The primary beamline consists of the preparation section (54 m long), arc section (147 m) and final focusing section (37 m). The uncertainty on the beam intensity is 2%, which comes from the calibration accuracy (1.7%), the effect of secondary electrons produced at the SSEM foils (<0.7%), the long-term stability of the individual CT monitors vs. each other and the CT monitor measurement from the main ring (0.5%). The distance between the center of the target and the upstream surface of beam spill is 109 m.
All remnants of decayed pions and other hadrons are stopped by the beam dump. A comparison of the expected field with the data taken at the right upstream port is shown in the figure. The magnitude of this field is 3.7% of the field magnitude just outside the inner conductor, and conservative estimates from Monte Carlo simulations suggest that the effect on the neutrino flux is small, as discussed in V D .
The direction of the neutrino beam is measured as the direction from the target to the center of the muon profile. The accuracy of measurement at a short distance (e.g. direction towards nearby detectors) is about 7×10−5 rad. The deviation of the beam angle measured by MU-MON from the mean is within 1 mrad.
The stability of the beam direction and intensity is also monitored by measuring the neutrino beam itself .
THE NEUTRINO FLUX SIMULATION The prediction of the flux and spectrum of neutrinos at
On-target primary beam interaction Simulation of primary beam proton interactions with cladding graphite and target core is performed using FLUKA 2008. Off-target, where GEANT3 controls the simulation, interactions are modeled with GCALOR. The distribution of the predicted flux for a given flavor from the final hadron in the interaction chain is shown in Table X .
An additional data set, obtained with the target removed, was used to account for contamination from particles produced in proton beam interactions occurring outside the target. Charged particles are identified using specific energy loss (dE/dx) and time-of-flight (T oF) measurements. More than 90% of the pion phase space is covered, and the K+ data cover a significant portion of the kaon phase space.
Inelastic cross-section measurements for proton, pion, and kaon beams with carbon and aluminum targets are used to reweight the particle interaction rates and absorption in the simulation. The differential production reweighting is evaluated using the differential multiplicity in the momentum, p, of the produced particle and its angle, θ, with respect to the incident particle:. For interactions of 31 GeV/c protons on carbon producing π± or K+ in the phase space covered by the NA61/SHINE data, the construction of the ratio in Eq.
The accuracy and precision of the scaling for the individual data points is discussed in Sec. The relationship between the data and the FLUKA predictions is evaluated, and the corresponding distributions of weights from each data set are shown in Fig. For regions not covered by any data, no reweighting is applied and the effect is examined as part of uncertain-.
The quasi-elastic cross section is extrapolated from hadron+nucleon scattering data using a modification of the empirical dependence derived by Bellettiniet al.:. V A 4, the uncertainties on the weights are conservatively set in the magnitude of the quasi-elastic correction used to derive the production cross section. Interaction rate reweighting models the change in particle survival probability as the cross section changes, as well as the change in velocity at a given interaction point.
The effect of the weights is seen by taking the energy-dependent ratio of the flux with and without the applied weights, as shown in Fig. Summary of the T2K flux prediction. hadron interaction probabilities outlined here.
UNCERTAINTIES ON THE FLUX PREDICTION
The total streamflow forecast uncertainty is simply represented by the sum of the covariances from each independent source of uncertainty described in the following text. Total errors are typically 5 to 10% in the most important regions of phase space. Emaxcm , (20) where Ecm is the energy of the produced particle in the frame of the center of mass, and Ecmmaxi is the maximum energy.
The NA61/SHINE data cover most of the phase space for secondary pions contributing to the T2K neutrino flux. In the case of the NA61/SHINEK+ data, the systematic uncertainties (apart from the overall normalization) are treated as uncorrelated between different data bins. These uncertainties range in the region of 10–22% depending on the momentum bin, while the systematic uncertainties are around 4% for most bins.
For the NA61/SHINE K+ data a coarse moment and angular data fitting had to be adopted due to limited statistics. For kaon production from interactions in Al around the target, the uncertainties are estimated based on the comparison of Eichtenet al. Secondary proton (neutron) interactions within the target contribute about 16% (5%) to the neutrino flux.
This is a conservative estimate of the uncertainty since no constraint is imposed on the average nucleon abundance in the reweighting procedure. The results of the next batch of measurements from NA61/SHINE will reduce the overall uncertainty in the neutrino flux prediction. 39 shows the neutrino flux calculated using the positively charged pion production reweighting based on the replica target data compared to the flux obtained with the reweighting based on thin measurements of the NA61/SHINE target.
To study the effects of the systematic errors in the proton beam measurements on the neutrino flux, these parameters were varied within the errors given in Ta-. In the case of horn position alignment uncertainties, the effects of horn movements along each coordinate axis were investigated. Of the three directions, only the uncertainty in y results in a significant change (at the level of a few percent) in the predicted flux.
The effects of the systematic uncertainties in the target and horn adjustments on the predicted νµ fluxes at ND280 and SK are summarized in fig. Shifts in the off-axis angle of the proton beam tend to shift the peak position of the flux in energy.
FLUX PREDICTION AND T2K NEUTRINO DATA
An inclusive choice of νµ is used for interactions at ND280 by searching for events with a negatively charged trace originating from the fiducial volume of the first fine-grained detector followed by the time-projection chamber immediately behind and identified as muon-like by dE/dx. The predicted muon momentum distribution for this selection is compared with the measured distribution from data collected in The profile of the number of events on each detector module is fitted with a Gaussian function.
The interactions of neutrinos produced in pion decay tend to produce events with lower muon momentum (since the neutrino energy is typically smaller), while neutrinos from kaon decay are the dominant contribution for interactions with higher muon momenta. The predicted and measured spectra show good agreement within the uncertainty of the flux prediction, which is ∼10% for all muon momenta. Rdata/M C stat.)±0.098(f lux) (24) This equation does not include uncertainties in the neutrino interaction model or the detector simulation and event reconstruction.
The total systematic uncertainty at the peak energy is approx. 15% for both the near and far detector, with the dominant source being the hadron interaction uncertainties. The uncertainty on the relationship between the flux predictions at the far and near detectors forνµ. The predicted flux with simulated neutrino interactions is compared with the measurements at the near detectors.
We thank the J-PARC accelerator team for the excellent accelerator performance and the J-PARC Center for the continuous support of the T2K experiment. We are grateful to the NA61/SHINE collaboration and FLUKA team for their assistance in making our data-driven flood forecast. We acknowledge the support of MEXT, Japan; NSERC, NRC and CFI, Canada; CEA and CNRS/IN2P3, France; DFG, Germany; INFN, Italy; National Science Centre, Poland; RAS, RFBR and the Ministry of Education and Science of the Russian Federation;.
We also thank CERN for their donation of the UA1/NOMAD magnet and DESY for the HERA-B magnet mover system. In addition, the participation of individual researchers and institutions in T2K has been further supported by funds from: ERC (FP7), EU; JSPS, Japan; Royal Society, UK; DOE Early Career Program, and the A.