Toward the confirmation of atmospheric neutrino oscillations

The atmospheric muon neutrino deficit, which was possible evidence of $\nu_\mu \leftrightarrow \nu_\tau$ oscillation, was reported by the Kamiokande experiment from 1988. Many experimental efforts were made to examine the Kamiokande results. Experiments which contributed to the confirmation of $\nu_\mu \leftrightarrow \nu_\tau$ oscillation are reviewed. Especially, long-baseline neutrino-oscillation experiments are described in detail.


Introduction
The atmospheric muon neutrino deficit, which might be evidence of neutrino oscillations, was initially reported by the Kamiokande experiment. The collaboration published three atmospheric neutrino papers [1][2][3] in 1988, 1992 and 1994. Details about the three Kamiokande papers were reported in Ref. [4]. The history of the birth of the Kamiokande experiment with the strong leadership of Prof. Masatoshi Koshiba was given in Ref. [5].
Motivated by the Kamiokande observation, other underground experiments examined the atmospheric muon neutrino deficit. The IMB experiment [6,7], which is another water Cherenkov detector, reported results consistent with Kamiokande. However, two tracking type experiments, Nusex [8] and Frejus [9] could not find any anomaly, and their results were inconsistent with Kamiokande. A summary of the results from various experiments is shown in Fig. 1, which was given in a review article [10] written in 2004.
In the middle of 1990s, the Kamiokande results were not widely accepted because of the following reasons. into e + νν, since the observed small µ/e ratio could be interpreted as due to an excess of e-like signal by these positrons.

Zenith angle distribution
The atmospheric neutrino flux is predicted to be up-down symmetric above a few GeV neutrino energies. For downward-going neutrinos, the flight length is about 15 km, while that for vertically upward-going neutrinos it is 13 000 km. Therefore, if the neutrino oscillation length is O(100-1000 km), it should be possible to observe up-down asymmetry of the flux while the (1) The e/µ identification capability of the water Cherenkov detectors was suspicious because only two water Cherenkov detectors claimed an atmospheric muon neutrino deficit. Tracking type detectors could not find the anomaly.
(2) The number of total atmospheric neutrino events was ∼1000. The statistics of the data were obviously poor. Much more data were definitely needed.
(3) Atmospheric neutrino flux had large uncertainty. Their systematic errors were not sufficiently small for studies of neutrino oscillations.
(4) Independent confirmation by completely different type of experiment was required.
From middle of the 1990s, experimental efforts to settle these problems one by one were started. Especially, long-baseline neutrino-oscillation experiments, the main subject of this article, contributed for the third and fourth problems.
2 E261A experiment (1992)(1993)(1994) The e/µ identification in water Cherenkov detectors played a crucial role in the analysis of the muon neutrino deficit. However, the e/µ identification had been examined only by Monte Carlo events. The E261A experiment [11] in KEK Proton Synchrotron (KEK-PS) was executed between 1992 and 1994. It was a "beam test" of the water Cherenkov detector for a verification of the particle identification capability. A pipe from the North Counter Hall was inserted to the tank as shown in Fig. 3 (left).
Electrons or muons from the KEK-PS were injected along the beam pipe. Charged particles which travel in the pipe were observed in the water Cherenkov detector just after they exited from the end from the pipe. They had the same geometry as neutrino interactions at the end of the pipe.
The particle kinds could be known by the threshold-type gas Cherenkov detector and time-of-flight counters along the beam pipe. The momentum was controlled by the bending magnets in the North Counter Hall.
The same ring reconstruction program and e/µ identification algorithm as Kamiokande were applied using charge/timing information obtained from the PMTs. e-likelihood (L e ) and µ-likelihood (L µ ) were calculated respectively. From a comparison between L e and L µ , particle ID was judged. The result of the particle identification is shown in Fig. 4. The particle   identification algorithm could clearly separate electron beam events and muon beam events.
It was experimentally verified that the e/µ identification capability was better than 99%. The possibility that the atmospheric muon neutrino deficit was due to poor identification of the water Cherenkov detectors was clearly excluded.  At the 18th International Conference on Neutrino Physics and Astrophysics (NEUTRINO 1998) in Takayama [12], the Super-Kamiokande collaboration announced the discovery of atmospheric neutrino oscillations with a statistical significance of 6.2σ. Just after the conference, the results were officially published [13] based on 4654 atmospheric neutrino events accumulated in 535 days, corresponding to 33.0 kton·yr.
In the paper, the number of electron neutrinos well agreed with expectation, but the number of muon neutrinos was clearly smaller than the expectation in all energy regions as case overlapped at 1 3 10 , Dm , 4 3 10 eV for sin 2 2u 1.
As a cross-check of the above analyses, we have reconstructed the best estimate of the ratio L͞E n for each event. The neutrino energy is estimated by applying a correction to the final state lepton momentum. Typi-current interactions in the data sample. Using the current sample, oscillations between n m and n t are indistinguishable from oscillations between n m and a noninteracting sterile neutrino. Figure 2 shows the Super-Kamiokande results overlaid with the allowed region obtained by the Kamiokande The constraints on the neutrino oscillation parameters (∆m 2 , sin 2 2θ) were obtained as shown in Fig. 6. The data were consistent with two-flavor ν µ ↔ ν τ oscillation with sin 2 2θ > 0.82 and 5 × 10 −4 eV 2 < ∆m 2 < 6 × 10 −3 eV 2 at 90% confidence level. The best fit parameters are sin 2 2θ = 1.0 and ∆m 2 = 2.2 × 10 −3 eV 2 After more than 20 years, this parameter region still agrees well with the updated numbers; sin 2 θ = 0.545 ∼ 0.547 and |∆m 2 | = (2.453 ∼ 2.546) × 10 −3 eV 2 , which are given in PDG 2020 [14]. 6 VOLUME 81, NUMBER 8 The 68%, 90%, and 99% confidence intervals are shown for sin 2 2u and Dm 2 for n m $ n t two-neutrino oscillations based on 33.0 kton yr of Super-Kamiokande data. The 90% confidence interval obtained by the Kamiokande experiment is also shown.
As a cross-check of the above analyses, we have reconstructed the best estimate of the ratio L͞E n for each event. The neutrino energy is estimated by applying a correction to the final state lepton momentum. Typi-cally, final state leptons with p of the incoming neutrino ener p 1 GeV͞c. The neutrino mated following Ref. [18] usi energy and the reconstructed l Figure 4 shows the ratio of FC e-like and m-like events with tion of L͞E n , compared to the oscillations with our best-fit pa show no significant variation i events show a significant defic L͞E n , the n m have presumably cillations and have averaged initial rate.
The asymmetry A of the e-lik is consistent with expectations tions and two-flavor n e $ n m o This is in agreement with recen experiment [22]. The LSND e appearance of n e in a beam o pions [23]. The LSND resu present results if they are obse With the best-fit parameters for expect a total of only 15-20 current interactions in the data sample, oscillations between n m able from oscillations between sterile neutrino. Figure 2 shows the Super-K with the allowed region obta Constraints on neutrino oscillation parameters given in Ref. [13]. The 68%, 90%, and 99% confidence intervals are shown for sin 2 2θ and ∆m 2 for ν µ ↔ ν τ two-neutrino oscillations based on 33.0 kt·yr of Super-Kamiokande data. The 90% confidence interval obtained by the Kamiokande experiment is also shown.

K2K experiment (1999-2004)
After the drastic improvement of the statistics of the neutrino events in Super-Kamiokande, the remaining key issue was the neutrino source used for experiments. The calculation of atmospheric neutrino flux was based on many ambiguous measurements. They are primary proton (and heavier nuclei) fluxes, geomagnetic field including effects from solar activity, hadronic interaction models, and atmospheric temperature. All of these measurements had large uncertainties [15]. The atmospheric muon neutrino deficit papers claimed that even though absolute atmospheric neutrino fluxes have large uncertainty, the ν e /ν µ ratio is robust. However, it is obvious that atmospheric neutrinos were not well understood for the final confirmation of neutrino oscillations. In addition, high energy physicists strongly hope to examine neutrino oscillations using their own neutrino beam. Artificial neutrino beam can be controlled by themselves, and the neutrino fluxes just after their production can be measured by physicists directly.  The first long-baseline neutrino-oscillation experiment was K2K (KEK to Kamioka) experiment started in 1999 [17]. A muon neutrino beam generated at KEK was shot toward the Super-Kamiokande detector located 250 km away from KEK. The purpose of the experiment was an examination of the ν µ ↔ ν τ oscillation reported by Kamiokande and Super-Kamiokande using an artificial neutrino beam. Two near detectors were constructed 300 m downstream of the target. They were the "one kton water Cherenkov detector (1kt)" and "Fine-Grained detector (FGD)". The schematic view of the near detectors is shown in Fig. 8.
The 1kt detector was a 1/50 miniature of the Super-Kamiokande detector. Since the experimental technology was exactly the same as that of the far detector, systematic errors related to the detection method were cancelled out, and direct comparisons of the data between the near detector and the far detector were possible. The FGD consisted of four detector components. They were a scintillating fiber tracker with water target, trigger counter, lead glass counters, and muon range detector. The lead glass counters were replaced with a SciBar detector in the second half of the experiment. The purpose of the FGD was to obtain precise measurements of neutrino beam properties. From the analysis of the near detector data, many properties of the neutrino beam were experimentally obtained. Firstly, the energy spectrum of the beam was precisely calculated.  Table 1 The criteria of the KEK beam neutrino event selection in the Super-Kamiokande detector were almost the same as those for atmospheric neutrino events. One additional condition was the coincidence with the neutrino beam period because the neutrino beam period was only  Among the 112 neutrino events, 58 events were single ring µ-like events, which were thought to be generated by quasi-elastic charged current interaction, For these events, neutrino energy (E ν ) can be calculated from the muon energy and opening angle from the neutrino travel direction (θ µ ).
The neutrino energy spectrum is shown in Fig. 9. The result showed a clear distortion in the 0.5-1.0 GeV range, which reflects the energy dependence of neutrino survival probability.
Both the total number of neutrino events and the shape of the neutrino energy spectrum showed clear disagreement with the expectation for null oscillation. If null oscillation was assumed, such poor agreements happened with a probability of 0.0015%(4.3σ).

Fig. 10
Constraints for ν µ ↔ ν τ neutrino oscillation parameter region in the (∆m 2 , sin 2 2θ) plane by the K2K experiment. The constraints from the Super-Kamiokande experiment are also shown.
The constraints agreed with atmospheric neutrino results from Super-Kamiokande. This is the first confirmation of ν µ ↔ ν τ oscillation by an artificial neutrino beam.

MINOS experiment (2005-2012)
Although the K2K experiment confirmed ν µ ↔ ν τ neutrino oscillation by an artificial neutrino beam, it was not recognized as an experiment that was perfectly independent from Super-Kamiokande. This was because the K2K experiment used Super-Kamiokande as the far detector, and the members of collaborations had a large overlap with each other.
The first completely independent experiment was the MINOS experiment [18]. The MINOS experiment was a long-baseline neutrino-oscillation experiment using the FNAL 120 GeV Main Injector (NuMI) and far detector in Soudan Mine, 735 km away. The far detector was a "sandwich" of iron plate of 2.54 cm thickness and scintillator of 1.00 cm thickness.
The total volume was 5.4 kton. They were in 1.3 Tesla of magnetic field. A 0.98-kton near detector of similar design was also constructed in FNAL.
where L km is the distance from the target, E GeV is the neutrino energy, and jm 2 32 j [38] is measured in eV 2 =c 4 . The FD data are binned in reconstructed event where 336±14 events were expected if no oscillation was assumed. A distortion of the energy spectrum which was a strong indication of neutrino oscillation was also found, as shown in Fig. 11.
The data were consistent with muon neutrino disappearance via oscillations with sin 2 2θ 23 > 0.87 (68% C.L.) and ∆m 2 32 = (2.74 +0.44 −0.27 ) × 10 −3 eV 2 The result was consistent with Super-Kamiokande and K2K, and was the first perfectly independent and convincing confirmation of the ν µ ↔ ν τ neutrino oscillation discovered by Super-Kamiokande. The independence includes different detector type, different neutrino source, and different collaboration members. 13 6 Summary and beyond The atmospheric muon neutrinos deficit observed by Kamiokande was thought to be evidence of ν µ ↔ ν τ neutrino oscillation. The evidence was experimentally examined and ν µ ↔ ν τ oscillation was finally confirmed by contributions from many experiments, E261A, Super-Kamiokande, K2K, and MINOS. It was widely recognized that ν µ ↔ ν τ oscillation was discovered by Super-Kamiokande experiment because of its large event numbers and sufficient statistical significance. The Nobel Prize in Physics 2015 was awarded to Prof. T.
Kajita of the Super-Kamiokande collaboration "for the discovery of neutrino oscillations, which shows that neutrinos have mass".
After independent discoveries of ν µ ↔ ν τ and ν e ↔ ν µ oscillations, study of neutrino oscillations was extended to three flavor oscillations [24]. In the framework of three flavor oscillations, the mass matrix, which expresses the correlation between the flavor eigenstates and the mass eigenstates, has six parameters. Among these six parameters, the remaining unknown parameters were mixing angle between first and third generation, θ 13 , and the CP violation phase, δ CP .
Determination of the remaining unknown parameters became the most important research subject of neutrino experiments from the middle of the 2000s. The appearance of electron neutrinos in the muon neutrino beam, which is evidence of finite θ 13 , was found by the T2K experiment [25]. Possible evidence of the CP violation phase was found from the difference of the oscillation probabilities between neutrino and anti-neutrino also by the T2K experiment [26]. There were also contributions from NOvA experiment [27], which is another long-baseline neutrino-oscillation experiment in the United States. The Hyper-Kamiokande experiment [28] and DUNE experiment [29] for the precise measurement of the CP violation phase are in preparation. However, these advances are outside of the scope of this document, and are not described in this article.
The evidences for neutrino oscillations, both ν µ ↔ ν τ and ν e ↔ ν µ , observed by Kamiokande led to many discoveries and progresses in neutrino physics. Pioneering contributions from Prof. M. Koshiba should be emphasized. 14