the neutrino interactions move through the water.
Although ANTARES was not designed to contribute to the determination of the oscillation parameters, it was the first large volume Cherenkov-based neutrino telescope performing such analysis with atmospheric neutrinos. They managed to do it as a result of an important reduction of their threshold energy, from 50 GeV, when only multi-line events are considered, to 20 GeV for single-line events.

IceCube DeepCore
IceCube is a 1 km 3 multipurpose neutrino telescope placed near the Amundsen-Scott South Pole Station, buried beneath the surface and extending up to a depth of about 2500 meters. Similarly to ANTARES, it uses Cherenkov light to detect high energy neutrinos, with the difference that IceCube uses the polar ice as the medium where this light is produced. It has 86 strings with 60 digital optical modules (DOMs) each, placed at a depth that goes from 1450 m to 2450 m into the ice. In this analysis we use the data from DeepCore, a denser region of strings inside IceCube, designed to measure the atmospheric neutrino flux at low energies. The observed energy lies between 6.3 GeV and 56.2 GeV, way below the energy threshold of IceCube, which is about 100 GeV.

The NOνA experiment
The NOνA experiment is a long-baseline neutrino oscillation facility, with a 810 km baseline, which makes it the biggest long baseline experiment to date. It was designed to observe ν µ -disappearance as well as ν e -appearance in both neutrino and antineutrino channels. In order to accomplish this, it uses an intense and (nearly) pure beam of ν µ generated at the Fermilab accelerator complex. These neutrinos go through the Earth to northern Minnesota, 810 km away, to be detected at the Ash River far detector. The NOνA experiment has collected an equivalent of 8.85 × 10 20 protons on target of data in the neutrino mode and is now taking data with the antineutrino beam. Because of its 810 km baseline, it is more sensitive to matter effects than the T2K experiment. With further data taking, this may translate into a better sensitivity to the neutrino mass ordering. The detectors are 14 mrad off-axis, which results in a narrow neutrino energy spectrum, peaked around 2 GeV, which coincides with the oscillation maximum for ν µ → ν e oscillations.

III. NEW DATA
We now describe the new data samples used in this updated global neutrino oscillation analysis.

Updated solar neutrino data sample
We have updated our solar oscillation analysis including the 2055-day D/N (day/night) spectrum from the fourth phase of the Super-Kamiokande experiment, according to Ref. [63]. This new sample includes the D/N energy spectrum  The left (right) panels correspond to normal (inverted) mass ordering.

New data from Daya Bay
Daya Bay is a multi-core and multi-detector experiment, with eight 20 ton Gd-doped liquid scintillator antineutrino detectors (ADs) located at three experimental halls (EHs). At EH1 and EH2, two ADs were deployed while the remaining ADs were assigned to the far site, EH3. The thermal power of each reactor is 2.9 GW th and the baseline to the near and far sites (EH1 and EH2) are in the range 0.35 − 0.6 km and 1.5 − 1.9 km, respectively. After 1230 days of data taking, Daya Bay has measured approximately two hundred thousand inverse beta decay events at the far site.
Thanks to the large statistics and the reduction of systematical errors, due to having several functionally identical ADs, Daya Bay has provided the most precise determination of the reactor mixing angle to date.
In this analysis, we have included the antineutrino event energy spectra from the three EHs. Systematical errors accounting for total and detector normalization, as well as core-related errors and energy scale errors were included in the analysis. Systematical errors accounting for the background normalization in each experimental hall have been also included in the analysis, where we have used the background expectations from the ancillary files from Ref. [56].

New data from RENO
The RENO experiment has recently reported 1500 live days of data from antineutrinos produced at six reactor cores each one with a ∼ 2.8 GW th thermal power. The experiment detects neutrinos at a near and at a far detector (each detector with 16 ton of fiducial mass) located at 0.294 km and 1.383 km from the line joining the six reactor cores, respectively 2 . Thanks to the improved precision, the spectral fit analysis of RENO data is now sensitive to the neutrino oscillation phase, as reported in Refs. [57,58]. In our analysis, we have considered the near and far detector event energy distribution. We have fitted the measured energy spectrum at each detector after the subtraction of the background, normalizing our simulation to the expected spectra reported by the RENO collaboration. Systematical errors accounting for core-related (0.9% for each core) and detector uncertainties (0.2% for each detector) [66], have been included in our analysis in the form of nuisance parameters. We have also included a nuisance parameter accounting for the total normalization uncertainty, that has been left completely free in the analysis.

New data from Double Chooz
The Double Chooz experiment detects antineutrinos produced at two reactor cores with a 2 × 4.27 GW th total thermal power with a near and far detector of 8 ton fiducial mass each, located at 0.4 km and 1.05 km, respectively.
The data set considered in this analysis corresponds to 461 days of data with far detector only (far-I) plus 212 days of far detector data with a near detector (far-II), as reported in Ref. [59] 3 . The event energy spectrum from the far-I and far-II data periods were included in the analysis. Systematical errors considered in our simulation account for the signal and background normalization as well as for the total normalization. The total background has been extracted from the data reported in Ref. [59]. The results of the analysis of the three reactor experiments are given in Fig.1 and will be discussed in detail in the next section.

Atmospheric data from ANTARES
We analyze atmospheric data from the ANTARES collaboration following Ref. [61], taking also into account matter effects, and including electron neutrino and neutral current interaction events. In order to calibrate our simulation we have first reproduced very well the analysis performed by the collaboration using their assumptions and approximations. Afterwards we have included neutral current interactions and matter effects to our simulation. In Fig. 2 we plot the allowed regions in the atmospheric parameters at 90 and 99% C.L. from our analysis of ANTARES data.
One sees the regions are still very large and therefore the sensitivity is not competitive with the other experiments, described in the following sections. It is expected that the ANTARES collaboration will update their analysis with more data, hopefully improving their sensitivity to the atmospheric neutrino oscillation parameters.

Atmospheric data from IceCube DeepCore
In order to determine the atmospheric neutrino oscillation parameters, in this simulation we use data published by IceCube DeepCore in Ref. [60], analyzed following all the updates presented by the collaboration. Neutrino data are presented in 64 bins, with 8 energy-bins and 8 bins in zenith-angle, see [68]. Tables with systematic detector uncertainties, optical efficiencies and uncertainties produced through scattering at holes opened in the ice for the depletion of the DOMs are also provided. The fluxes for atmospheric neutrinos are taken from [69,70]. We perform the numerical integration in matter using the Preliminary Reference Earth Model (PREM) [71]. In Fig. 2

Atmospheric data from Super-Kamiokande
In this work we include the most recent atmospheric neutrino results from the Super-Kamiokande experiment [62], corresponding to the combined analysis of phases I to IV of the experiment, with a total of 328 kton-year exposure of the detector. The data analysis performed by the Super-K collaboration, optimized to enhance the sensitivity to the neutrino mass ordering, includes the impact of the atmospheric oscillation parameters as well as the reactor angle and the CP phase. As stressed in [73], the most recent atmospheric neutrino Super-K data samples are not presented in a form that allows a reliable use outside the collaboration. Therefore, here we follow the same procedure adopted in previous publications (Refs. [1,74,75]) which consists of directly incorporating to our global neutrino analysis the χ 2 -tables provided by the Super-K collaboration [76], obtained in Ref. [62].

New long-baseline data from T2K
In addition to the data used in the neutrino oscillation global fit published in Ref. [1], the T2K collaboration has new results in the neutrino mode. Therefore, this updated analysis includes the latest T2K antineutrino sample as well as their updated neutrino data, as published in Refs. [50][51][52]. With an accumulated statistics of 14.6×10 20 POT in the neutrino run, the T2K collaboration now observes 240 disappearance and 74+15 appearance (charged current quasi-elastic and charged current single-pion, respectively) neutrino events. Note, however, that the CC-1π appearance events have not been included in our simulation. In the antineutrino channel, with 7.6×10 20 POT, a total of 68 disappearanceν µ events and 7 appearanceν e events were recorded. In the present analysis we have included the newest neutrino fluxes in Super-K provided by the T2K web page [77]. The simulation of the experiment and the statistical analysis were performed with the GLoBES package [78,79], including all systematic uncertainties reported in Ref. [52].
Notice that T2K has already achieved some CP sensitivity, as seen in Fig. 4. Indeed, thanks to the combination of the results in the neutrino and the antineutrino channel, T2K is the first experiment able to exclude on its own certain values of the CP phase at more than 2σ for normal ordering (NO), and even at 3σ for inverted ordering (IO). The allowed regions for other oscillation parameters, such as θ 13 and ∆m 2 31 , are found to be consistent with the reactor experiments.

New long-baseline data from NOνA
In our global fit we also include the latest results for ν µ -disappearance and ν e -appearance of the NOνA experiment.
NOνA has recently published the results of their neutrino run with an accumulated statistics of 8.85×10 20 POT [55].
In the disappearance channel, a total of 126 events have been observed, while 763 events were expected under the no-oscillation hypothesis. In the appearance channel, a total of 66 events have been detected. The neutrino oscillation analysis reported by the NOνA collaboration imposing a prior on θ 13 slightly disfavors inverted mass ordering, with a significance of approximately 2σ. Our simulation of the NOνA experiment has been performed using GLoBES [78,79], including all the systematic errors reported in [53,54] and updated in Ref. [55].
In Fig. 3 we compare the restrictions on the atmospheric neutrino parameters derived from long-baseline accelerator data coming from the T2K, NOνA and MINOS experiments, at 90 and 99% confidence level. Further results are summarized in Figs. 4, 5, 6, 7 and 8 and discussed in the following section.

IV. GLOBAL FIT RESULTS
We now describe the global results of our updated neutrino oscillation fit. There are no significant changes derived from the new solar neutrino data, hence we move directly to the results for atmospheric neutrinos. Here there are new data from the ANTARES and IceCube collaborations as well as from Super-Kamiokande phase IV. As seen in  In what follows we highlight the main features of our neutrino oscillation global fit results, focusing upon the main open challenges of the three-neutrino picture: CP violation, the neutrino mass ordering and the θ 23 octant problem.

Sensitivity to CP violation
Long-baseline neutrino oscillation data play an important role in determining the CP violating phase, δ. In order to highlight this point we present the ∆χ 2 -profile for the CP phase, as determined from T2K, NOνA and Super-K atmospheric data alone, as well as by the global oscillation data sample, as shown in the right panels in Fig. 4. Note that here the ∆χ 2 -profile has been obtained from the local minimum for each mass ordering.
This result shows how the current global sensitivity to the CP phase is dominated by the T2K experiment, with added rejection against δ = π/2 obtained after combining with the other experiments. Indeed, we find that the combination with reactor data is crucial to enhance the rejection against δ = π/2. As a result, we find that in the global analysis, δ = π/2 is disfavoured with ∆χ 2 = 22.9 (4.8σ) for normal ordering. The rejection against δ = π/2 is found to be stronger for inverted mass spectrum, where it is excluded with ∆χ 2 = 37.3 (6.1σ), with respect to the minimum for this ordering. As can also be seen from the figure, the current preferred value of δ depends on the mass ordering, lying closer to 3π/2 for inverted ordering. The current best fit values for the CP violating phase are located at δ = 1.21π for NO and at δ = 1.56π for IO.

Neutrino mass ordering
Concerning the sensitivity to the neutrino mass ordering, our global fit shows for the first time a hint in favour of normal neutrino mass ordering, with inverted ordering disfavoured with ∆χ 2 = 11.7 (3.4σ). In order to disentangle the origin of the preference for NO in our global analysis, we display in Figs indicates a preference for normal ordering with ∆χ 2 = 3.7. In the case of T2K, the combination with reactor data results in a stronger preference for normal over inverted mass ordering, with ∆χ 2 = 5.3. This enhanced sensitivity to the mass ordering is due to the tension that exists between the value of the atmospheric mass splitting preferred by reactor, mainly Daya Bay, and T2K. One finds that Daya Bay prefers a higher value for ∆m 2 31 with respect to the one indicated by T2K, and the difference is larger for inverted mass ordering. The combined analysis of all long-baseline and reactor data yields a preference for normal mass ordering with ∆χ 2 = 7.5.
By combining these data samples with atmospheric data, one gets the final global results indicated by the coloured regions in Figs. 5 and 6. In principle, one may expect the largest sensitivity to the neutrino mass ordering to come from the observation of matter effects in the atmospheric neutrino flux. However, we find that the neutrino telescope experiments IceCube DeepCore and ANTARES are not yet very sensitive to the mass ordering. In fact, the difference between normal and inverted mass ordering from the combined analysis of DeepCore and ANTARES Despite the recent progress on this matter, the octant discrimination problem lies far beyond the current generation of neutrino oscillation experiments, and will be a particularly stubborn problem in the years to come. On the positive side, however, it has been noted that the task of octant discrimination and probing for leptonic CP violation in current and future long-baseline experiments can be facilitated by prior model-specific theoretical knowledge of the predicted pattern of leptonic mixing. See, as an example, Figure 1 given in [82] and the associated discussion.

V. SUMMARY AND DISCUSSION
We have discussed in detail the origin of the mass ordering, CP violation and octant discrimination, analyzing the interplay among the different neutrino oscillation data samples. The results obtained in our global fit are summarized in Table I   values close to π/2 at more than 4σ. Concerning the octant of θ 23 , this global analysis prefers the second octant slightly, in agreement with the previous one in Ref. [1]. We have found that for normal neutrino mass ordering the upper atmospheric octant is now preferred with ∆χ 2 = 1.6, while for the case of inverted ordering, values of the atmospheric mixing angle in the lower octant are allowed with ∆χ 2 ≥ 3.2. More remarkably, our global analysis favours for the first time the normal mass ordering over the inverted one at 3.4σ. As discussed in the previous section, part of the sensitivity to the mass ordering comes from the more recent atmospheric analysis of Super-K. This new analysis shows a preference for normal over inverse mass ordering with ∆χ 2 = 3.5. On the other hand, a mismatch between the values of θ 13 preferred by long-baseline and reactor data (larger for IO) also gives a relevant contribution to the global sensitivity to the mass ordering. This effect is also enhanced due to a tension between the preferred values of the atmospheric mass splitting by T2K and reactor experiments. In short, we have seen how the precision in the determination of the best-known oscillation parameters has improved thanks to the recent long-baseline neutrino oscillation and reactor data. Also the sensitivity to mass ordering,