Measurement of neutrino and antineutrino oscillations by the T2K experiment including a new additional sample of ${\nu }_e$ interactions at the far detector

The T2K experiment reports an updated analysis of neutrino and antineutrino oscillations in appearance and disappearance channels. A sample of electron neutrino candidates at Super-Kamiokande in which a pion decay has been tagged is added to the four single-ring samples used in previous T2K oscillation analyses. Through combined analyses of these five samples, simultaneous measurements of four oscillation parameters, $|\mathrm{\Delta }{m}_{32}^2|$, ${\sin }^2{\theta }_{23}$, ${\sin }^2{\theta }_{13}$, and ${\delta }_{\mathrm{CP}}$ and of the mass ordering are made. A set of studies of simulated data indicates that the sensitivity to the oscillation parameters is not limited by neutrino interaction model uncertainty. Multiple oscillation analyses are performed, and frequentist and Bayesian intervals are presented for combinations of the oscillation parameters with and without the inclusion of reactor constraints on ${\sin }^2{\theta }_{13}$. When combined with reactor measurements, the hypothesis of $CP$ conservation (${\delta }_{\mathrm{CP}}=0$ or $\pi$) is excluded at 90% confidence level. The 90% confidence region for ${\delta }_{\mathrm{CP}}$ is $[-2.95,-0.44]$ ($[-1.47,-1.27]$) for normal (inverted) ordering. The central values and 68% confidence intervals for the other oscillation parameters for normal (inverted) ordering are $\mathrm{\Delta }{m}_{32}^2=2.54\pm 0.08(2.51\pm 0.08)\times {10}^{-3}{\mathrm{eV}}^2/c^4$ and ${\sin }^2{\theta }_{23}=0.55_{-0.09}^{+0.05}$ ($0.55_{-0.08}^{+0.05}$), compatible with maximal mixing. In the Bayesian analysis, the data weakly prefer normal ordering (Bayes factor 3.7) and the upper octant for ${\sin }^2{\theta }_{23}$ (Bayes factor 2.4).

Figure 1

The T2K unoscillated neutrino flux prediction at SK for $\nu$ (left) and $\overline{\nu }$ (right) modes. The binning used for the flux systematic parameters is also shown.

Figure 2

The T2K fractional systematic uncertainties on the SK flux arising from the beamline configuration and hadron production prior to constraints from near detector data. Uncertainties are given for $\nu$’s in a $\nu$-mode beam (top left), $\overline{\nu }$’s in a $\nu$-mode beam (top right), $\overline{\nu }$’s in an $\overline{\nu }$-mode beam (bottom left), and $\nu$’s in an $\overline{\nu }$-mode beam (bottom right). For the $\nu$-mode plots, the total current uncertainties (NA61 2009 data) are compared to the total uncertainties estimated for the previous T2K results (NA61 2007 data) [27].

Figure 3

Effective RPA with error band from the fit to external data compared with RPA corrections computed in Ref. [40].

Figure 4

Multinucleon interactions (2p2h) cross section on ${}^{12}\mathrm{C}$ as a function of energy from the models of Nieves (reference model in the text) [40] and Martini (alternative model in the text) [70].

Figure 5

Neutrino energy calculated with the CCQE two-body assumption for CCQE and 2p2h interactions of 600 MeV muon neutrinos on ${}^{12}\mathrm{C}$ simulated with the reference model. The different components of 2p2h show differing amounts of bias.

Figure 6

The event rate at INGRID as a function of time is shown in the top panel. The horizontal dashed redline corresponds to the best fit for the different horn currents with a constant function. The central and bottom panels show the neutrino beam direction measured at INGRID and at MUMON along the horizontal and vertical transverse directions with respect to the beam as a function of time. The dashed vertical lines separate the seven T2K physics runs.

Figure 7

Top: muon momentum distributions of the $\nu$-mode ${\nu }_{\mu }$ $\mathrm{CC}\text{−}0\pi$ samples in FGD1 (left) and FGD2 (right). Bottom: muon momentum distributions of the $\nu$-mode ${\nu }_{\mu }$ $\mathrm{CC}\text{−}1{\pi }^{+}$ samples in FGD1 (left) and FGD2 (right). All distributions are shown prior to the ND280 fit.

Figure 8

Top: muon momentum distributions for the $\overline{\nu }$-mode ${\overline{\nu }}_{\mu }$ CC-1-track (left) and CC-N-tracks (right) samples. Bottom: muon momentum distributions for the $\overline{\nu }$-mode ${\nu }_{\mu }$ CC-1-track (left) and CC-N-tracks (right) samples. All distributions are shown prior to the ND280 fit.

Figure 9

The SK flux parameters for the ${\stackrel{(-)}{\nu }}_{\mu }$ (left) and ${\stackrel{(-)}{\nu }}_e$ (right) neutrino species in the $\nu$ (top) and $\overline{\nu }$ modes (bottom), shown as a fraction of the nominal value. The bands indicate the $1\sigma$ uncertainty on the parameters before (solid, red) and after (hatched, blue) the near detector fit.

Figure 10

Cross section parameters before (solid, red) and after (hatched, blue) the near detector fit, shown as a fraction of the nominal value (given in Table 9). The extent of the colored band shows the $1\sigma$ uncertainty.

Figure 11

Distribution of the minimum negative log-likelihood values from fits to the mock data sets (black), with the value from the fit to the data superimposed in red.

Figure 12

Distribution of the minimum negative log-likelihood values from fits to the mock data sets (black), with the value from the fit to the data superimposed in red. The distributions shown make up the contribution from the flux (top) and cross section (bottom) prior terms.

Figure 13

Comparison of the fitted SK $\nu$-mode flux parameters (top) and cross section parameters (bottom) between the ND280 fit (red, solid) and the Bayesian analysis (blue, hashed).

Figure 14

Data MC comparison of $\nu$-mode ${\nu }_{\mu }$ $\mathrm{CC}\text{−}0\pi$ (top) and $\mathrm{CC}\text{−}1{\pi }^{+}$ (bottom) samples in FGD1 (left) and FGD2 (right) after the ND280 fit. The simulation is broken down by neutrino reaction type.

Figure 15

Top: data MC comparison of ${\overline{\nu }}_{\mu }$ (right-sign) CC-1-track (left) and CC-N-tracks (right) samples after the ND280 fit. The simulation is broken down by neutrino reaction type. Bottom: same muon momentum distributions for ${\nu }_{\mu }$ background samples.

Figure 16

$\mathrm{\Delta }{T}_0$ distribution of all FC, OD, and LE events within $\pm 500\mu \mathrm{s}$ of the expected beam arrival time observed during T2K Run 1-7. The histograms are stacked in that order.

Figure 17

$\mathrm{\Delta }{T}_0$ distribution of all FC events observed during T2K Run 1-7 zoomed in on the expected beam arrival time.

Figure 18

The PID likelihood distribution of the observed $\nu$-mode CC event samples after FCFV and single-ring cuts have been applied. The data are shown as points with statistical error bars and the shaded, stacked histograms are the MC predictions. The expectation is based on the parameters of Table 13.

Figure 19

The reconstructed energy spectra of the observed ${\nu }_e$ in $\nu$-mode (left) and ${\overline{\nu }}_e$ in $\overline{\nu }$-mode (right) CC candidate event samples assuming CCQE interaction kinematics. The data are shown as points with statistical error bars, and the shaded, stacked histograms are the MC predictions. The expectation is based on the parameters of Table 13.

Figure 20

Two-dimensional vertex distributions of the observed ${\nu }_e$ CC candidate events in $(X,Y)$ and $(R^2,Z)$ for the $\nu$ mode (top) and $\overline{\nu }$ mode (bottom). The arrow indicates the neutrino beam direction, and the dashed line indicates the fiducial volume boundary. Events indicated by open square markers passed all of the ${\nu }_e$ selection cuts except for the fiducial volume cut.

Figure 21

The reconstructed energy spectra of the observed ${\nu }_{\mu }$ in $\nu$-mode (left) and ${\overline{\nu }}_{\mu }$ in $\overline{\nu }$-mode (right) CC candidate event samples assuming CCQE interaction kinematics. The data are shown as points with statistical error bars, and the shaded, stacked histograms are the MC predictions, and the rightmost bin includes overflow. The expectation is based on the parameters of Table 13.

Figure 22

The true momentum distribution for tagged Michel electrons from true $\mathrm{CC}1{\pi }^{+}$ simulated events reconstructed in the fiducial volume (left) and the tagging efficiency for these events (right). The expectation is based on the parameters of Table 13.

Figure 23

The true momentum distribution for selected simulated signal events in the $\mathrm{CC}1{\pi }^{+}$ candidate sample (left) and the selection efficiency for these events (right). The expectation is based on the parameters of Table 13. The red dashed line indicates the Cherenkov threshold for charged pions.

Figure 24

Difference between true and reconstructed energy of the ${\nu }_e$ CCQE-like (left) and $\mathrm{CC}1{\pi }^{+}$ (right) simulated samples. The energy for the CCQE-like sample is reconstructed using Eq. (4). For the $\mathrm{CC}1{\pi }^{+}$ sample, the modified interaction kinematics in Eq. (5) are used. The expectation is based on the parameters of Table 13.

Figure 25

The reconstructed energy spectrum of the observed ${\nu }_e$ $\mathrm{CC}1{\pi }^{+}$ candidate events assuming the modified interaction kinematics in Eq. (5). The data are shown as points with statistical error bars, and the shaded, stacked histograms are the MC predictions. The expectation is based on the parameters of Table 13.

Figure 26

Two-dimensional vertex distributions of the observed ${\nu }_e$ $\mathrm{CC}1{\pi }^{+}$ candidate events in $(X,Y)$ and $(R^2,Z)$. The arrow indicates the neutrino beam direction, and the dashed line indicates the fiducial volume boundary. Events indicated by open square markers passed all of the ${\nu }_e$ $\mathrm{CC}1{\pi }^{+}$ selection cuts except for the fiducial volume cut.

Figure 27

The oscillation probability for ${\nu }_{\mu }\to {\nu }_e$ and ${\overline{\nu }}_{\mu }\to {\overline{\nu }}_e$ transitions as a function of ${\delta }_{CP}$ and MO for $E_{\nu }=0.6\mathrm{GeV}$ and a baseline of 295 km. The other oscillation parameters are fixed to the values shown in Table 13. The dashed line indicates $P({\nu }_{\mu }\to {\nu }_e)=P({\overline{\nu }}_{\mu }\to {\overline{\nu }}_e)$.

Figure 28

Expected $\{E_{\nu }^{\mathrm{rec}},{\theta }_{\mathrm{lep}}\}$ distributions for the signal ${\overline{\nu }}_{\mu }\to {\overline{\nu }}_e$ (top) and wrong-sign background ${\nu }_{\mu }\to {\nu }_e$ (bottom) in the $e$-like CCQE-like selection in the $\overline{\nu }$ mode. The superimposed gray dots correspond to the data. The expectation is based on the parameters of Table 13.

Figure 29

$\{E_{\nu }^{\mathrm{rec}},{\theta }_{\mathrm{lep}}\}$ templates for the ${\nu }_e$ CCQE-like (top), ${\nu }_e$ $\mathrm{CC}1{\pi }^{+}$ (middle) in the $\nu$-mode, and ${\overline{\nu }}_e$ CCQE-like (bottom) in $\overline{\nu }$-mode candidate samples. Both signal and background events are included in the expected distributions based on the oscillation parameters of Table 13. The superimposed gray dots correspond to the data.

Figure 30

Ratio of the alternative 2p2h simulated data (left) and alternative 1p1h simulated data (right) to the nominal MC, shown as a function of reconstructed lepton kinematics for the FGD1 $\mathrm{CC}\text{−}0\pi$ sample.

Figure 31

The nominal values (red) and postfit values (blue) of the ND $280\nu$-mode ${\nu }_{\mu }$ flux (left) and the cross section (right) parameters, shown as a fraction of their nominal value, following the near detector fit to the alternative 2p2h ND280 simulated data.

Figure 32

Single-ring expected event spectrum at SK as a function of $E_{\nu }^{\mathrm{rec}}$, assuming CCQE kinematics, for the selected $\mu$-like (left) and $e$-like (right) events in the $\nu$ mode. The nominal SK prediction is shown by the dashed blue line, the SK simulated data are shown by the solid black line, and the prediction from the ND280 simulated data fit is shown by the hashed red region.

Figure 33

The likelihood surfaces (red) from the oscillation fit of the alternative 2p2h simulated data at SK, using the result of the fit to the ND280 simulated data as an input. The oscillation parameters of Table 21 (maximal mixing) were used. The likelihood surfaces from the nominal fit are shown by the black line. The contours for ${\sin }^2{\theta }_{23}$ (top left), $\mathrm{\Delta }{m}_{32}^2$ (top right), ${\delta }_{CP}$ (bottom left), and ${\delta }_{CP}$ vs ${\sin }^2{\theta }_{13}$ (bottom right) are shown. For the one-dimensional likelihoods, the point of minimum $\mathrm{\Delta }{\chi }^2$ is given in each legend.

Figure 34

The likelihood surfaces (red) from the oscillation fit of the alternative 2p2h simulated data at SK, using the result of the fit to the ND280 simulated data as an input. The oscillation parameters of Table 21 (nonmaximal mixing) were used. The likelihood surfaces from the nominal fit are shown by the black line. The contours for ${\sin }^2{\theta }_{23}$ (top left), $\mathrm{\Delta }{m}_{32}^2$ (top right), ${\delta }_{CP}$ (bottom left), and ${\delta }_{CP}$ vs ${\sin }^2{\theta }_{13}$ (bottom right) are shown. For the one-dimensional likelihoods, the point of minimum $\mathrm{\Delta }{\chi }^2$ is given in each legend.

Figure 35

The likelihood surfaces (red) from the oscillation fit of the alternative 1p1h simulated data at SK, using the result of the fit to the ND280 simulated data as an input. The oscillation parameters of Table 21 (maximal mixing) were used. The likelihood surfaces from the nominal fit are shown by the black line. The contours for ${\sin }^2{\theta }_{23}$ (top left), $\mathrm{\Delta }{m}_{32}^2$ (top right), ${\delta }_{CP}$ (bottom left), and ${\delta }_{CP}$ vs ${\sin }^2{\theta }_{13}$ (bottom right) are shown. For the one-dimensional likelihoods, the point of minimum $\mathrm{\Delta }{\chi }^2$ is given in each legend.

Figure 36

One-dimensional $\mathrm{\Delta }{\chi }^2$ surfaces for oscillation parameters ${\delta }_{CP}$ and ${\sin }^2{\theta }_{13}$ using T2K-only data. The yellow band on the right plot corresponds to the reactor value on ${\sin }^2{\theta }_{13}$ from the PDG 2015 [75].

Figure 37

Two-dimensional constant $\mathrm{\Delta }{\chi }^2$ contours for oscillation parameters ${\delta }_{CP}$ and ${\sin }^2{\theta }_{13}$ using T2K data only. The yellow band corresponds to the reactor value on ${\sin }^2{\theta }_{13}$ from the PDG 2015 [75].

Figure 38

A comparison of one-dimensional constant $\mathrm{\Delta }{\chi }^2$ contours for normal ordering for ${\delta }_{CP}$ using T2K-only data for the four- and five-sample fits.

Figure 39

Contours in the ${\sin }^2{\theta }_{13}–{\delta }_{CP}$ plane using T2K-only data, obtained by analysing either the $\nu$- or $\overline{\nu }$-mode appearance data sets, are compared for both orderings. Both $\nu$- and $\overline{\nu }$-mode disappearance data sets were used in all fits. The yellow band corresponds to the reactor value on ${\sin }^2{\theta }_{13}$ from the PDG 2015 [75].

Figure 40

Allowed region at 90% confidence level for oscillation parameters ${\sin }^2{\theta }_{23}$ and $\mathrm{\Delta }{m}_{32}^2$ using T2K data with the reactor constraint (${\sin }^2(2{\theta }_{13})=0.085\pm 0.005$). The normal mass ordering is assumed, and the T2K results are compared with $\mathrm{NO}\nu \mathrm{A}$ [86], MINOS [4], Super-K [87], and IceCube [88].

Figure 41

Comparison of the T2K data in ${\nu }_{\mu }$ (left) and ${\overline{\nu }}_{\mu }$ (right) disappearance channels with the expected spectra obtained with the T2K most probable values of the oscillation parameters and using the $\mathrm{NO}\nu \mathrm{A}$ most probable values for ${\sin }^2{\theta }_{23}$ (higher octant) and $\mathrm{\Delta }{m}_{32}^2$ taken from Ref. [86].

Figure 42

A comparison of two-dimensional constant $\mathrm{\Delta }{\chi }^2$ contours in the ${\delta }_{CP}–{\sin }^2{\theta }_{13}$ plane using T2K data with the reactor constraint, for both four-sample (red) and five-sample (black) analyses with normal (left) and inverted (right) mass ordering hypotheses. The contours are produced by marginalizing the likelihood with respect to all parameters other than the parameters of interest.

Figure 43

One-dimensional $\mathrm{\Delta }{\chi }^2$ surfaces for oscillation parameter ${\delta }_{CP}$ using T2K data with the reactor constraint. The critical $\mathrm{\Delta }{\chi }^2$ values obtained with the Feldman-Cousins method are used to evaluate the 90% confidence level with the proper coverage.

Figure 44

Total predicted ${\stackrel{(-)}{\nu }}_e$-appearance event rates in the $\nu$-mode samples and in the $\overline{\nu }$-mode sample as a function of ${\delta }_{CP}$ for different values of ${\sin }^2{\theta }_{23}$ and both mass orderings, compared to T2K data. The dashed line distinguishes the two solutions for the octant of ${\theta }_{23}$.

Figure 45

One-dimensional marginal $\mathrm{\Delta }{\chi }^2$ surfaces for oscillation parameters ${\delta }_{CP}$ and ${\sin }^2{\theta }_{13}$ using T2K data with the reactor constraint. The contour is produced by marginalizing the likelihood with respect to all parameters other than the parameter of interest. The red line shows the critical $\mathrm{\Delta }{\chi }^2$ values obtained with the Feldman-Cousins method, used to evaluate the 90% confidence level with the proper coverage. The green line shows the $\mathrm{\Delta }{\chi }^2$ obtained with the fit to the T2K data.

Figure 46

The two-dimensional histograms represent the marginal posterior probability in the two-parameter space as a blue gradient. The white solid (dashed) line is the 90% ($1\sigma$) credible interval. The one-dimensional histograms represent the posterior probability density (post. proba.) of the oscillation parameter in the x axis of the column marginalized over all other parameters. The blue areas are, respectively, the $1\sigma$ (dark), 90% (medium), and 95% (light) credible interval.

Figure 47

${\delta }_{\mathrm{CP}}$ marginal posterior probability as obtained with the MCMC method. The credible intervals for $\pm 1\sigma$, $\pm 90\%$, and $\pm 95\%$ are shown when using a flat prior in ${\delta }_{CP}$ (usual fit) and when converting to a flat prior in $\sin {\delta }_{\mathrm{CP}}$.

Figure 48

Constant $\mathrm{\Delta }{\chi }^2$ 68% and 90% intervals in the ${\sin }^2{\theta }_{13}\text{−}{\delta }_{CP}$ plane for both frequentist analyses and the Bayesian fit.

Figure 49

Constant $\mathrm{\Delta }{\chi }^2$ 68% and 90% intervals in the ${\sin }^2{\theta }_{23}\text{−}\mathrm{\Delta }{m}_{32}^2$ plane for the frequentist fit which uses 2D $\{E_{\nu }^{\mathrm{rec}},{\theta }_{\mathrm{lep}}\}$ templates and the Bayesian fit, assuming normal ordering.

Figure 50

Comparison of the best-fit oscillated MC energy spectra, unoscillated spectra, and T2K data for the five samples used in the fit: $\mu$-like sample in the $\nu$ mode and $\overline{\nu }$ mode (top left and right), single-ring $e$-like appearance sample in the $\nu$ mode and $\overline{\nu }$ mode (middle left and right), and $\mathrm{CC}1{\pi }^{+}$ $e$-like appearance sample in the $\nu$ mode (bottom). The larger unoscillated spectra in the $\mathrm{CC}1{\pi }^{+}$ $e$-like sample compared to the single-ring sample is due to the relatively large background of ${\nu }_{\mu }$ in the $\mathrm{CC}1{\pi }^{+}$ sample, which does not disappear in the no-oscillation case. The ratio of the best fit to unoscillated spectra are also shown.