New results from T2K

The T2K experiment is a 295-km long-baseline neutrino experiment in Japan employing an off-axis muon neutrino beam with a ∼ 0.6 GeV peak energy. The beam, produced from 30-GeV protons at the J-PARC complex on the Pacific coast, is directed to the Super-Kamiokande detector. T2K released the first long-baseline measurement of a nonzero value for the θ13 mixing parameter through the observation of electron neutrino appearance (νμ → νe) and produced the most precise measurement of θ23 through the observation of muon neutrino disappearance (νμ → νμ). T2K data, in combination with reactor experiments, also excludes at 90% C.L. a significant region of the Dirac CP phase: δCP < −3.02(−1.87) and δCP > −0.49(−0.98) for the normal (inverted) hierarchy. A full joint appearance and disappearance fit including both neutrino (7×1020 protons on target, PoT) and anti-neutrino (4× 1020 PoT) data and, for the first time, a constraint from water target data in the near detector, is presented yielding improved sensitivity on δCP and improved precision on sin 2θ23 and the atmospheric mass splitting. 1 The T2K experiment T2K is a long-baseline neutrino oscillation experiment located in Japan, exploiting 30 GeV protons from the Japan Proton Accelerator Research Center (J-PARC, in Tōkai, Ibaraki Prefecture) to create a muon neutrino beam. The proton beam is directed onto a graphite target and the resulting pions and kaons focussed by a system of three magnetic horns into a 96 m-long decay tunnel filled with helium gas. Depending on the direction of the 250 kA pulsed current, horns can select either positively charged particles, for a beam composed mainly of νμ (ν-mode), or negatively charged particles, for a beam composed mainly of ν̄μ (ν̄-mode). The neutrino beam is measured by two near detectors (INGRID, ND280) located 280 m from the target and a far detector, Super-Kamiokande (SK). The far detector and one of the near detectors (ND280) are placed 2.5◦ off-axis with respect to the protons’ direction, which results in a narrow neutrino energy spectrum with a peak at about 0.6 GeV. The baseline between neutrino production and the far detector, 295 km, is chosen to correspond to the first minimum in the νμ survival probability at the peak energy. T2K can measure neutrino oscillation in two channels: νμ disappearance (νμ → νμ), which is dominated by the oscillation parameters sin2 2θ23 and ∆m32 and νe appearance (νμ → νe), which is sensitive to sin2 2θ13, the octant of θ23 and through subleading terms to δCP and the mass hierarchy1 ae-mail: longhin@pd.infn.it 1“Normal” mass hierarchy (NH) indicates the ∆m32,∆m 2 31 > 0 case (state m3 having the largest mass) while the other case is denoted as “inverted” mass hierarchy (IH). © The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0/). EPJ Web of Conferences 164, 01017 (2017) DOI: 10.1051/epjconf/201716401017 ICNFP 2016 EPJ Web of Conferences via matter effects 2. Variations in δCP induce asymmetries in the probabilities for the CP-conjugate channels νμ → νe and ν̄μ → ν̄e. Negative values of sin δCP enhance νμ → νe and suppresses ν̄μ → ν̄e oscillations and vice versa. T2K has been taking data since 2010. The beam power has been steadily increasing (see Fig. 1) and stable running at 420 kW beam power was achieved in 2016. From mid-2013 until spring 2016, the beam ran in ν̄-mode. The event rates in ν̄-mode are significantly lower than in the ν-mode beam, mainly due to the lower ν̄ cross section and secondly to charge asymmetries in hadroproduction. Sensitivity studies show that the optimal strategy to constrain δCP is achieved when collecting roughly equal amounts of ν-mode and ν̄-mode protons on target (PoT) [1]. Using both beam polarities T2K can test the PMNS framework and search in an optimal way for CP violation (sin δCP 0) implying P(νμ → νe) P(ν̄μ → ν̄e) or CPT violation or non-standard matter effects by comparing P(νμ → νμ) = P(ν̄μ → ν̄μ). The results considered in this report are based on a sample of 1.1 × 1021 PoT, 0.7 and 0.4 ×1021 in ν-mode and ν̄-mode respectively (the full Run 1–7b data set). Figure 1. Time evolution of the integrated PoT (cumulative histogram, left side scale) and beam power on target (markers, right side scale). 1.1 The neutrino beam A data-driven simulation is used to predict the neutrino flux from the T2K beam line. It is based on FLUKA (primary proton-target interactions) and the GEANT3 (propagation, reinteractions) Monte Carlo and incorporates data from the NA61/SHINE experiment [2–4], which has provided measurements of the hadron production cross sections using a thin carbon and a T2K replica target [5]. Beam monitor data (direction, profile and stability) as measured by the on-axis near detector INGRID [6], are also used as inputs to estimate the flux and its systematic uncertainty, currently at the O(10%) level [7]. The predicted fluxes in both ν and ν̄ modes at SK are shown in Fig. 2. 2Matter effects are moderate due to the 295 km baseline amounting at most to ∼ 1/3 of the effects ruled by δCP. 2 EPJ Web of Conferences 164, 01017 (2017) DOI: 10.1051/epjconf/201716401017 ICNFP 2016 EPJ Web of Conferences via matter effects 2. Variations in δCP induce asymmetries in the probabilities for the CP-conjugate channels νμ → νe and ν̄μ → ν̄e. Negative values of sin δCP enhance νμ → νe and suppresses ν̄μ → ν̄e oscillations and vice versa. T2K has been taking data since 2010. The beam power has been steadily increasing (see Fig. 1) and stable running at 420 kW beam power was achieved in 2016. From mid-2013 until spring 2016, the beam ran in ν̄-mode. The event rates in ν̄-mode are significantly lower than in the ν-mode beam, mainly due to the lower ν̄ cross section and secondly to charge asymmetries in hadroproduction. Sensitivity studies show that the optimal strategy to constrain δCP is achieved when collecting roughly equal amounts of ν-mode and ν̄-mode protons on target (PoT) [1]. Using both beam polarities T2K can test the PMNS framework and search in an optimal way for CP violation (sin δCP 0) implying P(νμ → νe) P(ν̄μ → ν̄e) or CPT violation or non-standard matter effects by comparing P(νμ → νμ) = P(ν̄μ → ν̄μ). The results considered in this report are based on a sample of 1.1 × 1021 PoT, 0.7 and 0.4 ×1021 in ν-mode and ν̄-mode respectively (the full Run 1–7b data set). Figure 1. Time evolution of the integrated PoT (cumulative histogram, left side scale) and beam power on target (markers, right side scale). 1.1 The neutrino beam A data-driven simulation is used to predict the neutrino flux from the T2K beam line. It is based on FLUKA (primary proton-target interactions) and the GEANT3 (propagation, reinteractions) Monte Carlo and incorporates data from the NA61/SHINE experiment [2–4], which has provided measurements of the hadron production cross sections using a thin carbon and a T2K replica target [5]. Beam monitor data (direction, profile and stability) as measured by the on-axis near detector INGRID [6], are also used as inputs to estimate the flux and its systematic uncertainty, currently at the O(10%) level [7]. The predicted fluxes in both ν and ν̄ modes at SK are shown in Fig. 2. 2Matter effects are moderate due to the 295 km baseline amounting at most to ∼ 1/3 of the effects ruled by δCP. ICNFP 2016 (GeV) ν E 0 1 2 3 4 5 6 7 8 9 10 p. o. t) 21

1 The T2K experiment T2K is a long-baseline neutrino oscillation experiment located in Japan, exploiting 30 GeV protons from the Japan Proton Accelerator Research Center (J-PARC, in Tōkai, Ibaraki Prefecture) to create a muon neutrino beam.The proton beam is directed onto a graphite target and the resulting pions and kaons focussed by a system of three magnetic horns into a 96 m-long decay tunnel filled with helium gas.Depending on the direction of the 250 kA pulsed current, horns can select either positively charged particles, for a beam composed mainly of ν µ (ν-mode), or negatively charged particles, for a beam composed mainly of νµ (ν-mode).
The neutrino beam is measured by two near detectors (INGRID, ND280) located 280 m from the target and a far detector, Super-Kamiokande (SK).The far detector and one of the near detectors (ND280) are placed 2.5 • off-axis with respect to the protons' direction, which results in a narrow neutrino energy spectrum with a peak at about 0.6 GeV.The baseline between neutrino production and the far detector, 295 km, is chosen to correspond to the first minimum in the ν µ survival probability at the peak energy.
T2K has been taking data since 2010.The beam power has been steadily increasing (see Fig. 1) and stable running at 420 kW beam power was achieved in 2016.From mid-2013 until spring 2016, the beam ran in ν-mode.The event rates in ν-mode are significantly lower than in the ν-mode beam, mainly due to the lower ν cross section and secondly to charge asymmetries in hadroproduction.Sensitivity studies show that the optimal strategy to constrain δ CP is achieved when collecting roughly equal amounts of ν-mode and ν-mode protons on target (PoT) [1].Using both beam polarities T2K can test the PMNS framework and search in an optimal way for CP violation (sin δ CP 0) implying P(ν µ → ν e ) P(ν µ → νe ) or CPT violation or non-standard matter effects by comparing P(ν µ → ν µ ) = P(ν µ → νµ ).The results considered in this report are based on a sample of 1.1 × 10 21 PoT, 0.7 and 0.4 ×10 21 in ν-mode and ν-mode respectively (the full Run 1-7b data set).

The neutrino beam
A data-driven simulation is used to predict the neutrino flux from the T2K beam line.It is based on FLUKA (primary proton-target interactions) and the GEANT3 (propagation, reinteractions) Monte Carlo and incorporates data from the NA61/SHINE experiment [2][3][4], which has provided measurements of the hadron production cross sections using a thin carbon and a T2K replica target [5].Beam monitor data (direction, profile and stability) as measured by the on-axis near detector INGRID [6], are also used as inputs to estimate the flux and its systematic uncertainty, currently at the O(10%) level [7].The predicted fluxes in both ν and ν modes at SK are shown in Fig. 2. 2 Matter effects are moderate due to the 295 km baseline amounting at most to ∼ 1/3 of the effects ruled by δ CP .

The near detectors: ND280 and INGRID
The INGRID [6] near detector (Fig. 3, left) is aligned with the proton beam axis while ND280 (Fig. 3, right) is at the same effective off-axis angle as SK.INGRID, is an array of iron/scintillator (scintillator/water) detectors arranged in a cross shape centered on the beam axis.The beam direction has been shown to be stable within 0.4 mrad.ND280 consists of several sub-detectors installed inside the refurbished UA1/NOMAD magnet, providing a 0.2 T uniform magnetic field for charge identification.Three time projection chambers (TPC [8]) are interleaved with two fine-grained detectors (FGD [9]).The upstream FGD detector (FGD1) is composed of 15 scintillators layers, while the downstream one (FGD2) contains 7+6 scin-tillator+water alternated layers.Energy loss in the TPC gas and track bending allow for good particle identification.ν µ and νµ interactions are separated by tagging the primary µ ± and the neutrino energy can be measured (especially for charged-current quasi-elastic interactions, CCQE, where, to a good approximation, it only depends on lepton kinematics).ND280 data (in particular from TPCs and FGD 1, 2) are used directly in the oscillation fits to reduce the flux and cross-section uncertainties and provide a data-driven contraint to the expected number of interactions at SK.

The far detector: Super-Kamiokande
SK [10] is a 50 kt (22.5 kt fiducial) water Cherenkov detector located 1000 m underground in the Kamioka mine in the Japanese Alps (Gifu Prefecture).The water volume is divided into an outer detector which acts as a veto for entering particles (1885 outward-facing 8-inch photomultipliers -PMTs) and an inner detector lined with 11129, 20-inch PMTs for imaging Cherenkov rings.SK is capable of very good µ/e separation by the pattern of Cherenkov light cones from the charged lepton.

The oscillation analysis
The T2K oscillation results feature a joint appearance and disappearance fit using the ν-mode and ν-mode data.Data samples of charged current (CC) interactions are fit at ND280 to provide a tuned prediction of the unoscillated spectrum at the far detector and its associated uncertainty.This is then compared to the data at the far detector, where µ-like or e-like data samples are fit to estimate the oscillation parameters.

The near detector fit
The near detector fit takes inputs from the flux, cross section and detector models with associated uncertainties.The cross-section and flux uncertainties in the predicted rates at SK are reduced by fitting the parameter values in the underlying models.The differences in target materials in the near detector (carbon, oxygen) and far detector (primarily oxygen) is dealt by including large prior uncertainties as the differences in the interactions on different nuclei are not well understood.Separate parameters are used for Fermi momentum, binding energy, multinucleon event normalisation and CC coherent pion production nomalisation on oxygen.The flux model takes into account the correlations between the neutrino fluxes at the near and far detectors.
The ν-mode ν µ -CC candidates originating in the FGD fiducial volumes are split into three samples depending on the number of tagged pions: CC0π, CC1π + and CC-other.In terms of interaction processes these samples are dominated by CCQE interactions (ν µ n → µ − p or νµ p → µ + n, the SK golden sample), CC resonant pion production and deep inelastic scattering, respectively [12].For νmode data, both ν µ and νµ CC interactions are selected and then divided into two subsamples, defined by the number of reconstructed tracks: νµ (ν µ ) CC-1-track, dominated by CCQE interactions and νµ (ν µ ) CC-N-tracks consisting of resonant production and deep inelastic scattering [13].
An important update in the near detector analysis is the use of interactions in the water modules of FGD2 which allow reducing the uncertainties related to the extrapolation across differing nuclear targets in the near and far detectors.
Using FGD1 and FGD2 interaction samples separately results in a total of six samples in ν-mode and eight samples in ν-mode.The binned distributions in p µ and cos θ µ for the 14 samples are fitted simultaneously to constrain parameters representing the systematic uncertainties in the flux and interaction models.As an example, the muon momentum distributions are shown in Fig. 4 for the CC-0π, CC-1π + and CC-other samples in ν-mode in FGD1 before (top row) and after (bottom row) the ND280 fit.The goodness of fit is 8.6%.The reduction of the uncertainty on the expected number of events at SK is substantial passing from 12-14% to 5-6%, as it can be seen in Tab. 1.The overall error is dominated by the cross-section parameters which are not constrained by the near detector (in particular the multinucleon event normalisation systematic).

Far detector fit
To enhance the purity of the selected sample in CCQE interactions candidates must have a single identified Cherenkov ring associated to the outgoing lepton.The neutrino energy (E ν ) for CC-QE interactions can be reconstructed from momentum and direction of the lepton assuming a two body interaction.Candidates must be on time with the accelerator, fully contained in the fiducial volume and must have E ν < 1.25 GeV.
The ν µ and νµ samples are defined by a single ring muon-like pattern (1Rµ) with a visible energy (E vis ) above 200 MeV and having at most one delayed electron signature (from the primary µ decay).The ν e and νe samples are defined by a single ring electron-like candidatee (1Re) with E vis > 100 MeV and no decay electrons that may signal the presence of pions in the event.In addition the 1Re events are classified by a likelihood discriminator that separates out events containing a π 0 .The number of events selected at each step in the ν e selection chain are shown in the upper plots of Fig. 5 for ν and ν-modes both for data (bullets) and Monte Carlo (histogram).The distributions of the reconstructed neutrino energy for the final ν e or νe in both beam modes are shown in the bottom plots of the same figure.T2K observes a total of 32 ν e candidate events in the far detector with a purity above 80% and 4 νe candidates with ∼ 50% purity.The reconstructed energy distributions of the 125 ν µ candidates in ν-mode running are shown in the left plot of Fig. 6.The same distribution for the 66 νµ candidates in ν-mode running is shown by the right-side plot in the same figure.
Table 7 shows the measured and expected event rates under different assumptions for the δ CP phase: 0, ±π/2, π.In ν-mode, the observed 1Re events are larger than the expected ν e appearance  events for any choice of δ CP , the lowest difference happening for δ CP = −π/2 while in ν-mode the observation lies below the expectation also in this case favoring δ CP = −π/2 which is the value inducing the largest ν-ν asymmetry.This behavior in the observed data is such that the resulting constraints on δ CP are tighter than what is expected given the sensitivity of the measurement (see Fig. 9).
The result of the near detector fit is propagated to the far detector.This is used as a prior for the far detector fit, which includes additional uncertainties from the SK detector model.The electron and muon samples in the ν-mode and ν-mode are fitted simultaneously with nuisance parameters shared between the samples.The results in the δ CP -sin 2 2θ 13 space are shown in Fig. 8  Figure 9 (left) shows the observed ∆χ 2 as a function of δ CP and mass hierarchy (black is NH, red IH), with the reactor constraint on sin 2 2θ 13 [14][15][16].The 90% confidence levels are built with the Feldman-Cousins method, resulting in intervals of [-3.02, -0.49] for NH and [-1.87, -0.98] for IH.CP conservation (sin δ CP = 0) is excluded then for both mass hierarchy hypotheses at 90% confidence level.Toy Monte Carlo studies indicate that if δ CP = −π/2 the probability to exclude δ CP = 0 or ±π with present data is about 20%.The right plot in Fig. 9 shows the expected contraints achievable on average on δ CP with this data sample.In these plots both NH and IH ∆χ 2 are with reference to the same global minimum which occurs in the NH hypothesis.All the oscillation parameters which are not parameters of interest are marginalised.The global values from PDG 2016 are used as uncertainties on sin 2 θ 13 , sin 2 θ 12 and ∆m 2 21 .The ν µ and νµ selection shown in Fig. 6 and Tab.7 show maximal disappearance occurring exactly in the highest statistics region of the energy spectrum of interacting neutrinos providing world-leading constraints in the sin 2 θ 23 and ∆m 2 23 parameters as shown in left plot of Fig. 10.The T2K contour (black) is obtained using ∆χ 2 critical values in the gaussian approximation.All the oscillation parameters which are not parameters of interest are marginalised.The reactor constraint on θ 13 is applied.The T2K contour is compared to the other experiment results (SK [18], MINOS+, NOνA [19] and IceCube DeepCore [20]).In the right plot of Fig. 10 it can be seen how T2K data tend to favour maximal disappearance (sin 2 2θ 23 = 1) also when fitting ν µ (red) and νµ (blue) data separately.The best fit for NH occurs at sin 2 2θ 23 = 0.532

Summary and future prospects
The results of a joint analysis of ν and ν oscillations at T2K with the ν µ (ν µ ) disappearance and ν µ (ν µ ) → ν e (ν e ) appearance channels, based on 7 × 10 20 PoT in ν-mode and 4.0 × 10 20 in ν-mode have been presented.Data show a preference for maximal θ 23 mixing with no hints for a violation of the CPT theorem.In the appearance channel, we observe a tendency for large ν e appearance and a low νe appearance with respect to expectations.This favours the δ CP ∼ −π/2 solution, with a 90% confidence The first-stage of the program has been approved to improve the J-PARC Main Ring power supplies and reduce the machine cycle from 2.48 s to 1.3 s, allowing the beam power to be raised from the current 420 kW to ∼ 800 kW.Further accelerator and secondary beamline upgrades will allow it to reach 1.3 MW. Figure 11 shows the expected future trends in terms of accelerator power and collected PoT.Further improvements will allow the magnetic horns to be operated with an increased current from 250 to 320 kA, an optimization of the far detector fiducial volume and of the samples used in the analysis.This could allow a 50% increase in the effective PoT.
The potential impact of the outlined program is quite significant: it may allow T2K-II to exclude CP conservation at more than 3 σ for any value of θ 23 provided that the true value would turn out to be the currently favoured one i.e. δ CP = −π/2 (see Fig. 12).

Figure 1 .
Figure 1.Time evolution of the integrated PoT (cumulative histogram, left side scale) and beam power on target (markers, right side scale).

Figure 2 .
Figure 2. Predicted fluxes at the SK detector in the absence of oscillation effects for ν-mode (left) and ν-mode (right).

Figure 4 .
Figure 4. Example distributions of momentum for the muon candidate for the CC-0π (left column), CC1π (middle column) and CC other (right column) samples in the FDG1 fiducial volume.The upper row shows the distributions before the ND280 fit while the distributions after the fit are in the lower row (see Sect. 2.1).

Figure 5 .
Figure 5. Reconstructed energy distributions for ν e candidates in ν-mode running (left) and νe candidates in ν-mode running (right)."Osc."stands for "Oscillated" and indicates the ν e component arising from ν µ → ν e transitions.The most relevant backgrounds are the intrinsic ν e or νe components in the beam and Neutral Current (NC) interactions due to π 0 production.

Figure 6 .
Figure 6.Reconstructed energy distributions for ν µ candidates in ν-mode running (left) and νµ candidates in ν-mode running (right).Left: best-fit neutrino reconstructed energy spectra for the ν-mode µ-like sample corresponding to the Run 1-7b statistic (red).The distribution is obtained by fitting sin 2 θ 23 , δ CP and mass hierarchy with reactor constraint and marginalising all the systematic parameters.The best-fit distributions are compared with the predicted unoscillated spectrum (blue) as well as the Run 1-7b data set (black dots).Right: anti-ν mode.

Figure 8 .
Figure 8. Measured ∆χ 2 distributions as a function of sin 2 θ 13 , δ CP and mass hierarchy with the full Run 1-7b data set.Both normal (black solid line) and inverted (black dashed line) hierarchies are shown.The constant ∆χ 2 critical values in the gaussian approximation are shown.The mass hierarchy was fixed, i.e. the contours are not produced with common χ 2 minimum value.All the oscillation parameters which are not parameters of interest are marginalised.The reactor constraint is not applied.

EPJ
Web of Conferences 164, 01017 (2017) DOI: 10.1051/epjconf/201716401017 ICNFP 2016 interval of [−3.02, −0.49] in normal mass hierarchy hypothesis and [−1.87, −0.98] in inverted mass hierarchy.The first combined neutrino and anti-neutrino oscillation analysis at T2K is well-advanced.3.1 The T2K-II phase T2K was originally approved to collect 7.8 × 10 21 PoT by 2021.An extension of the experiment (T2K-II phase) has been proposed recently aiming at a three-fold increase in the baseline sample by 2026 (20 × 10 21 PoT).This goal can be met by a staged upgrade program of the accelerator beamlines.

Figure 11 .
Figure 11.Projection of PoT (blue curve) and power on target (red curve) for the T2K-II program.

Figure 12 .
Figure 12.T2K-II physics reach.∆χ 2 to exclude sin δ CP = 0 as a function of PoT with a 50% effectively statistic improvement of T2K Phase 2 statistics and improved systematic errors.The δ CP = − π 2 and normal mass hierarchy are assumed to be true.Right: ∆χ 2 to exclude sin δ CP = 0 as function of true δ CP .Sensitivities at different values of sin 2 θ 23 (0.43, 0.5, 0.63) are compared.Mass hierarchy is assumed to be known.

Table 1 .
Relative total systematic error on the number of expected neutrino interactions in SK (single-ring e-like and µ-like) before and after the near detector data constraint.