Evidence of electron neutrino appearance in a muon neutrino beam

The T2K Collaboration reports evidence for electron neutrino appearance at the atmospheric mass splitting, $|\Delta m_{32}^2|\approx 2.4\times {10}^{-3}{\mathrm{eV}}^2$. An excess of electron neutrino interactions over background is observed from a muon neutrino beam with a peak energy of 0.6 GeV at the Super-Kamiokande (SK) detector 295 km from the beam’s origin. Signal and background predictions are constrained by data from near detectors located 280 m from the neutrino production target. We observe 11 electron neutrino candidate events at the SK detector when a background of $3.3\pm 0.4(\mathrm{syst})$ events is expected. The background-only hypothesis is rejected with a $p$ value of 0.0009 ($3.1\sigma$), and a fit assuming ${\nu }_{\mu }\to {\nu }_e$ oscillations with ${sin}^{2}2{\theta }_{23}=1$, ${\delta }_{CP}=0$ and $|\Delta m_{32}^2|=2.4\times {10}^{-3}{\mathrm{eV}}^2$ yields ${sin}^{2}2{\theta }_{13}={0.088}_{-0.039}^{+0.049}(\mathrm{stat}+\mathrm{syst})$.

Figure 1

The muon neutrino survival probability (top) and electron neutrino appearance probabilities (middle) at 295 km, and the unoscillated neutrino fluxes for different values of the off-axis angle (OA) (bottom). The appearance probability is shown for two values of the phase ${\delta }_{CP}$, and for normal (NH) and inverted (IH) mass hierarchies.

Figure 2

An exploded illustration of the ND280 detector. The description of the component detectors can be found in the text.

Figure 3

An illustration of the SK detector.

Figure 4

The time dependence of the POT-normalized reconstructed neutrino event rate (a) and the beam direction (b) measured by INGRID. The error bars show the statistical uncertainty only. The points shown for the direction measurement include sequential data grouped in periods of stable beam conditions.

Figure 5

The T2K flux prediction at SK (a) and ND280 (b) for neutrinos and antineutrinos with systematic error bars. The flux above $E_{\nu }=10\mathrm{GeV}$ is not shown; the flux is simulated up to $E_{\nu }=30\mathrm{GeV}$.

Figure 6

Ratio of the hadron interaction weighted flux to the nominal flux for ${\nu }_{\mu }$ (a), ${\nu }_e$ (b) flux predictions at SK. The effects of the pion production, kaon production and inclusive production cross section weighting are shown separately and in total.

Figure 7

The fractional hadron interaction errors on ${\nu }_{\mu }$ (a), ${\nu }_e$ (b) flux predictions at SK.

Figure 8

The fractional uncertainties on the ND280 ${\nu }_{\mu }$, SK ${\nu }_{\mu }$ and SK ${\nu }_e$ flux evaluated for the binning used in this analysis. This binning is coarser than the binning shown in Fig. 7 and includes the correlations between merged bins.

Figure 9

The correlations of the flux uncertainties in the $b_i$ bins for the ND280 ${\nu }_{\mu }$ and SK ${\nu }_{\mu }$ and ${\nu }_e$ fluxes. The axes are the bins in neutrino energy for each flavor/detector combination and are proportional to the neutrino energy up to 10 GeV.

Figure 10

The NEUT ${\nu }_{\mu }$ interaction cross section per nucleon on ${}^{16}\mathrm{O}$ with a breakdown by interaction process. The “NC Other” curve includes neutral current coherent pion production, resonant charged pion production, multipion production and deep inelastic scattering. The predicted ${\nu }_{\mu }$ flux spectrum at SK with no oscillations is shown for comparison.

Figure 11

The predicted $Q^2$ distributions for CCQE interactions in the ND280 CCQE selection, the MiniBooNE CCQE selection, and the SK ${\nu }_e$ appearance selection.

Figure 12

Differential cross sections for $\mathrm{CC}1{\pi }^{+}{Q}^2$ (top), $\mathrm{CC}1{\pi }^0{Q}^2$ (middle) and $\mathrm{NC}1{\pi }^0{p}_{{\pi }^0}$ (bottom) used in the single-pion fits to MiniBooNE data, and the NEUT nominal and best-fit predictions. The MiniBooNE data point errors are $\mathrm{\text{statistical}}+\mathrm{\text{systematic}}$.

Figure 13

The $\mathrm{CC}1{\pi }^{+}$ cross section as a function of energy as measured by MiniBooNE, with the NEUT nominal and best-fit models. The treatment in the analysis of the disagreement between the best-fit NEUT and data is discussed in the text.

Figure 14

Event displays of example ND280 CCQE-like (a) and CCnonQE-like (b) selected events.

Figure 15

Muon momentum for the CC-inclusive (a), CCQE-like (c), and CCnonQE-like (e) samples. Cosine of the muon angle for the CC-inclusive (b), CCQE-like (d), and CCnonQE-like (f) samples. The errors on the data points are the statistical errors.

Figure 16

The bin-to-bin correlation matrix from the systematic covariance matrix for the ${\nu }_{\mu }$ selected sample at ND280. The bins are ordered by increasing $\cos {\theta }_{\mu }$ in groups of increasing muon momentum ($p_0$ to $p_4$) for the two selections.

Figure 17

(a) Momentum distribution of the highest momentum track with negative charge for each event in the electron candidate sample at ND280. The inset shows the region with momentum $\ge 300\mathrm{MeV}/c$. (b) Momentum distribution of the highest momentum track with positive charge for each event of the positron candidate control sample. The “Other Backgrounds” component is mainly due to protons and pions from NC and CC ${\nu }_{\mu }$ interactions in the FGD. The energy loss of positrons and protons (pions) is similar at $p\approx 1000\mathrm{MeV}/c$ ($200\mathrm{MeV}/c$), resulting in the presence of these particles in the positron candidate sample.

Figure 18

The fitted $p_{\mu }$, $\cos {\theta }_{\mu }$ bins from the ND280 CCQE-like (left) and CCnonQE-like (right) samples. All values in the plot are divided by the shown bin width. The $p_{\mu }>900\mathrm{MeV}/c$ bin additionally contains the overflow bin, and is normalized by a bin width of $1100\mathrm{MeV}/c$. The prediction prior to the fit uses the modifications to the NEUT model parameters derived from fits of the MiniBooNE single pion data.

Figure 19

The neutrino flux and cross section parameter correlations before (a) and after (b) the fit to the ND280 data. The flux parameters are ordered by increasing energy with the binning listed in Table 12 (the correlations of the antineutrino flux parameters are not shown in this figure). The cross section parameter ordering is $M_A^{\mathrm{QE}}$, $M_A^{\mathrm{RES}}$, CCQE low energy normalization, $\mathrm{CC}1\pi$ low energy normalization and $\mathrm{NC}1{\pi }^0$ normalization.

Figure 20

Comparisons of the $p_{\mu }$ (left column) and $\cos {\theta }_{\mu }$ (right column) distributions for CCQE-like ${\nu }_{\mu }$ selected events in (a) and (b) and CCnonQE-like ${\nu }_{\mu }$ selected events in (c) and (d). The solid line represents the NEUT nominal prediction and the hatched region represents the postfit MC prediction. The dots are the data events. Below each graph, the data/MC ratio is shown for both the NEUT nominal prediction (empty triangle) and postfit MC prediction (full triangle). The error on the points is the statistical error on the data.

Figure 21

Example event displays for the SK simulation of (a) ${\nu }_{\mu }$ CCQE (single well-defined ring from the muon), (b) ${\nu }_e$ CCQE (single diffuse ring from the electron) and (c) ${\nu }_{\mu }$ $\mathrm{NC}1{\pi }^0$ interactions (two diffuse rings from the ${\pi }^0\to \gamma \gamma$ decay). The images show the detected light pattern at the ID wall, with the cylindrical SK detector shown as a flat projection. The color indicates the amount of charge detected by the PMT, with purple dots corresponding to the least amount of charge, and red the most.

Figure 22

$\Delta T_0$ distribution of all FC, OD and LE events observed in the $\pm 500\mu \mathrm{s}$ T2K windows. The OD histogram is stacked on the FC histogram, and the LE histogram is stacked on the OD and FC histograms.

Figure 23

$\Delta T_0$ distribution of FC events zoomed in on the spill time observed during T2K Run $1+2$ and Run 3. The eight dotted vertical lines represent the 581 ns interval bunch center position fitted to the observed FC event times.

Figure 24

Distribution of invariant mass $M_{\mathrm{inv}}$ when each event is forced to be reconstructed as two photon rings. The data are shown as points with error bars (statistical only) and the MC predictions are in shaded histograms. The last bin shows overflow entries. The arrow shows the selection criterion $M_{\mathrm{inv}}<105\mathrm{MeV}/c^2$.

Figure 25

Distribution of the reconstructed neutrino energy spectrum of the events which pass all ${\nu }_e$ appearance signal selection criteria with the exception of the energy cut. The data are shown as points with error bars (statistical only) and the MC predictions are in shaded histograms. The arrow shows the selection criterion $E_{\nu }^{\mathrm{rec}}<1250\mathrm{MeV}$.

Figure 26

The cumulative number of observed ${\nu }_e$ candidate events as a function of accumulated POT. The vertical dashed lines separate the three running periods, and the dotted line indicates the horn current change during Run 3. The solid line indicates a hypothesis of constant event rate.

Figure 27

(a) Two-dimensional $(x,y)$ distribution of the reconstructed vertex positions of observed ${\nu }_e$ candidate events. (b) Two-dimensional $(r^2=x^2+y^2,z)$ distribution of the reconstructed vertex positions of the observed ${\nu }_e$ candidate events. The arrow indicates the neutrino beam direction and the dashed line indicates the fiducial volume boundary. Black markers are events observed during Run $1+2$, and pink markers are events from Run 3. Open squares represent events which passed all the ${\nu }_e$ selection cuts except for the fiducial volume cut.

Figure 28

Distribution of events which pass ${\nu }_e$ selection cuts except for the FV cut as a function of the distance from the ID wall to the vertex, calculated along the beam direction. The solid line indicates the expected distribution for signal (${sin}^{2}2{\theta }_{13}=0.1$) and background, and the background prediction is shown with the dashed line. The hatch-filled histogram shows the subset of background whose true vertex is outside the ID.

Figure 29

The fractional errors on SK ${\nu }_e$ signal (top) and NC background (bottom) predictions from the SK detector response uncertainty as a function of the electron candidate momentum and angle.

Figure 30

$(p_e,{\theta }_e)$ distribution for ${\nu }_e$ signal (top left), ${\nu }_{\mu }$ background (top right), ${\nu }_e$ background (middle left), ${\overline{\nu }}_{\mu }$ background (middle right) and ${\overline{\nu }}_e$ background (bottom left). Each distribution is normalized to unit area.

Figure 31

The MC reconstructed neutrino energy distributions of ${\nu }_{\mu }\to {\nu }_e$ CC signal, intrinsic ${\nu }_e$ CC background and NC background components in the ${\nu }_e$ candidate event sample. The histograms are normalized to the same area.

Figure 32

The PDF as a function of momentum for different angular bins [10 of 15 $(p_e,{\theta }_e)$ bins are shown] and ${sin}^{2}2{\theta }_{13}=0.1$. The shaded areas represent one sigma deviations that are evaluated by fluctuating all of the systematic parameters according to a multivariate normal distribution using their prior values and covariance matrix.

Figure 33

The PDF as a function of momentum for the same bins as in Fig. 32 and ${sin}^{2}2{\theta }_{13}=0$. The shaded areas represent one sigma deviations that are evaluated by fluctuating all of the systematic parameters according to a multivariate normal distribution using their prior values and covariance matrix.

Figure 34

The $-2\Delta \ln \mathcal{L}$ average sensitivity curve for toy MC data generated at ${sin}^{2}2{\theta }_{13}=0.1$ with ${\delta }_{CP}=0$, normal hierarchy and $3.01\times {10}^{20}$ POT. The likelihood is shown for three cases: where rate, shape and ND280 information is used, where only rate and ND280 information is used, and where rate and shape information is used without ND280 information.

Figure 35

The $(p_e,{\theta }_e)$ distribution of the ${\nu }_e$ events (dots) (top) overlaid with the prediction. The prediction includes the rate tuning determined from the fit to near detector information and a signal assuming the best-fit value of ${sin}^{2}2{\theta }_{13}=0.088$. The angular distribution (middle) of the ${\nu }_e$ events in data overlaid with prediction, and the momentum distribution (bottom) with the same convention as above.

Figure 36

The 68% and 90% confidence intervals for ${sin}^{2}2{\theta }_{13}$ scanned over values of ${\delta }_{CP}$ assuming normal hierarchy [top, (b)] and inverted hierarchy [bottom, (d)] with all other oscillation parameters fixed at the values in Table 13. The best-fit value of ${sin}^{2}2{\theta }_{13}$ for each value of ${\delta }_{CP}$ is also shown for the $(p_e,{\theta }_e)$ analysis. The $-2\Delta \ln \mathcal{L}$ curve for normal hierarchy [top, (a)] and inverted hierarchy [bottom, (c)] at ${\delta }_{CP}=0$ are also shown vs ${sin}^{2}2{\theta }_{13}$.

Figure 37

The observed $E_{\nu }^{\mathrm{rec}}$ distribution and prediction, assuming ${sin}^{2}2{\theta }_{13}=0.092$, ${\delta }_{CP}=0$, and normal hierarchy. The background component is also shown.

Figure 38

The 68% and 90% confidence interval regions for ${sin}^{2}2{\theta }_{13}$ scanned over values of ${\delta }_{CP}$ assuming normal hierarchy (a) and inverted hierarchy (b) with the best-fit value of ${sin}^{2}2{\theta }_{13}$ shown for the $(p_e,{\theta }_e)$ analysis. The 90% confidence interval region for the $E_{\nu }^{\mathrm{rec}}$ analysis and rate-only analysis are overlaid. The best-fit values of ${sin}^{2}2{\theta }_{13}$ for the $E_{\nu }^{\mathrm{rec}}$ analysis and the rate-only analysis are also shown. All other oscillation parameters are fixed at the values in Table 13.

Figure 39

Pion absorption cross section as a function of pion momentum overlaid with ${\pi }^{+}\mathrm{\text{−}}{}^{12}\mathrm{C}$ scattering data, Ashery et al. [79], Jones et al. [80], and Giannelli et al. [81].

Figure 40

The CCQE cross section as a function of $Q^2$ (top) as measured by MiniBooNE (points), with the NEUT nominal and NEUT at the best-fit of the MiniBooNE CCQE $(T_{\mu },\cos {\theta }_{\mu })$ spectrum. Ratio of data to NEUT (bottom) for nominal (dashed line) and best fit (solid line).

Figure 41

The CCQE cross section as a function of neutrino energy (top) as measured by MiniBooNE (points), with the NEUT nominal and NEUT at the best fit of the MiniBooNE CCQE $(T_{\mu },\cos {\theta }_{\mu })$ spectrum. Ratio of data to NEUT (bottom) for nominal (dashed line) and best fit (solid line).

Figure 42

Differential $\mathrm{d}\sigma /\mathrm{d}{p}_{{\pi }^0}$ cross section measured by K2K and the nominal and best fit from the MiniBooNE single pion fits NEUT predictions, with error band showing the uncertainties after the fit to MiniBooNE data.