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The charge-conjugation and parity-reversal (CP) symmetry of fundamental particles is a symmetry between matter and antimatter. Violation of this CP symmetry was first observed in 1964 1 , and CP violation in the weak interactions of quarks was soon established 2 . Sakharov proposed 3 that CP violation is necessary to explain the observed imbalance of matter and antimatter abundance in the Universe. However, CP violation in quarks is too small to support this explanation. So far, CP violation has not been observed in non-quark elementary particle systems. It has been shown that CP violation in leptons could generate the matter–antimatter disparity through a process called leptogenesis 4 . Leptonic mixing, which appears in the standard model’s charged current interactions 5 , 6 , provides a potential source of CP violation through a complex phase δ CP , which is required by some theoretical models of leptogenesis 7 – 9 . This CP violation can be measured in muon neutrino to electron neutrino oscillations and the corresponding antineutrino oscillations, which are experimentally accessible using accelerator-produced beams as established by the Tokai-to-Kamioka (T2K) and NOvA experiments 10 , 11 . Until now, the value of δ CP has not been substantially constrained by neutrino oscillation experiments. Here we report a measurement using long-baseline neutrino and antineutrino oscillations observed by the T2K experiment that shows a large increase in the neutrino oscillation probability, excluding values of δ CP that result in a large increase in the observed antineutrino oscillation probability at three standard deviations (3 σ ). The 3 σ confidence interval for δ CP , which is cyclic and repeats every 2π, is [−3.41, −0.03] for the so-called normal mass ordering and [−2.54, −0.32] for the inverted mass ordering. Our results indicate CP violation in leptons and our method enables sensitive searches for matter–antimatter asymmetry in neutrino oscillations using accelerator-produced neutrino beams. Future measurements with larger datasets will test whether leptonic CP violation is larger than the CP violation in quarks. The T2K experiment constrains CP symmetry in neutrino oscillations, excluding 46% of possible values of the CP violating parameter at a significance of three standard deviations; this is an important milestone to test CP symmetry conservation in leptons and whether the Universe’s matter–antimatter imbalance originates from leptons.

Hyper-Kamiokande consists of two identical water-Cherenkov detectors of total 520 kt, with the first one in Japan at 295 km from the J-PARC neutrino beam with 2.5$^\\circ$ off-axis angles (OAAs), and the second one possibly in Korea at a later stage. Having the second detector in Korea would benefit almost all areas of neutrino oscillation physics, mainly due to longer baselines. There are several candidate sites in Korea with baselines of 1000–1300 km and OAAs of 1$^\\circ$–3$^\\circ$. We conducted sensitivity studies on neutrino oscillation physics for a second detector, either in Japan (JD $\\times$ 2) or Korea (JD + KD), and compared the results with a single detector in Japan. Leptonic charge–parity (CP) symmetry violation sensitivity is improved, especially when the CP is non-maximally violated. The larger matter effect at Korean candidate sites significantly enhances sensitivities to non-standard interactions of neutrinos and mass ordering determination. Current studies indicate the best sensitivity is obtained at Mt. Bisul (1088 km baseline, $1.3^\\circ$ OAA). Thanks to a larger (1000 m) overburden than the first detector site, clear improvements to sensitivities for solar and supernova relic neutrino searches are expected.

Hyper-Kamiokande will be a next-generation underground water Cherenkov detector with a total (fiducial) mass of 0.99 (0.56) million metric tons, approximately 20 (25) times larger than that of Super-Kamiokande. One of the main goals of Hyper-Kamiokande is the study of $CP$ asymmetry in the lepton sector using accelerator neutrino and anti-neutrino beams. In this paper, the physics potential of a long-baseline neutrino experiment using the Hyper-Kamiokande detector and a neutrino beam from the J-PARC proton synchrotron is presented. The analysis uses the framework and systematic uncertainties derived from the ongoing T2K experiment. With a total exposure of 7.5 MW $\\times 10^7$s integrated proton beam power (corresponding to $1.56 \\times 10^{22}$ protons on target with a 30 GeV proton beam) to a $2.5^\\circ$ off-axis neutrino beam, it is expected that the leptonic $CP$ phase $\\delta _{CP}$ can be determined to better than 19 degrees for all possible values of $\\delta _{CP}$, and $CP$ violation can be established with a statistical significance of more than $3\\,\\sigma$ ($5\\,\\sigma$) for $76{\\%}$ ($58{\\%}$) of the ${\\delta _{CP}}$ parameter space. Using both $\\nu _e$ appearance and $\\nu _\\mu$ disappearance data, the expected 1$\\sigma$ uncertainty of $\\sin ^2\\theta _{23}$ is 0.015(0.006) for $\\sin ^2\\theta _{23}=0.5(0.45)$.

Abstract A new event reconstruction algorithm based on a maximum likelihood method has been developed for Super-Kamiokande. Its improved kinematic and particle identification capabilities enable the analysis of atmospheric neutrino data in a detector volume 32% larger than previous analyses and increase the sensitivity to the neutrino mass hierarchy. Analysis of a 253.9 kton$\\cdot$year exposure of the Super-Kamiokande IV atmospheric neutrino data has yielded a weak preference for the normal hierarchy, disfavoring the inverted hierarchy at 74% assuming oscillations at the best fit of the analysis.

Bayesian analysis results require a choice of prior distribution. In long-baseline neutrino oscillation physics, the usual parameterisation of the mixing matrix induces a prior that privileges certain neutrino mass and flavour state symmetries. Here we study the effect of privileging alternate symmetries on the results of the T2K experiment. We find that constraints on the level of CP violation (as given by the Jarlskog invariant) are robust under the choices of prior considered in the analysis. On the other hand, the degree of octant preference for the atmospheric angle depends on which symmetry has been privileged.

Bayesian analysis results require a choice of prior distribution. In long-baseline neutrino oscillation physics, the usual parameterisation of the mixing matrix induces a prior that privileges certain neutrino mass and flavour state symmetries. Here we study the effect of privileging alternate symmetries on the results of the T2K experiment. We find that constraints on the level of CP violation (as given by the Jarlskog invariant) are robust under the choices of prior considered in the analysis. On the other hand, the degree of octant preference for the atmospheric angle depends on which symmetry has been privileged.

The T2K experiment presents new measurements of neutrino oscillation parameters using$$19.7(16.3)\\times 10^{20}$$19.7 ( 16.3 ) × 10 20 protons on target (POT) in (anti-)neutrino mode at the far detector (FD). Compared to the previous analysis, an additional$$4.7\\times 10^{20}$$4.7 × 10 20 POT neutrino data was collected at the FD. Significant improvements were made to the analysis methodology, with the near-detector analysis introducing new selections and using more than double the data. Additionally, this is the first T2K oscillation analysis to use NA61/SHINE data on a replica of the T2K target to tune the neutrino flux model, and the neutrino interaction model was improved to include new nuclear effects and calculations. Frequentist and Bayesian analyses are presented, including results on$$\\sin ^2\\theta _{13}$$sin 2 θ 13 and the impact of priors on the$$\\delta _{\\textrm{CP}}$$δ CP measurement. Both analyses prefer the normal mass ordering and upper octant of$$\\sin ^2\\theta _{23}$$sin 2 θ 23 with a nearly maximally CP-violating phase. Assuming the normal ordering and using the constraint on$$\\sin ^2\\theta _{13}$$sin 2 θ 13 from reactors,$$\\sin ^2\\theta _{23}=0.561^{+0.021}_{-0.032}$$sin 2 θ 23 = 0 . 561 - 0.032 + 0.021 using Feldman–Cousins corrected intervals, and$$\\varDelta {}m^2_{32}=2.494_{-0.058}^{+0.041}\\times 10^{-3}~\\text {eV}^2$$Δ m 32 2 = 2 . 494 - 0.058 + 0.041 × 10 - 3 eV 2 using constant$$\\varDelta \\chi ^{2}$$Δ χ 2 intervals. The CP-violating phase is constrained to$$\\delta _{\\textrm{CP}}=-1.97_{-0.70}^{+0.97}$$δ CP = - 1 . 97 - 0.70 + 0.97 using Feldman–Cousins corrected intervals, and$$\\delta _{\\textrm{CP}}=0,\\pi $$δ CP = 0 , π is excluded at more than 90% confidence level. A Jarlskog invariant of zero is excluded at more than$$2\\sigma $$2 σ credible level using a flat prior in$$\\delta _{\\textrm{CP}},$$δ CP , and just below$$2\\sigma $$2 σ using a flat prior in$$\\sin \\delta _{\\textrm{CP}}.$$sin δ CP . When the external constraint on$$\\sin ^2\\theta _{13}$$sin 2 θ 13 is removed,$$\\sin ^2\\theta _{13}=28.0^{+2.8}_{-6.5}\\times 10^{-3},$$sin 2 θ 13 = 28 . 0 - 6.5 + 2.8 × 10 - 3 , in agreement with measurements from reactor experiments. These results are consistent with previous T2K analyses.

The T2K experiment presents new measurements of neutrino oscillation parameters using $$19.7(16.3)\\times 10^{20}$$ 19.7(16.3)×1020 protons on target (POT) in (anti-)neutrino mode at the far detector (FD). Compared to the previous analysis, an additional $$4.7\\times 10^{20}$$ 4.7×1020 POT neutrino data was collected at the FD. Significant improvements were made to the analysis methodology, with the near-detector analysis introducing new selections and using more than double the data. Additionally, this is the first T2K oscillation analysis to use NA61/SHINE data on a replica of the T2K target to tune the neutrino flux model, and the neutrino interaction model was improved to include new nuclear effects and calculations. Frequentist and Bayesian analyses are presented, including results on $$\\sin ^2\\theta _{13}$$ sin2θ13 and the impact of priors on the $$\\delta _{\\textrm{CP}}$$ δCP measurement. Both analyses prefer the normal mass ordering and upper octant of $$\\sin ^2\\theta _{23}$$ sin2θ23 with a nearly maximally CP-violating phase. Assuming the normal ordering and using the constraint on $$\\sin ^2\\theta _{13}$$ sin2θ13 from reactors, $$\\sin ^2\\theta _{23}=0.561^{+0.021}_{-0.032}$$ sin2θ23=0.561-0.032+0.021 using Feldman–Cousins corrected intervals, and $$\\varDelta {}m^2_{32}=2.494_{-0.058}^{+0.041}\\times 10^{-3}~\\text {eV}^2$$ Δm322=2.494-0.058+0.041×10-3eV2 using constant $$\\varDelta \\chi ^{2}$$ Δχ2 intervals. The CP-violating phase is constrained to $$\\delta _{\\textrm{CP}}=-1.97_{-0.70}^{+0.97}$$ δCP=-1.97-0.70+0.97 using Feldman–Cousins corrected intervals, and $$\\delta _{\\textrm{CP}}=0,\\pi $$ δCP=0,π is excluded at more than 90% confidence level. A Jarlskog invariant of zero is excluded at more than $$2\\sigma $$ 2σ credible level using a flat prior in $$\\delta _{\\textrm{CP}},$$ δCP, and just below $$2\\sigma $$ 2σ using a flat prior in $$\\sin \\delta _{\\textrm{CP}}.$$ sinδCP. When the external constraint on $$\\sin ^2\\theta _{13}$$ sin2θ13 is removed, $$\\sin ^2\\theta _{13}=28.0^{+2.8}_{-6.5}\\times 10^{-3},$$ sin2θ13=28.0-6.5+2.8×10-3, in agreement with measurements from reactor experiments. These results are consistent with previous T2K analyses.

The observation of the recent electron neutrino appearance in a muon neutrino beam and the high-precision measurement of the mixing angle $\\theta _{13}$ have led to a re-evaluation of the physics potential of the T2K long-baseline neutrino oscillation experiment. Sensitivities are explored for CP violation in neutrinos, non-maximal $\\sin ^22\\theta _{23}$, the octant of $\\theta _{23}$, and the mass hierarchy, in addition to the measurements of $\\delta _{{\\rm CP}}$, $\\sin ^2\\theta _{23}$, and $\\Delta m^2_{32}$, for various combinations of $\\nu$-mode and $\\bar {\\nu }$-mode data-taking.With an exposure of $7.8\\times 10^{21}$ protons-on-target, T2K can achieve 1$\\sigma$ resolution of 0.050 (0.054) on $\\sin ^2\\theta _{23}$ and $0.040\\ (0.045)\\times 10^{-3}\\,\\rm {eV}^2$ on $\\Delta m^2_{32}$ for 100% (50%) neutrino beam mode running assuming $\\sin ^2\\theta _{23}=0.5$ and $\\Delta m^2_{32} = 2.4\\times 10^{-3}\\,\\hbox {eV}^2$. T2K will have sensitivity to the CP-violating phase $\\delta _{\\rm {CP}}$ at 90% C.L. or better over a significant range. For example, if $\\sin ^22\\theta _{23}$ is maximal (i.e. $\\theta _{23}=45^\\circ$) the range is $-115^\\circ \\lt \\delta _{\\rm {CP}}\\lt -60^\\circ$ for normal hierarchy and $+50^\\circ \\lt \\delta _{\\rm {CP}}\\lt +130^\\circ$ for inverted hierarchy. When T2K data is combined with data from the NO$\\nu$A experiment, the region of oscillation parameter space where there is sensitivity to observe a non-zero $\\delta _{{\\rm CP}}$ is substantially increased compared to if each experiment is analyzed alone.

Neutrinos from very nearby supernovae, such as Betelgeuse, are expected to generate more than ten million events over 10 s in Super-Kamokande (SK). At such large event rates, the buffers of the SK analog-to-digital conversion board (QBEE) will overflow, causing random loss of data that are critical for understanding the dynamics of the supernova explosion mechanism. In order to solve this problem, two new data-acquisition (DAQ) modules were developed to aid in the observation of very nearby supernovae. The first of these, the SN module, is designed to save only the number of hit photomultiplier tubes during a supernova burst and the second, the Veto module, prescales the high-rate neutrino events to prevent the QBEE from overflowing based on information from the SN module. In the event of a very nearby supernova, these modules allow SK to reconstruct the time evolution of the neutrino event rate from beginning to end using both QBEE and SN module data. This paper presents the development and testing of these modules together with an analysis of supernova-like data generated with a flashing laser diode. We demonstrate that the Veto module successfully prevents DAQ overflows for Betelgeuse-like supernovae as well as the long-term stability of the new modules. During normal running the Veto module is found to issue DAQ vetos a few times per month resulting in a total dead-time less than 1 ms, and does not influence ordinary operations. Additionally, using simulation data we find that supernovae closer than 800 pc will trigger the Veto module, resulting in a prescaling of the observed neutrino data.