Highlight Talk from Super-Kamiokande

: Super-Kamiokande (SK), a 50 kton water Cherenkov detector in Japan, is observing both atmospheric and solar neutrinos. It is also searching for supernova (relic) neutrinos, proton decays and dark matter-like particles. A three-ﬂavor oscillation analysis was conducted with the atmospheric neutrino data to study the mass hierarchy, the leptonic CP violation term, and other oscillation parameters. In addition, the observation of solar neutrinos gives precise measurements of the energy spectrum and oscillation parameters. In this proceedings, we given an overview of the latest results from SK and the prospect toward the future project of SK-Gd.


Introduction
A theoretical framework of neutrino oscillation has been established in the past 50 years [1,2]. Neutrino physics has been dominated by the measurement of oscillation parameters and such measurements suggest that neutrinos are massive and mixing in the lepton sector [3]. Within the threeflavor framework, three mixing angles (θ 12 , θ 23 , and θ 13 ) and two mass splittings (∆m 2 21 and ∆m 2 32,31 ) are measured among neutrino experiments.
However, more precise measurements are required to reveal CP violation phase and neutrino mass hierarchy. In addition, another interest is the change of the probability of neutrino oscillation when neutrinos pass through matter [4,5]. To address these unknown properties of neutrinos, any difference between neutrino and anti-neutrino should be tested among neutrino experiments.

Super-Kamiokande Detector
The Super-Kamiokande (SK) is a water Cherenkov detector located at 1000 m (2700 m water equivalent) below the top of Mt. Ikenoyama in Gifu prefecture, Japan [6]. It is a cylindrical stainless tank structure and contains 50 ktons of ultra pure water. (The resistivity of the purified water is close to the chemical limit of 18.07 MΩ·cm. Because of its high purity, the water transparency for light in water in the tank is longer than 100 m.) The detector is divided into two regions by the detector structure to separate themselves optically with Tyvek sheet [7]: one is the inner detector (ID) and the other is the outer detector (OD). The ID serves as the target of interactions and the OD is used to veto external cosmic ray muon. In the ID detector, the diameter (height) of the cylindrical tank is 33.8 m (36.2 m). It contains 32 kton of water and holds 11,129 inward-facing 20-inch photomultipliers (PMTs) [8] to observe the Cherenkov light produced by penetrating charged particles. On the other hand, the diameter (height) of the OD tank is 39.3 m (41.4 m). It holds 1885 outward-facing 8-inch PMTs to detect cosmic ray muons in the OD. The configuration of detector and performance is described in Refs. [6,7].
The first phase of the SK experiment (SK-I) began with the original configuration in April 1996. The latter phases are described in Table 1. On May 2018, the fourth phase of SK (SK-IV) ended physics data collection to refurbish the detector toward the next project of SK (SK-Gd) described in Section 5.  [11,12] The ring pattern of the observed Cherenkov light produced by charged particles enables the detector to reconstruct the initial interaction vertex and the energy. With this water Cherenkov technique, SK can study many interactions between neutrinos and nucleus as well as proton decay in the energy range from a few MeV to tens of GeV. Therefore, SK is a multi-purpose detector with rich physics targets. SK has obtained many physics results, such as atmospheric neutrino [13][14][15], solar neutrino [16,17], supernova (relic) neutrino [18], proton decay [19,20], dark matter-like particle (for example, weakly interacting massive particles (WIMPs) [21][22][23][24], neutralino [25][26][27] and boosted dark matter [28][29][30]) [31,32] and other exotic physics beyond the standard model [33,34]. The publications from the SK collaboration are summarized in Ref. [35].
In this proceedings, the results described in Ref. [14,15] as well as the updated results of Ref. [17] are briefly discussed. In addition, the future upgrade of the SK detector is also described.

Introduction
Atmospheric neutrinos are produced by interactions of primary cosmic rays with nuclei in upper atmosphere. They mainly consist of ν e and ν µ produced from the decays of charged mesons and muons and travel 10-13,000 km depending on the production point. Atmospheric neutrino oscillations are mainly described as the oscillation of ν µ → ν τ , which depends on the mixing angle θ 23 and the mass splitting ∆m 2 32,31 . Because the pattern of neutrino oscillations depends on the ratio of the travel length and the energy of neutrino (L/E), atmospheric neutrinos are an excellent tool for studies of neutrino oscillation. Their flux and energy distribution are well modeled [36][37][38][39] and are precisely measured by SK at Kamioka experimental site [13].
In particular, upward-going electron neutrinos passing through the earth give important information of neutrino properties because the resonant enhancement of the ν µ → ν e oscillation probability in multi-GeV region is expected due to the effect of θ 13 and earth's matter [40][41][42]. The resonance occurs only for electron neutrinos (anti-neutrinos) when the mass hierarchy is normal (inverted). In the same energy region, θ 23 octant also affects the amplitude of the resonance. In the sub-GeV region, the CP value affects the absolute flux of electron neutrinos [43].

Three-Flavor Oscillation Analysis
A study of the neutrino oscillation parameters (sin 2 θ 23 , ∆m 2 32 , δ CP and mass hierarchy) was performed using 5326 days of atmospheric neutrino data taken from SK-I to SK-IV. In the high energy region above 100 MeV, the neutrino events are categorized into three types, namely fully contained (FC), partially contained (PC) and upward-going muon (UPMU), based on the event topology. In addition, the atmospheric neutrino samples are divided into sub-groups, based on for example the energy range (sub-GeV and multi-GeV), e-like or µ-like of events and the number of Cherenkov rings. In particular, multi-GeV and e-like samples are further divided into neutrino-like and anti-neutrino-like samples to obtain sensitivity to the mass hierarchy. Finally, the atmospheric neutrino samples are divided into 19 samples in total. Figure 1a shows the momentum distribution and zenith angle distribution of atmospheric neutrino samples. Figure 1b shows the constraints on the neutrino nixing parameters from SK atmospheric neutrino data assuming sin 2 θ 13 = 0.0219 ± 0.0012 [44] according to the short baseline reactor measurements.
The obtained values in this analysis are summarized in Table 2. The oscillation values are in good agreement with other experiments, such as T2K, NOvA, IceCube and MINOS [45][46][47][48][49]. Based on the minimum value of χ 2 , the SK data prefer the normal hierarchy over the inverted hierarchy with
(a) (b)  [46], NovA [47], IceCube [48] and MiNOS [49]) assuming the normal hierarchy. The original figures are adapted from Ref. [14]. Table 2. Result of oscillation analysis from atmospheric neutrino data taken in SK assuming sin 2 θ 13 = 0.0219 ± 0.0012 [44]. As shown in Figure 1b, T2K's measurements of sin 2 θ 23 , and ∆m 2 32 are more constraining than those of SK [45,46]. Therefore, an external constraint with T2K experiment enhances the sensitivity of this analysis when combining with the atmospheric neutrino data in SK. Figure 2 shows the constraint on the neutrino parameters from a combined fit with SK atmospheric neutrino data with T2K public data.

IH NH
IH NH IH NH Figure 2. The constraint on the neutrino parameters from a combined fit with SK atmospheric neutrino data and the model of T2K experiment assuming sin 2 θ 13 = 0.0219 ± 0.0012 [44]. The original figure is adapted from Ref. [14].
The obtained values with the T2K constraints are summarized in Table 3. Based on the minimum value of χ 2 , the SK plus T2K data prefer the normal hierarchy over the inverted hierarchy with

Tau Neutrino Appearance
In the framework of three-flavor neutrino oscillation, neutrinos produced in a specific lepton flavor can change to a different flavor during their travel. In the upward neutrinos, ν µ can travel enough to oscillate to ν τ while the intrinsic ν τ in the atmospheric neutrino flux are negligible because of its small production rate [50].
To search for ν τ appearance in the atmospheric neutrinos, the charged current reaction (CC) of ν τ in SK have been searched. The CC ν τ reaction produces single tau lepton in the water. Then, tau lepton decays into secondary particles soon after its production because of short life-time. Finally, cascade-like events (with many Cherenkov rings) are detected in the SK detector. The cross-section of ν τ is greatly suppressed because the τ lepton has large mass relative to electron and muon at the low energy. Therefore, the search for ν τ in the SK has an energy threshold of 3.5 GeV.
To predict the rate of both CC tau interaction and atmospheric neutrino background, MC simulation is used based on the neutrino interaction model as well as the detector response of SK. SK performed a search for CC-event due to ν τ with a neural network algorithm developed in Ref. [51]. The selection efficiencies for this analysis are 86% for the ν τ CC event and 23% for the background of other atmospheric neutrino events. Although it is hard to identify ν τ CC reaction by reaction in this analysis, CC ν τ event can be statistically found over background in the up-going sample. The analysis was performed using two-dimensional unbinned maximum likelihood fit to the observed data including systematic uncertainties: where PDF Tau (PDF BG ) is a probability density function for τ-like (background), α is a scaling parameter (no τ contribution when α = 0 while MC expected when α = 1), ε i is a magnitude of ith systematic uncertainty and PDF i is a probability density function for ith systematic uncertainty. Figure 3a shows the zenith angle distribution of τ-like events overlaid with the MC prediction without the τ contribution. A clear excess, 338.1 ± 72.7 events, is observed over the background in the up-going bins (gray in Figure 3a). Assuming the normal hierarchy, the value of parameter α is 1.47 ± 0.32 (stat.+syst.), excluding the hypothesis of no-τ-appearance at a significance of 4.6σ. Among neutrino experiments, the cross-section of CC ν τ has been measured by DONUT, SK and OPERA [15,[51][52][53] while the cross-section of both neutral current (NC) and CC has been measured by IceCube [54]. (Comparison of the parameter α among OPERA, SK and IceCube is discussed in Ref. [54]. Currently, they are consistent with the standard neutrino oscillation framework within their uncertainties.) Based on the atmospheric neutrino flux model [39] and the observed events, the cross-section of the CC reaction is measured as (0.94 ± 0.20) × 10 −38 cm 2 between 3.5 GeV and 70 GeV, as shown in Figure 3b. This result is consistent with the standard model within 1.5σ.

Introduction
Solar neutrinos are produced by the nuclear fusion reaction, 4p → α + 2e + + 2ν e , in the core of the sun. Electron neutrinos (ν e ) produced in the sun are so-called pp, pep, 7 Be, 8 B and hep neutrinos as well as CNO neutrinos. Their fluxes are well predicted by the standard solar model [55] and are measured by several techniques, such as radiochemical (Homestake [56], SAGE and Gallex/GNO [57]), water Cherenkov (Kamiokande [58], SK and SNO [59]) and liquid scintillator (Borexino [60] and KamLAND [61]). Solar neutrino flux measurements from Super-Kamiokande (SK) [62] and the Sudbury Neutrino Observatory (SNO) [63] have provided direct evidence for solar neutrino flavor conversion. However, there is still no clear evidence that this solar neutrino flavor conversion is indeed due to neutrino oscillations alone [64]. Several models, which are combinations of the neutrino oscillation plus the physics beyond the standard model, have been proposed to demonstrate the current experiment data, for example sterile neutrinos [65,66], mass-varying neutrino [67] and non-standard interaction [68,69].
One of interesting physics motivations among solar neutrino experiments is to search for the matter effect, which is the so-called Mikheyev-Smirnov-Wolfenstein (MSW) effect [4,5]. The MSW effect leads to a resonant conversion of the higher energy solar neutrinos (especially 8 B) within the sun and results in an about 30% level of the survival probability above a few MeV (Up-turn).
SK searches for the "Spectrum up-turn" by measuring the recoil electron energy spectrum since the recoil electron energy spectrum reflects the survival probability of the electron neutrinos. To precisely test the MSW effect in the energy spectrum, several calibration source (or devices) have been used in SK. For example, the electron LINAC [70], which generates electron with uniform energy, and the deuterium-tritium neutron generator, which generates 16 N radioisotopes [71], are used to determine the energy scale and both energy and angle resolution. In addition, Ni-Cf calibration source [7] is used to estimate the resolution of the reconstructed position and the detection efficiency of the low energy neutrino-like event. Due to those calibrations, the systematic uncertainty on the 8 B solar neutrino flux measurement has achieved at ±1.7% in SK-IV.
In 2016, the Super-Kamiokande collaboration released a paper about the solar neutrino analysis results [17]. In this proceedings, the updated results, except for the day/night flux asymmetry measurement [16], are presented using data taken through the end of December 2017 (SK-IV 2860-day dataset). The total lifetime throughout the different phases of SK [72][73][74] is 5695 days.

Flux Measurement
The SK detector observes solar neutrinos via the elastic scattering between the solar neutrinos and the electron in pure water. In the case of ν-e interaction, the direction of the recoil electron is highly correlated with the direction of the incident neutrinos. Figure 4a shows the distribution of cosine between the reconstructed direction of observed recoil electrons and the direction of the sun. Using 2860 days of data in SK-IV, 55, 729 +363 −361 (stat.) events are observed over the background. Adding the solar neutrino events observed in other phases, the total number of the solar neutrino events reaches about 90,000 events thus far. Based on these data, the 8 B solar neutrino flux is determined to be (2.33 ± 0.04) × 10 6 /cm 2 /s assuming a pure electron neutrino flavor content. The ratio between the SK result and the SNO NC flux (5.25 × 10 6 /cm 2 /s) [75] becomes 0.4432 ± 0.0084. Since the SK has observed solar neutrinos for more than 20 years, this long term observation covers nearly two solar activity cycles. Figure 4b shows the SK yearly flux measured throughout the different phases of SK together with the corresponding sun spot number [76]. Using the present data, the χ 2 is calculated with the total experimental uncertainties as χ 2 = 21.57/21, where 21 is the degree of freedom for χ 2 . This corresponds to a probability of 41.4%. The solar rate measurements in SK are fully consistent with a constant solar neutrino flux emitted by the sun.

Energy Spectrum Analysis
Because of several efforts to reduce background in the SK water (induced by radioisotopes in pure water, especially 214 Bi) [77,78], SK-IV has achieved the lowest background among all SK phases. Finally, the energy threshold in SK-IV have been lowered at 3.5 MeV in recoil energy kinetic energy (SK-I: 4.5 MeV, SK-III: 4.0 MeV) and this enables SK to measure the solar neutrino energy spectrum with high sensitivity. In addition, on May 2015, the trigger threshold was changed from 34 observed PMT signals within 200 nsec to 31 hits [12,79]. With this lower threshold, the detection efficiency between 3.5 MeV and 4.0 MeV is improved from ∼86% to ∼100%. This improvement leads the further reduction of the statistics uncertainty below 5 MeV in SK-IV.
Although an energy of the incident neutrinos is not directly measured in the SK detector, the neutrino energy spectrum can be extracted from the recoil electron energy spectrum in SK. The energy spectrum of recoil electrons are extracted using an extended maximum likelihood fit [72].
The number of expected solar neutrino interactions without the neutrino oscillations is estimated by using the MC simulation considering the cross-section of the ν-e elastic scattering, recoil electron kinematics, the response of the SK detector (PMT and electronics) and the performance of the SK detector (energy scale, energy resolution and so on). After the MC production above, the number of the observed solar neutrino interactions is compared with the expected number of events, thus the survival probability of the electron neutrinos produced in the sun is obtained. Figure 5a shows the combined energy spectrum from SK-I to SK-IV with the predictions of the MSW effect assuming the current oscillation parameters described below. It is noted that all SK phases are combined without regard to energy resolution or systematic uncertainties in Figure 5a, but those uncertainties are taken into account in the χ 2 calculation between the data and the prediction. Comparing χ 2 between the data (black) and the predictions (green or blue), the energy spectrum of SK is consistent within ∼1.2σ with the MSW up-turn for the solar global best-fit parameters (green in Figure 5b) while it disfavors ∼2σ with the MSW up-turn for KamLAND best-fit parameters (blue in Figure 5b).

Physics Motivation
Diffused supernova neutrinos (relic neutrinos) are produced by past explosions in the universe. The galactic formation rate can be understood when the production rate of relic neutrinos is known.
Since the cross-section of the inverse beta decay reaction (IBD) between anti-electron neutrino and proton (ν e + p → e + + n) is relatively large below 100 MeV, there is a chance to search for relic neutrinos between 10 MeV and 30 MeV over backgrounds of reactor, solar and atmospheric neutrinos [85,86]. SK has measured the flux of relic neutrinos with the observed energy spectrum [87] as well as the delayed coincidence technique of neutron tagging on proton [18]. However, the current limit of flux is one order of magnitude higher than some of the theoretical models because the delayed signal of 2.2 MeV gamma ray from neutron capture on proton is difficult to detect in the current SK, where the detection efficiency of neutron tagging is only ∼18% [18,88].
To enhance the sensitivity to relic neutrinos, further reduction of background is required. For this purpose, adding 0.2% of gadolinium sulfate (Gd 2 (SO 4 ) 3 ) into the 50 kton of water tank enables the SK detector to tag neutron produced by the IBD with high efficiency [89]. Since Gd has larger cross-section for thermal neutrino than proton (five orders of magnitude) and emits ∼8 MeV of gamma rays, the detection efficiency for the IBD ofν e is dramatically improved to be 90% level after adding Gd into SK (SK-Gd).

Tank Refurbish Work and Future Plan
On 30 May 2018, SK stopped taking physics data to start the tank refurbishment work toward SK-Gd. This refurbishment work aims to replace broken PMTs in both ID and OD, to newly install the water piping line of the new water system for SK-Gd, and to stop water leak from the water tank by sealing the stainless tank wall.
The current plan for the implementation of SK-Gd has three steps. The first is the tank refurbishment, filling water into the tank and then the recirculation of water until the water transparency achieves a good quality. The second is loading Gd 2 (So 4 ) 3 up to 0.02% level, where the neutron tagging efficiency on Gd achieves about 50%. Under this condition, we will evaluate the performance of the detector and estimate the background level. The third is loading Gd 2 (So 4 ) 3 up to 0.2% level, where the efficiency finally achieves a 90% level. It is noted that the detector performance for neutron tagging is evaluated with a special calibration by putting an apparatus of Am/Be-incorporated BGO crystal into the water tank [88]. Based on the calibration result and MC simulation considering Gd-doped water, the detection efficiency of the neutron tagging in SK with Gd is estimated.

Conclusions
Super-Kamiokande is a multi-purpose detector with rich physics targets using the water Cherenkov technique. We measured the neutrino oscillation parameters as well as δ CP using atmospheric neutrinos with the external constraint of T2K data. The SK+T2K data prefer the normal hierarchy over the inverted hierarchy with ∆χ 2 = −5.27. An analysis searching for the appearance of ν τ in an atmospheric neutrino sample was conducted. The significance of 4.6σ was observed assuming the normal hierarchy.
Due to the large statistics of solar neutrino observation in SK, precise measurements of the solar neutrino flux and the energy spectrum were made. No significant correlation between the 8 B solar neutrino flux and the sunspot number was observed. No distortion of the energy spectrum has been observed yet. The value of ∆m 2 21 obtained from the SK solar neutrino data combined with the other solar neutrino experiments has a tension with that from KamLAND reactor neutrino measurements by about 2σ.
To detect supernova relic neutrinos, we are planning to dissolve gadolinium in the SK's water tank to enhance the tagging efficiency of neutrino produced via the inverse beta decay between the anti-electron neutrino and the proton in water. The refurbish works toward SK-Gd started on 30 May 2018.
Author Contributions: These authors contributed equally to this work.
Funding: This work was supported by JSPS KAKENHI, Grant-in-Aid for Young Scientific Research (B) with Grant Number 17K17880 (Y.N.). We gratefully acknowledge cooperation of the Kamioka Mining and Smelting Company. The Super-Kamiokande experiment was built and has been operated with funding from the Japanese Ministry of Education, Science, Sports and Culture, and the U.S. Department of Energy.