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A side view of the T2K neutrino beamline. See Ref.~\cite{T2K-NIM-paper} for a detailed description and for notations used.

Prediction (based on FLUKA2008.3b and re-weighted by the NA61 thin target data) of the $\nu_{\mu}$ [left] and $\nu_e$ [right] fluxes at the near detector of T2K. Different colours refer to the contributions of the various parent particles.

Prediction (based on FLUKA2008.3b and re-weighted by the NA61 thin target data) of the $\nu_{\mu}$ [left] and $\nu_e$ [right] fluxes at the near detector of T2K. The contribution of different parent particles to the total flux are shown.

Prediction (based on FLUKA2008.3b and re-weighted by the NA61 thin target data) of the $\nu_{\mu}$ [left] and $\nu_e$ [right] fluxes at the near detector of T2K. Different colours refer to the contributions of the various parent particles.

{\it Secondary} and {\it tertiary} components of the $\nu_\mu$ [top left] and $\nu_e$ [top right] fluxes at the far detector. The contribution of parents originating from the target sums up to 90~\%, among which 60~\% are due to the {\it secondary} component and 30~\% due to re-interactions in the target (the in-target component). The relative contributions of the secondary and total in-target (secondary$+$tertiary in-target) components are shown for $\nu_\mu$ [bottom left] and $\nu_e$ [bottom right] as a function of energy. The dashed vertical line shows the location of the peak of the beam energy spectrum (600~MeV). Predictions are based on FLUKA2008.3b and re-weighted by the NA61 thin-target data.

Prediction (based on FLUKA2008.3b and re-weighted by the NA61 thin target data) of the $\nu_{\mu}$ [left] and $\nu_e$ [right] fluxes at the near detector of T2K. The contribution of different parent particles to the total flux are shown.

{\it Secondary} and {\it tertiary} components of the $\nu_\mu$ [top left] and $\nu_e$ [top right] fluxes at the far detector. The contribution of parents originating from the target sums up to 90~\%, among which 60~\% are due to the {\it secondary} component and 30~\% due to re-interactions in the target (the in-target component). The relative contributions of the secondary and total in-target (secondary$+$tertiary in-target) components are shown for $\nu_\mu$ [bottom left] and $\nu_e$ [bottom right] as a function of energy. The dashed vertical line shows the location of the peak of the beam energy spectrum (600~MeV). Predictions are based on FLUKA2008.3b and re-weighted by the NA61 thin-target data.

{\it Secondary} and {\it tertiary} components of the $\nu_\mu$ [top left] and $\nu_e$ [top right] fluxes at the far detector. The contribution of parents originating from the target sums up to 90~\%, among which 60~\% are due to the {\it secondary} component and 30~\% due to re-interactions in the target (the in-target component). The relative contributions of the secondary and total in-target (secondary$+$tertiary in-target) components are shown for $\nu_\mu$ [bottom left] and $\nu_e$ [bottom right] as a function of energy. The dashed vertical line shows the location of the peak of the beam energy spectrum (600~MeV). Predictions are based on FLUKA2008.3b and re-weighted by the NA61 thin-target data.

{\it Secondary} and {\it tertiary} components of the $\nu_\mu$ [top left] and $\nu_e$ [top right] fluxes at the far detector. The contribution of parents originating from the target sums up to 90~\%, among which 60~\% are due to the {\it secondary} component and 30~\% due to re-interactions in the target (the in-target component). The relative contributions of the secondary and total in-target (secondary$+$tertiary in-target) components are shown for $\nu_\mu$ [bottom left] and $\nu_e$ [bottom right] as a function of energy. The dashed vertical line shows the location of the peak of the beam energy spectrum (600~MeV). Predictions are based on FLUKA2008.3b and re-weighted by the NA61 thin-target data.

{\it Secondary} and {\it tertiary} components of the $\nu_\mu$ [top left] and $\nu_e$ [top right] fluxes at the far detector. The contribution of parents originating from the target sums up to 90~\%, among which 60~\% are due to the {\it secondary} component and 30~\% due to re-interactions in the target (the in-target component). The relative contributions of the secondary and total in-target (secondary$+$tertiary in-target) components are shown for $\nu_\mu$ [bottom left] and $\nu_e$ [bottom right] as a function of energy. The dashed vertical line shows the location of the peak of the beam energy spectrum (600~MeV). Predictions are based on FLUKA2008.3b and re-weighted by the NA61 thin-target data.

Systematic errors of the $\nu_\mu$ [top left] and $\nu_e$ [top right] fluxes at the far detector of T2K for the analysis described in Ref.~\cite{T2K-nue-paper,T2K-numu-paper}. The {\it beam line} uncertainty combines contributions from the proton beam, off-axis angle, target-horn alignment and horn current uncertainties. The bottom plot shows the breakdown of the uncertainty on the pion multiplicity in secondary and tertiary contributions for the $\nu_{\mu}$ fractional error.

{\it Secondary} and {\it tertiary} components of the $\nu_\mu$ [top left] and $\nu_e$ [top right] fluxes at the far detector. The contribution of parents originating from the target sums up to 90~\%, among which 60~\% are due to the {\it secondary} component and 30~\% due to re-interactions in the target (the in-target component). The relative contributions of the secondary and total in-target (secondary$+$tertiary in-target) components are shown for $\nu_\mu$ [bottom left] and $\nu_e$ [bottom right] as a function of energy. The dashed vertical line shows the location of the peak of the beam energy spectrum (600~MeV). Predictions are based on FLUKA2008.3b and re-weighted by the NA61 thin-target data.

Systematic errors of the $\nu_\mu$ [top left] and $\nu_e$ [top right] fluxes at the far detector of T2K for the analysis described in Ref.~\cite{T2K-nue-paper,T2K-numu-paper}. The {\it beamline} uncertainty combines contributions from the proton beam, off-axis angle, target-horn alignment and horn current uncertainties. The bottom plot shows the breakdown of the uncertainty on the pion multiplicity in secondary and tertiary contributions for the $\nu_{\mu}$ fractional error.

Systematic errors of the $\nu_\mu$ [top left] and $\nu_e$ [top right] fluxes at the far detector of T2K for the analysis described in Ref.~\cite{T2K-nue-paper,T2K-numu-paper}. The {\it beam line} uncertainty combines contributions from the proton beam, off-axis angle, target-horn alignment and horn current uncertainties. The bottom plot shows the breakdown of the uncertainty on the pion multiplicity in secondary and tertiary contributions for the $\nu_{\mu}$ fractional error.

Systematic errors of the $\nu_\mu$ [top left] and $\nu_e$ [top right] fluxes at the far detector of T2K for the analysis described in Ref.~\cite{T2K-nue-paper,T2K-numu-paper}. The {\it beamline} uncertainty combines contributions from the proton beam, off-axis angle, target-horn alignment and horn current uncertainties. The bottom plot shows the breakdown of the uncertainty on the pion multiplicity in secondary and tertiary contributions for the $\nu_{\mu}$ fractional error.

Systematic errors of the $\nu_\mu$ [top left] and $\nu_e$ [top right] fluxes at the far detector of T2K for the analysis described in Ref.~\cite{T2K-nue-paper,T2K-numu-paper}. The {\it beamline} uncertainty combines contributions from the proton beam, off-axis angle, target-horn alignment and horn current uncertainties. The bottom plot shows the breakdown of the uncertainty on the pion multiplicity in secondary and tertiary contributions for the $\nu_{\mu}$ fractional error.

An example of a reconstructed p+C interaction at 30~GeV beam energy in the replica of the T2K target showing tracks reconstructed in the TPCs and associated with hits in the ToF-F detector. The incoming beam direction is along the $z$ axis. The magnetic field bends the trajectory of outgoing charged particles in the $x-z$ (horizontal) plane. The drift direction in the TPCs is along the $y$ axis.

Technical drawing with dimensions given in mm (side view) of the replica target used during the NA61 data taking [top left] consisting of a 90~cm long graphite rod and aluminium support flanges. Drawing of the complete geometry of the T2K target [top right]. The overlaid red rectangle represents the simplified geometry of the replica target. View of the T2K target and its cooling envelope embedded in the first focusing horn of the T2K beamline [bottom].

Technical drawing (side view) of the replica target used during the NA61 data taking [top left] consisting of a 90~cm long graphite rod and aluminium support flanges. Drawing of the complete geometry of the T2K target [top right]. The overlaid red rectangle represents the simplified geometry of the replica target. View of the T2K target and its cooling envelope embedded in the first focusing horn of the T2K beam line [bottom].

Kinematical phase space of positively charged pions (for 10$^{21}$ pot) exiting from the side of the target (summed over five longitudinal bins along the target, see text) [left] or from the downstream face [right], and producing neutrinos in the direction of the far detector of T2K. The respective analysis binning of the NA61 data with the replica of the T2K target is overlaid on top. Predictions obtained from the T2K beam simulation.

Technical drawing (side view) of the replica target used during the NA61 data taking [top left] consisting of a 90~cm long graphite rod and aluminium support flanges. Drawing of the complete geometry of the T2K target [top right]. The overlaid red rectangle represents the simplified geometry of the replica target. View of the T2K target and its cooling envelope embedded in the first focusing horn of the T2K beam line [bottom].

Kinematical phase space of positively charged pions (for 10$^{21}$ pot) exiting from the side of the target (summed over five longitudinal bins along the target, see text) [left] or from the downstream face [right], and producing neutrinos in the direction of the far detector of T2K. The respective analysis binning of the NA61 data with the replica of the T2K target is overlaid on top. Predictions obtained from the T2K beam simulation.

Distribution of the azimuthal angle, $\phi$, of all TPC tracks in data (markers) and MC (line).

Time distribution of beam particles in a 40~$\mu$s time window for single beam particle events [left] ($\sim$60 \% of all events), and events with two beam particles [right] ($\sim$40 \% of all events). The beam time is centered at -300~ns.

Time distribution of beam particles in a 40~$\mu$s time window for single beam particle events [left] ($\sim$60 \% of all events), and events with two beam particles [right] ($\sim$40 \% of all events). The beam time is centered at -300~ns.

Track multiplicity in the TPCs without (solid) and with (dashed) the \mbox{ToF-F} requirement for events with different numbers of beam particles [left]. Multiplicity distributions normalised to the number of single beam particle events with the \mbox{ToF-F} requirement [right].

Track multiplicity in the TPCs without (solid) and with (dashed) the \mbox{ToF-F} requirement for events with different numbers of beam particles [left]. Multiplicity distributions normalised to the number of single beam particle events with the \mbox{ToF-F} requirement [right].

Sketch depicting the backward extrapolation of TPC tracks onto the surface of the target. The point of closest approach is determined and the track parameters $p$ and $\theta$ are calculated at this point. Only tracks for which this point lies within a distance of 0.6 cm around the target surface are accepted. The resolution for the different track parameters are also given in the figure.

noimgError on the polar angle [left] and momentum resolution [right] as a function of momentum of the TPC tracks for data (solid) and MC (dashed). Labels refer to track topologies defined in the text.

Profile [left] and radial distribution [right] of the beam on the upstream face of the replica target. The radial distribution is shown before (solid) and after (dashed) applying a beam track selection defined in the text. The solid (dashed) circle shows the position of the upstream (downstream) face. The dotted vertical line shows the radius of the target.

Profile [left] and radial distribution [right] of the beam on the upstream face of the replica target. The radial distribution is shown before (solid) and after (dashed) applying a beam track selection defined in the text. The solid (dashed) circle shows the position of the upstream (downstream) face. The dotted vertical line shows the radius of the target.

Distribution of the point of closest approach of the TPC tracks in the $x-z$ [left] and $y-z$ [right] projections after backward extrapolation to the surface of the target. The fact that the side of the target appears fuzzy in the vertical projection ($y$) is a consequence of the azimuthal acceptance of the detector (see Fig.~\ref{na61-azimuthal-acc}) which is further constrained by the $\pm$30 degree wedge cut defined in the text.

Distribution of the point of closest approach of the TPC tracks in the $x-z$ [left] and $y-z$ [right] projections after backward extrapolation to the surface of the target. The fact that the side of the target appears fuzzy in the vertical projection ($y$) is a consequence of the azimuthal acceptance of the detector (see Fig.~\ref{na61-azimuthal-acc}) which is further constrained by the $\pm$30 degree wedge cut defined in the text.

Top panel: $dE/dx$ [left] and mass squared [right] distributions for all TPC tracks as a function of the track momentum at the first fitted TPC cluster. Bottom panel: $(m^2,dE/dx)$ distributions of positively charged tracks for $40<\theta<100$~mrad polar angle and $2.4

Top panel: $dE/dx$ [left] and mass squared [right] distributions for all TPC tracks as a function of the track momentum at the first fitted TPC cluster. Bottom panel: $(m^2,dE/dx)$ distributions of positively charged tracks for $40<\theta<100$~mrad polar angle and $2.4

Top panel: $dE/dx$ [left] and mass squared [right] distributions for all TPC tracks as a function of the track momentum at the first fitted TPC cluster. Bottom panel: $(m^2,dE/dx)$ distributions of positively charged tracks for $40<\theta<100$~mrad polar angle and $2.4

Top panel: $dE/dx$ [left] and mass squared [right] distributions for all TPC tracks as a function of the track momentum at the first fitted TPC cluster. Bottom panel: $(m^2,dE/dx)$ distributions of positively charged tracks for $40<\theta<100$~mrad polar angle and $2.4

Two-dimensional fit of the data in the $(m^2,dE/dx)$ plane [left] and respective mass squared projection [right], for $40<\theta<100$~mrad and $2.4

Two-dimensional fit of the data in the $(m^2,dE/dx)$ plane [left] and respective mass squared projection [right], for $40<\theta<100$~mrad and $2.4

Distributions of momentum [left] and polar angle [right] of TPC tracks at the surface of the target for data (markers) and MC (solid smoothed curves). The different track topologies are specified in the legend on the right plot and described in the text. Small data--MC differences at large angles (above $\sim$250~mrad) do not influence the results reported here.

Distributions of momentum [left] and polar angle [right] of TPC tracks at the surface of the target for data (markers) and MC (solid smoothed curves). The different track topologies are specified in the legend on the right plot and described in the text. Small data--MC differences at large angles (above $\sim$250~mrad) do not influence the results reported here.

Momentum distribution of negatively charged pion-like tracks [left] after backward extrapolation, requirement for a point of closest approach closer than 0.6 cm to the surface of the target and a simple $dE/dx$-based PID selection to reject electrons. Ratio of data to MC [right].

Momentum distribution of negatively charged pion-like tracks [left] after backward extrapolation, requirement for a point of closest approach closer than 0.6 cm to the surface of the target and a simple $dE/dx$-based PID selection to reject electrons. Ratio of data to MC [right].

Two-dimensional fit of the simulated data in the $(m^2,dE/dx)$ plane [left] and respective $dE/dx$ projection [right], for $40<\theta<100$~mrad and $2.4

Two-dimensional fit of the simulated data in the $(m^2,dE/dx)$ plane [left] and respective $dE/dx$ projection [right], for $40<\theta<100$~mrad and $2.4

Spectra of outgoing positively charged pions normalised to the momentum bin size and number of protons on target in the angular interval [40-100]~mrad for the most upstream [top left], central [top right] and most downstream [bottom left] longitudinal bins, and in the angular interval [0-40]~mrad for the downstream face of the target [bottom right]. Error bars correspond to the sum in quadrature of statistical and systematic uncertainties. Smooth curves show the prediction of FLUKA2011.2 associated to tracks reconstructed within the acceptance of the NA61 detector (described in Section~\ref{track-reconstruction}). FLUKA+GCALOR refers to the MC yields after reconstruction and PID analysis.

Spectra of outgoing positively charged pions normalised to the momentum bin size and number of protons on target in the angular interval [40-100]~mrad for the most upstream [top left], central [top right] and most downstream [bottom left] longitudinal bins, and in the angular interval [0-40]~mrad for the downstream face of the target [bottom right]. Error bars correspond to the sum in quadrature of statistical and systematic uncertainties. Smooth curves show the prediction of FLUKA2011.2 associated to tracks reconstructed within the acceptance of the NA61 detector (described in Section~\ref{track-reconstruction}). FLUKA+GCALOR refers to the MC yields after reconstruction and PID analysis.

Spectra of outgoing positively charged pions normalised to the momentum bin size and number of protons on target in the angular interval [40-100]~mrad for the most upstream [top left], central [top right] and most downstream [bottom left] longitudinal bins, and in the angular interval [0-40]~mrad for the downstream face of the target [bottom right]. Error bars correspond to the sum in quadrature of statistical and systematic uncertainties. Smooth curves show the prediction of FLUKA2011.2 associated to tracks reconstructed within the acceptance of the NA61 detector (described in Section~\ref{track-reconstruction}). FLUKA+GCALOR refers to the MC yields after reconstruction and PID analysis.

Spectra of outgoing positively charged pions normalised to the momentum bin size and number of protons on target in the angular interval [40-100]~mrad for the most upstream [top left], central [top right] and most downstream [bottom left] longitudinal bins, and in the angular interval [0-40]~mrad for the downstream face of the target [bottom right]. Error bars correspond to the sum in quadrature of statistical and systematic uncertainties. Smooth curves show the prediction of FLUKA2011.2 associated to tracks reconstructed within the acceptance of the NA61 detector (described in Section~\ref{track-reconstruction}). FLUKA+GCALOR refers to the MC yields after reconstruction and PID analysis.

Re-weighting factors for outgoing positively charged pions in the angular interval [40-100]~mrad for the most upstream [top left], central [top right] and most downstream [bottom left] longitudinal bins, and in the angular interval [0-40]~mrad for the downstream face of the target [bottom right]. Error bars correspond to the sum in quadrature of statistical and systematic uncertainties.

Re-weighting factors for outgoing positively charged pions in the angular interval [40-100]~mrad for the most upstream [top left], central [top right] and most downstream [bottom left] longitudinal bins, and in the angular interval [0-40]~mrad for the downstream face of the target [bottom right]. Error bars correspond to the sum in quadrature of statistical and systematic uncertainties.

Re-weighting factors for outgoing positively charged pions in the angular interval [40-100]~mrad for the most upstream [top left], central [top right] and most downstream [bottom left] longitudinal bins, and in the angular interval [0-40]~mrad for the downstream face of the target [bottom right]. Error bars correspond to the sum in quadrature of statistical and systematic uncertainties.

Re-weighting factors for outgoing positively charged pions in the angular interval [40-100]~mrad for the most upstream [top left], central [top right] and most downstream [bottom left] longitudinal bins, and in the angular interval [0-40]~mrad for the downstream face of the target [bottom right]. Error bars correspond to the sum in quadrature of statistical and systematic uncertainties.

Re-weighted $\nu_{\mu}$ flux predictions at the far detector of T2K based on the NA61 thin-target and replica-target data [left] and ratio of the two predictions [right]. Details about the associated errors are given in the text. A linear fit to the ratio [right] is shown by the solid line.

Re-weighted $\nu_{\mu}$ flux predictions at the far detector of T2K based on the NA61 thin-target and replica-target data [left] and ratio of the two predictions [right]. Details about the associated errors are given in the text. A linear fit to the ratio [right] is shown by the solid line.