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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.

The ICARUS collaboration employed the 760-ton T600 detector in a successful 3-year physics run at the underground LNGS laboratory, performing a sensitive search for LSND-like anomalous ν e appearance in the CERN Neutrino to Gran Sasso beam, which contributed to the constraints on the allowed neutrino oscillation parameters to a narrow region around 1 eV 2 . After a significant overhaul at CERN, the T600 detector has been installed at Fermilab. In 2020 the cryogenic commissioning began with detector cool down, liquid argon filling and recirculation. ICARUS then started its operations collecting the first neutrino events from the booster neutrino beam (BNB) and the Neutrinos at the Main Injector (NuMI) beam off-axis, which were used to test the ICARUS event selection, reconstruction and analysis algorithms. ICARUS successfully completed its commissioning phase in June 2022. The first goal of the ICARUS data taking will be a study to either confirm or refute the claim by Neutrino-4 short-baseline reactor experiment. ICARUS will also perform measurement of neutrino cross sections with the NuMI beam and several Beyond Standard Model searches. After the first year of operations, ICARUS will search for evidence of sterile neutrinos jointly with the Short-Baseline Near Detector, within the Short-Baseline Neutrino program. In this paper, the main activities carried out during the overhauling and installation phases are highlighted. Preliminary technical results from the ICARUS commissioning data with the BNB and NuMI beams are presented both in terms of performance of all ICARUS subsystems and of capability to select and reconstruct neutrino events.

The T2K experiment presents new measurements of neutrino oscillation parameters using protons on target (POT) in (anti-)neutrino mode at the far detector (FD). Compared to the previous analysis, an additional 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 and the impact of priors on the measurement. Both analyses prefer the normal mass ordering and upper octant of with a nearly maximally CP-violating phase. Assuming the normal ordering and using the constraint on from reactors, using Feldman-Cousins corrected intervals, and using constant intervals. The CP-violating phase is constrained to using Feldman-Cousins corrected intervals, and is excluded at more than 90% confidence level. A Jarlskog invariant of zero is excluded at more than credible level using a flat prior in and just below using a flat prior in When the external constraint on is removed, 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 ) × 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.

Abstract We report a measurement of the flux-integrated $\\nu_{\\mu}$ charged-current cross sections on water, hydrocarbon, and iron in the T2K on-axis neutrino beam with a mean neutrino energy of 1.5 GeV. The measured cross sections on water, hydrocarbon, and iron are $\\sigma^{\\rm{H_{2}O}}_{\\rm{CC}} = (0.840\\pm 0.010(\\mathrm{stat.})^{+0.10}_{-0.08}(\\mathrm{syst.}))\\times10^{-38}\\,\\mathrm{cm}^2$/nucleon, $\\sigma^{\\rm{CH}}_{\\rm{CC}} = (0.817\\pm 0.007(\\mathrm{stat.})^{+0.11}_{-0.08}(\\mathrm{syst.}))\\times10^{-38}\\,\\mathrm{cm}^2$/nucleon, and $\\sigma^{\\rm{Fe}}_{\\rm{CC}} = (0.859\\pm 0.003(\\mathrm{stat.})^{+0.12}_{-0.10}(\\mathrm{syst.}))\\times10^{-38}\\,\\mathrm{cm}^2$/nucleon, respectively, for a restricted phase space of induced muons: $\\theta_{\\mu}<45^{\\circ}$ and $p_{\\mu}>$0.4 GeV/$c$ in the laboratory frame. The measured cross section ratios are ${\\sigma^{\\rm{H_{2}O}}_{\\rm{CC}}}/{\\sigma^{\\rm{CH}}_{\\rm{CC}}} = 1.028\\pm 0.016(\\mathrm{stat.})\\pm 0.053(\\mathrm{syst.})$, ${\\sigma^{\\rm{Fe}}_{\\rm{CC}}}/{\\sigma^{\\rm{H_{2}O}}_{\\rm{CC}}} = 1.023\\pm 0.012(\\mathrm{stat.})\\pm 0.058(\\mathrm{syst.})$, and ${\\sigma^{\\rm{Fe}}_{\\rm{CC}}}/{\\sigma^{\\rm{CH}}_{\\rm{CC}}} = 1.049\\pm 0.010(\\mathrm{stat.})\\pm 0.043(\\mathrm{syst.})$. These results, with an unprecedented precision for the measurements of neutrino cross sections on water in the studied energy region, show good agreement with the current neutrino interaction models used in the T2K oscillation analyses.

Abstract 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.

We report measurements of the flux-integrated ν̅μ and ν̅μ + νμ charged-current cross-sections on water and hydrocarbon targets using the T2K anti-neutrino beam with a mean beam energy of 0.86 GeV. The signal is defined as the (anti-)neutrino charged-current interaction with one induced$\\mu^\\pm$and no detected charged pion or proton. These measurements are performed using a new WAGASCI module recently added to the T2K setup in combination with the INGRID Proton Module. The phase space of muons is restricted to the high-detection efficiency region,$p_{\\mu}>400~{\\rm MeV}/c$and$\\theta_{\\mu}<30^{\\circ}$ , in the laboratory frame. An absence of pions and protons in the detectable phase spaces of$p_{\\pi}>200~{\\rm MeV}/c$ ,$\\theta_{\\pi}<70^{\\circ}$and$p_{\\rm p}>600~{\\rm MeV}/c$ ,$\\theta_{\\rm p}<70^{\\circ}$is required. In this paper, both the$\\overline{\\nu}_\\mu$cross-sections and$\\overline{\\nu}_\\mu+\\nu_\\mu$cross-sections on water and hydrocarbon targets and their ratios are provided by using the D’Agostini unfolding method. The results of the integrated$\\overline{\\nu}_\\mu$cross-section measurements over this phase space are$\\sigma_{\\rm H_{2}O}=(1.082\\pm0.068(\\rm stat.)^{+0.145}_{-0.128}(\\rm syst.)) \\times 10^{-39}\\,{\\rm cm^{2} / nucleon}$ ,$\\sigma_{\\rm CH}=(1.096\\pm0.054(\\rm stat.)^{+0.132}_{-0.117}(\\rm syst.)) \\times 10^{-39}\\,{\\rm cm^{2} / nucleon}$ , and$\\sigma_{\\rm H_{2}O}/\\sigma_{\\rm CH} = 0.987\\pm0.078(\\rm stat.)^{+0.093}_{-0.090}(\\rm syst.)$ . The$\\overline{\\nu}_\\mu+\\nu_\\mu$cross-section is$\\sigma_{\\rm H_{2}O} = (1.155\\pm0.064(\\rm stat.)^{+0.148}_{-0.129}(\\rm syst.)) \\times 10^{-39}\\,{\\rm cm^{2} / nucleon}$ ,$\\sigma_{\\rm CH}=(1.159\\pm0.049(\\rm stat.)^{+0.129}_{-0.115}(\\rm syst.)) \\times 10^{-39}\\,{\\rm cm^{2} / nucleon}$ , and$\\sigma_{\\rm H_{2}O}/\\sigma_{\\rm CH}=0.996\\pm0.069(\\rm stat.)^{+0.083}_{-0.078}(\\rm syst.)$ .

We report measurements of the flux-integrated $\\overline{\\nu}_\\mu$ and $\\overline{\\nu}_\\mu+\\nu_\\mu$ charged-current cross-sections on water and hydrocarbon targets using the T2K anti-neutrino beam with a mean beam energy of 0.86 GeV. The signal is defined as the (anti-)neutrino charged-current interaction with one induced $\\mu^\\pm$ and no detected charged pion or proton. These measurements are performed using a new WAGASCI module recently added to the T2K setup in combination with the INGRID Proton Module. The phase space of muons is restricted to the high-detection efficiency region, $p_{\\mu}>400~{\\rm MeV}/c$ and $\\theta_{\\mu}<30^{\\circ}$, in the laboratory frame. An absence of pions and protons in the detectable phase spaces of $p_{\\pi}>200~{\\rm MeV}/c$, $\\theta_{\\pi}<70^{\\circ}$ and $p_{\\rm p}>600~{\\rm MeV}/c$, $\\theta_{\\rm p}<70^{\\circ}$ is required. In this paper, both the $\\overline{\\nu}_\\mu$ cross-sections and $\\overline{\\nu}_\\mu+\\nu_\\mu$ cross-sections on water and hydrocarbon targets and their ratios are provided by using the D’Agostini unfolding method. The results of the integrated $\\overline{\\nu}_\\mu$ cross-section measurements over this phase space are $\\sigma_{\\rm H_{2}O}=(1.082\\pm0.068(\\rm stat.)^{+0.145}_{-0.128}(\\rm syst.)) \\times 10^{-39}\\,{\\rm cm^{2} / nucleon}$, $\\sigma_{\\rm CH}=(1.096\\pm0.054(\\rm stat.)^{+0.132}_{-0.117}(\\rm syst.)) \\times 10^{-39}\\,{\\rm cm^{2} / nucleon}$, and $\\sigma_{\\rm H_{2}O}/\\sigma_{\\rm CH} = 0.987\\pm0.078(\\rm stat.)^{+0.093}_{-0.090}(\\rm syst.)$. The $\\overline{\\nu}_\\mu+\\nu_\\mu$ cross-section is $\\sigma_{\\rm H_{2}O} = (1.155\\pm0.064(\\rm stat.)^{+0.148}_{-0.129}(\\rm syst.)) \\times 10^{-39}\\,{\\rm cm^{2} / nucleon}$, $\\sigma_{\\rm CH}=(1.159\\pm0.049(\\rm stat.)^{+0.129}_{-0.115}(\\rm syst.)) \\times 10^{-39}\\,{\\rm cm^{2} / nucleon}$, and $\\sigma_{\\rm H_{2}O}/\\sigma_{\\rm CH}=0.996\\pm0.069(\\rm stat.)^{+0.083}_{-0.078}(\\rm syst.)$.