T2K neutrino flux prediction

The Tokai-to-Kamioka (T2K) experiment studies neutrino oscillations using an off-axis muon neutrino beam with a peak energy of about 0.6 GeV that originates at the Japan Proton Accelerator Research Complex accelerator facility. Interactions of the neutrinos are observed at near detectors placed at 280 m from the production target and at the far detector—Super-Kamiokande—located 295 km away. The flux prediction is an essential part of the successful prediction of neutrino interaction rates at the T2K detectors and is an important input to T2K neutrino oscillation and cross section measurements. A FLUKA and GEANT3-based simulation models the physical processes involved in the neutrino production, from the interaction of primary beam protons in the T2K target, to the decay of hadrons and muons that produce neutrinos. The simulation uses proton beam monitor measurements as inputs. The modeling of hadronic interactions is reweighted using thin target hadron production data, including recent charged pion and kaon measurements from the NA61/SHINE experiment. For the first T2K analyses the uncertainties on the flux prediction are evaluated to be below 15% near the flux peak. The uncertainty on the ratio of the flux predictions at the far and near detectors is less than 2% near the flux peak.

Figure 1

Muon neutrino survival probability at 295 km and neutrino fluxes for different off-axis angles.

Figure 2

An overview of the T2K neutrino beam line.

Figure 3

Location of the primary beam line monitors in the final focusing section.

Figure 4

Side view of the secondary beam line.

Figure 5

The predicted flux of ${\nu }_{\mu }$ at the SK far detector for operation at different horn currents. The flux histogram (top) ranges from 0 to 3 GeV, while the ratios (bottom) range from 0 to 10 GeV.

Figure 6

Cross section view of horns.

Figure 7

Measurements of the magnetic field magnitude taken at the right upstream port of horn 1. The curve shows the expected field strength, including a small correction to account for fringe effects near the instrumentation port at large radii.

Figure 8

A sample of data from the Hall probe showing the field strength in the $x$ direction in the beam coordinates. This data was taken 100 cm along the axis of the horn. The Rogowski coil output, showing the current time dependence, is drawn with unfilled markers and is not to scale. The peaks are offset by approximately 0.7 ms.

Figure 9

The correlations between the beam position measurements in $x$ (top) and $y$ (bottom) by the OTR monitor and the SSEM monitors extrapolated to the OTR position. The intercept and slope are from a linear fit (red line) to the measurements.

Figure 10

History of total accumulated protons and protons per pulse for the good quality beam data. The solid line shows the accumulated POT. The dot points show the number of protons per pulse.

Figure 11

Time history of the measured muon profile center at MUMON in all run periods. A top and bottom figure shows the profile center in the horizontal ($X$) and the vertical ($Y$), respectively. A dashed line corresponds to 1 mrad at MUMON. Both directions are controlled within 1 mrad.

Figure 12

Neutrino events per ${10}^{14}$ POT measured by INGRID (points) overlaid with mean value (dashed lines). The error bar represents the statistical error on the INGRID measurement.

Figure 13

Flow diagram of the flux prediction.

Figure 14

A two dimensional view of the geometrical setup in the FLUKA simulation of the baffle and the target.

Figure 15

The phase space of pions and kaons contributing to the predicted neutrino flux at SK, and the regions covered by NA61/SHINE measurements.

Figure 16

The differential production weights from NA61/SHINE data for ${\pi }^{+}$ (top), ${\pi }^{-}$ (middle) and $K^{+}$ (bottom).

Figure 17

Examples of the material scaling exponent $\alpha$ fit for a few angular bins in the [27] $K^{+}$ data.

Figure 18

The differential production weights for GCALOR from $A$-scaled NA61/SHINE data for ${\pi }^{+}$ (top), ${\pi }^{-}$ (bottom).

Figure 19

The interpolated kaon production double differential cross section measurements of Eichten et al. [27] (top) and Allaby et al. [28] (bottom). The markers indicate the locations of the data points.

Figure 20

Ratios of the interpolated charged kaon double differential production multiplicity measurements from Eichten et al. [27] and Allaby et al. [28] over the FLUKA predicted yields from Be for $24\mathrm{GeV}/c$ and $19.2\mathrm{GeV}/c$ proton beam momenta, respectively.

Figure 21

Ratios of the interpolated $K_L^0$ double differential production multiplicity derived from Eichten et al. [27] and Allaby et al. [28] over the FLUKA predicted yields from Be for $24\mathrm{GeV}/c$ and $19.2\mathrm{GeV}/c$ proton beam momenta, respectively.

Figure 22

The elastic cross sections for protons scattering on protons and neutrons and the derived quasi-elastic cross section for a carbon target.

Figure 23

Comparisons of ${\sigma }_{\mathrm{prod}}$ measurements and the values used in the simulation (solid line for FLUKA and dashed line for GCALOR), for incident protons (top left) and charged pions (top right), $K^{+}$ (bottom left) and $K^{-}$ (bottom right).

Figure 24

Ratio of the hadron interaction reweighted flux over the nominal flux for ${\nu }_{\mu }$ (upper left), ${\overline{\nu }}_{\mu }$ (upper right), ${\nu }_e$ (lower left), ${\overline{\nu }}_e$ (lower right).

Figure 25

The flux predictions for the SK far detector and ND280 near detector broken down by the neutrino parent particle type. The error bars, which are too small to be seen in most energy bins, are due to the MC statistical error.

Figure 26

The fractional error on the NA61/SHINE measurements in each of the $p\mathrm{\text{−}}\theta$ bins. The gap at ${\pi }^{+}$ momentum of $1.0–1.2\mathrm{GeV}/c$ is a region with no NA61/SHINE data points.

Figure 27

The weights for FLUKA $\mathrm{p}+\mathrm{C}$ interactions derived from the BMPT fits of BNL-E910 ${\pi }^{+}$ (top) and ${\pi }^{-}$ (bottom) multiplicity data with $17.5\mathrm{GeV}/c$ protons.

Figure 28

The BMPT fits to the NA61/SHINE pion production data.

Figure 29

Fractional flux error due to pion production as a function of neutrino energy, for each flavor and at the near and far detectors.

Figure 30

The BMPT fits to the NA61/SHINE $K^{+}$ data.

Figure 31

The BMPT fits to the kaon data of Eichten et al. [27].

Figure 32

The BMPT fits to the kaon data of Allaby et al. [28].

Figure 33

Distribution of the ratios of Al to scaled Be yields, $R_{\mathrm{Al}/\mathrm{Scaled}\mathrm{Be}}$, for the [27] $K^{+}$ data. The fit (Gaussian function), which extracts the mean and r.m.s. of the distribution, is overlaid.

Figure 34

Fractional flux error due to kaon production as a function of neutrino energy, for each flavor and at the near and far detectors.

Figure 35

Distribution of secondary protons and neutrons contributing to the neutrino flux at SK, evaluated with the FLUKA hadron interaction model.

Figure 36

Ratio of the secondary proton measurements from Eichten et al. [27] and Allaby et al. [28] and the FLUKA modeling of secondary protons. Each circle is a point from the data sets.

Figure 37

Production cross section measurements for protons on graphite targets for momenta $20–60\mathrm{GeV}/c$. The data from Denisov et al. are shown with and without the quasi-elastic estimate subtracted since the quantity that is measured is ambiguous.

Figure 38

Fractional flux error due to hadron production uncertainties.

Figure 39

Reweighted ${\nu }_{\mu }$ flux at the far detector based on the NA61/SHINE thin target and replica target measurements.

Figure 40

An example of the fractional change of SK ${\nu }_{\mu }$ flux when the beam center position ($Y$) and center angle (${\theta }_Y$) measured in run 1 are changed by $1\sigma$, i.e. set to 1.42 mm and 0.29 mrad, respectively.

Figure 41

Fractional change of the ${\nu }_{\mu }$ flux at ND280 (top) and SK (bottom) corresponding to the systematics error of the off-axis angle.

Figure 42

Fractional uncertainties due to the target and horn alignment in the ${\nu }_{\mu }$ flux for ND280 (top) and SK (bottom).

Figure 43

Fractional flux error including all sources of uncertainties.

Figure 44

Correlations of the flux for a given flavor, energy and detector. The binning on the $y$ axis is identical to the binning on the $x$ axis.

Figure 45

The far/near ratio for the ${\nu }_{\mu }$ flux prediction (top) and the uncertainty on the ratio (bottom).

Figure 46

The predicted flux at each of the horizontal INGRID detector modules from the center module (3) to the edge module (0).

Figure 47

The accumulated horizontal neutrino beam profile reconstructed by INGRID for the run 1 period. The profile of the number of events at each detector module is fitted with a Gaussian function. Systematic errors are not shown in this plot.

Figure 48

The predicted and measured muon momentum spectrum at ND280 for the inclusive selection (top) and the fractional flux uncertainty (not including neutrino interaction uncertainties nor the detector systematic error) and deviations of the data from the prediction on that sample (bottom).