Measurements of neutrino oscillation in appearance and disappearance channels by the T2K experiment with $6.6\ifmmode\times\else\texttimes\fi{}1{0}^{20}$ protons on target

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Measurements of neutrino oscillation in appearance and disappearance channels by the T2K experiment with $6.6 \times 1 0^{20}$ protons on target

K. Abe et al. (T2K Collaboration)

Phys. Rev. D 91, 072010 – Published 29 April 2015

Abstract

We report on measurements of neutrino oscillation using data from the T2K long-baseline neutrino experiment collected between 2010 and 2013. In an analysis of muon neutrino disappearance alone, we find the following estimates and 68% confidence intervals for the two possible mass hierarchies: $normal hierarchy : \sin^{2} θ_{23} = 0.51 4_{- 0.056}^{+ 0.055}$ and $Δ m_{32}^{2} = (2.51 \pm 0.10) \times 1 0^{- 3} {eV}^{2} / c^{4}$ and $inverted hierarchy : \sin^{2} θ_{23} = 0.511 \pm 0.055$ and $Δ m_{13}^{2} = (2.48 \pm 0.10) \times 1 0^{- 3} {eV}^{2} / c^{4}$ . The analysis accounts for multinucleon mechanisms in neutrino interactions which were found to introduce negligible bias. We describe our first analyses that combine measurements of muon neutrino disappearance and electron neutrino appearance to estimate four oscillation parameters, $| Δ m^{2} |$ , $\sin^{2} θ_{23}$ , $\sin^{2} θ_{13}$ , $δ_{C P}$ , and the mass hierarchy. Frequentist and Bayesian intervals are presented for combinations of these parameters, with and without including recent reactor measurements. At 90% confidence level and including reactor measurements, we exclude the region $δ_{C P} = [0.15, 0.83] π$ for normal hierarchy and $δ_{C P} = [- 0.08, 1.09] π$ for inverted hierarchy. The T2K and reactor data weakly favor the normal hierarchy with a Bayes factor of 2.2. The most probable values and 68% one-dimensional credible intervals for the other oscillation parameters, when reactor data are included, are $\sin^{2} θ_{23} = 0.52 8_{- 0.038}^{+ 0.055}$ and $| Δ m_{32}^{2} | = (2.51 \pm 0.11) \times 1 0^{- 3} {eV}^{2} / c^{4}$ .

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Received 6 February 2015

DOI:https://doi.org/10.1103/PhysRevD.91.072010

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

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Vol. 91, Iss. 7 — 1 April 2015

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Figure 1
The T2K unoscillated neutrino flux prediction at SK is shown with bands indicating the systematic uncertainty prior to applying near detector data. The flux in the range $8 GeV < E_{ν} < 30 GeV$ is simulated but not shown. The binning for the vector of systematic parameters, $\vec{b}$ , for each neutrino component is shown by the four scales. The same binning is used for the ND280 and SK flux systematic parameters, ${\vec{b}}_{n}$ and ${\vec{b}}_{s}$ .
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Figure 2
Fractional systematic error on the $ν_{μ}$ flux at SK arising from the beam line configuration and hadron production, prior to applying near detector data constraints.
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Figure 3
Overview of the INGRID viewed from beam upstream. Two separate modules are placed at off-axis positions off the main cross to monitor the asymmetry of the beam.
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Figure 4
Daily event rate of the neutrino events normalized by protons on target. The error bars show the statistical errors. The horn current was reduced to 205 kA for part of Run 3.
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Figure 5
History of neutrino beam directions for horizontal (left) and vertical (right) directions as measured by INGRID and by the muon monitor (MUMON). The zero points of the vertical axes correspond to the nominal directions. The error bars show the statistical errors.
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Figure 6
Fractional uncertainties of the $ν_{μ}$ flux at SK due to the beam direction uncertainty evaluated from the previous and this INGRID beam analyses. These evaluations do not include constraints from ND280.
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Figure 7
History of neutrino beam width for horizontal (left) and vertical (right) directions for the horn 250 kA operation. The error bars show the statistical errors.
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Figure 8
Sketch of the ND280 off-axis detector in an exploded view. A supporting basket holds the $π^{0}$ detector (P0D) as well as the time projection chambers (TPCs) and fine grained detectors (FGDs) that make up the ND280 tracker. Surrounding the basket is a calorimeter (ECal) and within the magnet yoke is the side muon range detector (SMRD).
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Figure 9
Muon momentum and angle distribution for the CC-inclusive sample. These are compared to the simulation, broken down into the different reaction types shown in Table 9 and where non- $ν_{μ}$ CC refers to NC, ${\bar{ν}}_{μ}$ , and $ν_{e}$ interactions. All systematic parameters are set to their nominal values.
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Figure 10
Muon momentum and angle distribution for the $CC 0 π$ -like sample. These are compared to the simulation, broken down into the different reaction types, with all systematic parameters set to their nominal values.
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Figure 11
Muon momentum and angle distribution for the $CC 1 π^{+}$ -like sample. These are compared to the simulation, broken down into the different reaction types, with all systematic parameters set to their nominal values.
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Figure 12
Muon momentum and angle distribution for the CCOther-like sample. These are compared to the simulation, broken down into the different reaction types, with all systematic parameters set to their nominal values.
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Figure 13
The $p_{μ} − \cos θ_{μ}$ binning for the systematic parameters $\vec{d}$ that propagate the base detector systematic effects are shown in the left figure for the three event selections. The binning for the observed number of events is shown in the right figure. For the $CC 1 π^{+}$ -like sample, the bin division at $p_{μ} = 3.0 GeV / c$ is not used.
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Figure 14
Comparison of the data and Monte Carlo distributions for muon momentum (top) and angle (bottom) in the $CC 0 π$ -like sample, using the nominal and fitted values for the systematic parameters.
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Figure 15
Comparison of the data and Monte Carlo distributions for muon momentum (top) and angle (bottom) in the $CC 1 π^{+}$ -like sample, using the nominal and fitted values for the systematic parameters.
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Figure 16
Comparison of the data and Monte Carlo distributions for muon momentum (top) and angle (bottom) in the CCOther-like sample, using the nominal and fitted values for the systematic parameters.
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Figure 17
Prior and fitted values and uncertainties for the SK $ν_{μ}$ flux parameters (upper figure) and cross-section parameters (lower figure) constrained by the near detector analysis for the oscillation analyses. Uncertainties are calculated as the square root of the diagonal of the relevant covariance matrix. The value of $M_{A}^{QE}$ and $M_{A}^{RES}$ are given in units of $GeV / c^{2}$ , and all other parameters are multiplicative corrections.
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Figure 18
$Δ T_{0}$ distribution of all FC, OD, and LE events within $\pm 500 μ s$ of the expected beam arrival time. The histograms are stacked in that order.
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Figure 19
$Δ T_{0}$ distribution of all FC events within the beam spill window.
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Figure 20
The reconstructed energy spectra of the observed $ν_{e}$ (a) and $ν_{μ}$ (b) CC candidate events 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 following oscillation parameters: $\sin^{2} 2 θ_{13} = 0.1$ , $\sin^{2} 2 θ_{23} = 1.0$ , $δ_{C P} = 0$ , $Δ m_{23}^{2} = 2.4 \times 1 0^{- 3} {eV}^{2} / c^{4}$ and normal mass hierarchy.
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Figure 21
Two-dimensional vertex distributions of the observed $ν_{e}$ CC candidate events in (a) $x, y$ and (b) $r^{2} = x^{2} + y^{2}, z$ . The arrow indicates the neutrino beam direction and the dashed (blue online) line indicates the fiducial volume boundary. Events indicated by open square markers passed all of the $ν_{e}$ selection cuts except for the fiducial volume cut.
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Figure 22
Two-dimensional distributions of the logarithm of the likelihood ratio $\ln (L_{π^{0}} / L_{e})$ vs. the reconstructed invariant mass $m_{γ γ}$ , for signal $ν_{e}$ CCQE(left) and background NC $π^{0}$ (right) events. The diagonal line indicates the $π^{0}$ rejection criterion, and events lying above the line are rejected as $π^{0}$ background. The size of each box is proportional to the number of events the bin. The two figures use the same scale for representing the number of events and are normalized to the same POT.
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Figure 23
Efficiencies for rejecting NC $π^{0}$ events for the previous and the new $π^{0}$ rejection methods, plotted in bins of the energy of the less energetic $γ$ .
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Figure 24
The correlations between the estimated efficiencies for the final state topologies CC $1 e$ and CC $e$ other for the $ν_{e}$ CC event selection and CC $1 μ$ and CC $μ$ other for the $ν_{μ}$ CC event selection. The upper figure shows the combinations with positive correlation, and the lower with negative correlation. The diagonal correlations ( $correlation = 1$ ) are not shown.
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Figure 25
The $P (ν_{μ} \to ν_{μ})$ survival probability and $P (ν_{μ} \to ν_{e})$ appearance probability for different values of $\sin^{2} θ_{23}$ and for $δ_{C P}$ in the interval $[- π, π]$ for normal (solid) and inverted (dashed) mass hierarchy. The highlighted dot on each ellipse is the point for $δ_{C P} = 0$ and $δ_{C P}$ increases clockwise (anticlockwise) for normal (inverted) mass hierarchy. The other oscillation parameter values are fixed (solar parameters as established in Sec. 7b and $\sin^{2} θ_{13} = 0.0243$ ) and the neutrino energy is fixed to 0.6 GeV.
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Figure 26
Total error envelopes for the reconstructed energy distributions of $ν_{μ}$ CC (left) and $ν_{e}$ CC (right) candidate events, using typical oscillation parameter values, with and without the ND280 constraint applied.
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Figure 27
The 68% (dashed) and 90% (solid) C.L. intervals for the M1 $ν_{μ}$ -disappearance analysis assuming normal and inverted mass hierarchies. The 90% C.L. sensitivity contour for the normal hierarchy is overlaid for comparison.
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Figure 28
Top: Reconstructed neutrino energy spectrum for data, best-fit prediction, and unoscillated prediction. Bottom: Ratio of oscillated to unoscillated events as a function of neutrino energy for the data and the best-fit spectrum.
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Figure 29
Profiled - $2 Δ \ln L$ as a function of $\sin^{2} θ_{23}$ (left) and $| Δ m^{2} |$ (right), for the normal and inverted mass hierarchy assumptions. The 90% C.L. critical values are indicated by the lines with points.
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Figure 30
Difference in the point estimates of $\sin^{2} θ_{23}$ (left) and $| Δ m^{2} |$ (right) between pairs of toy MC data sets with and without including multinucleon effects.
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Figure 31
Profiled $Δ χ^{2}$ for the joint three-flavor oscillation analysis without using reactor data. The parameter $| Δ m^{2} |$ represents $Δ m_{32}^{2}$ or $Δ m_{13}^{2}$ for normal and inverted mass hierarchy assumptions, respectively. The horizontal lines show the critical $Δ χ^{2}$ values for one-dimensional fits at the 68% and 90% C.L. ( $Δ χ^{2} = 1.00$ and 2.71, respectively).
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Figure 32
The 68% (dashed) and 90% (solid) C.L. regions, from the analysis without using reactor data, with different mass hierarchy assumptions using $Δ χ^{2}$ with respect to the best-fit point—that from the inverted hierarchy. The parameter $| Δ m^{2} |$ represents $Δ m_{32}^{2}$ or $Δ m_{13}^{2}$ for normal and inverted mass hierarchy assumptions, respectively. The lower left plot shows one-dimensional confidence intervals in $\sin^{2} θ_{13}$ for different values of $δ_{C P}$ .
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Figure 33
Profiled $Δ χ^{2}$ for the joint three-flavor oscillation analysis combined with the results from reactor experiments. The parameter $| Δ m^{2} |$ represents $Δ m_{32}^{2}$ or $Δ m_{13}^{2}$ for normal and inverted mass hierarchy assumptions, respectively. The horizontal lines show the critical $Δ χ^{2}$ values for one-dimensional fits at the 68% and 90% C.L. ( $Δ χ^{2} = 1.00$ and 2.71, respectively).
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Figure 34
The 68% (dashed) and 90% (solid) C.L. regions from the analysis that includes results from reactor experiments with different mass hierarchy assumptions using $Δ χ^{2}$ with respect to the best-fit point, the one from the fit with normal hierarchy. The parameter $| Δ m^{2} |$ represents $Δ m_{32}^{2}$ or $Δ m_{13}^{2}$ for normal and inverted mass hierarchy assumptions, respectively.
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Figure 35
Comparison of 68% (dashed) and 90% (solid) C.L. regions combined with the results from reactor experiments with different mass hierarchy assumptions using $Δ χ^{2}$ with respect to the best-fit point, the one from the fit with normal hierarchy. The parameter $| Δ m^{2} |$ represents $Δ m_{32}^{2}$ or $Δ m_{13}^{2}$ for normal and inverted mass hierarchy assumptions, respectively.
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Figure 36
The 68% (dashed) and 90% (solid) C.L. regions for normal (top) and inverted (bottom) mass hierarchy combined with the results from reactor experiments in the ( $\sin^{2} θ_{23}$ , $Δ m_{32}^{2}$ ) space compared to the results from the Super-Kamiokande [131] and MINOS [132] experiments.
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Figure 37
Profiled $Δ χ^{2}$ as a function of $δ_{C P}$ with the results of the critical $Δ χ^{2}$ values for the normal and inverted hierarchies for the joint fit with reactor constraint, with the excluded regions found overlaid.
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Figure 38
Credible regions for $\sin^{2} θ_{13}$ and $δ_{C P}$ for T2K-only and $T 2 K + reactor$ combined analyses. These are constructed by marginalizing over both mass hierarchies. For the T2K-only analysis, the best fit line is shown instead of the best fit point because the analysis has little sensitivity to $δ_{C P}$ .
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Figure 39
Credible regions for $\sin^{2} θ_{23}$ and $Δ m_{32}^{2}$ for T2K-only and $T 2 K + reactor$ combined analyses. The normal hierarchy corresponds to positive values of $Δ m_{32}^{2}$ and the inverted hierarchy to negative values.
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Figure 40
The posterior probability for $δ_{C P}$ , marginalized over all other parameters, including mass hierarchy, for the $T 2 K + reactor$ combined analysis.
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Figure 41
T2K-only and $T 2 K + reactor$ prior best-fit spectra overlaid with SK $ν_{μ}$ CC and $ν_{e}$ CC candidate samples.
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Figure 42
Distributions of posterior probability between the oscillation parameters of interest for the T2K-only analysis. These posteriors use only MCMC points that are in the inverted hierarchy.
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Figure 43
Distributions of posterior probability between the oscillation parameters of interest for the $T 2 K + reactor$ analysis. These posteriors use only MCMC points that are in the normal hierarchy. In comparing to Fig. 42, note the change in scales for some parameters.
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Figure 44
Posterior probabilities for $δ_{C P}$ obtained by the two joint Bayesian analyses using the reactor experiments prior for $\sin^{2} θ_{13}$ .
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Figure 45
Marginal and profile likelihoods of the T2K data with reactor constraint assuming normal hierarchy.
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Physical Review D

covering particles, fields, gravitation, and cosmology

Measurements of neutrino oscillation in appearance and disappearance channels by the T2K experiment with $6.6 \times 1 0^{20}$ protons on target

K. Abe et al. (T2K Collaboration)

Phys. Rev. D 91, 072010 – Published 29 April 2015

Abstract

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Physical Review D

covering particles, fields, gravitation, and cosmology

Measurements of neutrino oscillation in appearance and disappearance channels by the T2K experiment with 6.6×1020 protons on target

K. Abe et al. (T2K Collaboration)

Phys. Rev. D 91, 072010 – Published 29 April 2015

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Measurements of neutrino oscillation in appearance and disappearance channels by the T2K experiment with $6.6 \times 1 0^{20}$ protons on target