Measurement of $K^{+}$ production cross section by 8 GeV protons using high-energy neutrino interactions in the SciBooNE detector

The SciBooNE Collaboration reports $K^{+}$ production cross section and rate measurements using high-energy daughter muon neutrino scattering data off the SciBar polystyrene (${\mathrm{C}}_8{\mathrm{H}}_8$) target in the SciBooNE detector. The $K^{+}$ mesons are produced by 8 GeV protons striking a beryllium target in Fermilab Booster Neutrino Beam line (BNB). Using observed neutrino and antineutrino events in SciBooNE, we measure $\frac{d^2\sigma }{dpd\Omega }=(5.34\pm 0.76)\mathrm{mb}/(\mathrm{GeV}/c\times \mathrm{sr})$ for $p+Be\to K^{+}+X$ at mean $K^{+}$ energy of 3.9 GeV and angle (with respect to the proton beam direction) of 3.7 degrees, corresponding to the selected $K^{+}$ sample. Compared to Monte Carlo predictions using previous higher energy $K^{+}$ production measurements, this measurement, which uses the NUANCE neutrino interaction generator, is consistent with a normalization factor of $0.85\pm 0.12$. This agreement is evidence that the extrapolation of the higher energy $K^{+}$ measurements to an 8 GeV beam energy using Feynman scaling is valid. This measurement reduces the error on the $K^{+}$ production cross section from 40% to 14%.

Figure 1

Neutrino flux predictions at the SciBooNE detector as a function of neutrino energy $E_{\nu }$, normalized per unit area, POT, and neutrino energy bin width, in neutrino (top) and antineutrino (bottom) modes. The spectra is averaged within a circle with radius 2.12 m from beam center (coincides with center of detector cross-sectional area), which covers the entire $3\mathrm{m}\times 3\mathrm{m}$ cross-sectional area of the SciBooNE detector. The total flux and contributions from individual neutrino flavors are shown.

Figure 2

(Top) ${\nu }_{\mu }$ flux prediction at the SciBooNE detector as a function of neutrino energy $E_{\nu }$ in neutrino running mode. The total flux and contributions from ${\pi }^{+}$ and $K^{+}$ decays are shown. (Bottom) Fractional uncertainties of the ${\nu }_{\mu }$ flux prediction due to ${\pi }^{+}$ and $K^{+}$ production from the p-Be interaction in neutrino running mode. The figures are from Ref. [32].

Figure 3

(Top) ${\nu }_{\mu }$ and ${\overline{\nu }}_{\mu }$ flux predictions at the SciBooNE detector as a function of neutrino energy $E_{\nu }$ in antineutrino running mode. The total flux and contributions from ${\overline{\nu }}_{\mu }$ from ${\pi }^{-}$ decay and ${\nu }_{\mu }$ from ${\pi }^{+}$ and $K^{+}$ decays are shown. (Bottom) Fractional uncertainties of the ${\nu }_{\mu }$ and $\overline{{\nu }_{\mu }}$ flux predictions due to ${\pi }^{-}$, ${\pi }^{+}$ and $K^{+}$ production from p-Be interactions in antineutrino running mode with respect to the total ${\nu }_{\mu }+\overline{{\nu }_{\mu }}$ flux.

Figure 4

Schematic overview of the Booster Neutrino Beam line and the location of the SciBooNE and the MiniBooNE detectors.

Figure 5

Number of SciBar reconstructed tracks for the selected event sample in neutrino mode for data and NUANCE MC. MC histogram includes all events and $K^{+}$ shows the component of ${\nu }_{\mu }$ from $K^{+}$.

Figure 6

Reconstructed muon angle for the SciBar 1-track, 2-track, and 3-track samples in the neutrino-mode analysis. The background contributions from $K^{-}$ and $K_L^0$ are very small but included in the MC histogram. The grey area represents the total systematic uncertainty in the MC.

Figure 7

Two-dimensional plots of the energy vs angle relative to the proton beam axis for the $K^{+}$ selected events in the SciBar 1-track, 2-track, and 3-track MC samples for the neutrino-mode analysis.

Figure 8

Number of SciBar reconstructed tracks for the selected event sample in antineutrino mode for data and NUANCE MC. MC histogram includes all events and $K^{+}$ shows the component of ${\nu }_{\mu }$ from $K^{+}$ and $K^{+}+{\pi }^{+}$ shows the component of ${\nu }_{\mu }$ from $K^{+}$ and ${\pi }^{+}$.

Figure 9

Reconstructed muon angle for the SciBar 1-track, 2-track, and 3-track sample in the antineutrino-mode analysis. The background contributions from $K^{-}$ and $K_L^0$ are small but included in the MC histogram. The grey area represents the total systematic uncertainty in the MC.

Figure 10

Two-dimensional plots of the energy vs angle relative to the proton beam axis for the $K^{+}$ selected events in the SciBar 1-track, 2-track, and 3-track MC samples for the antineutrino-mode analysis. The $K^{+}$ are much more forward than in neutrino-mode (Fig. 7) otherwise they would have been swept out by the horn; this can be seen also in the angular distribution difference between Table 4 and 6.

Figure 11

The various meson contributions that decay into ${\nu }_{\mu }$ and ${\overline{\nu }}_{\mu }$ as a function of reconstructed muon angle in the 2-track sample in antineutrino mode.

Figure 12

Correlation matrix associated with the systematic and statistical uncertainties for the neutrino and antineutrino angular distributions using NUANCE.

Figure 13

Reconstructed muon angle for the SciBar 1-track, 2-track, and 3-track samples after the fit in neutrino-mode running for NUANCE. The $K^{+}$ production weight and the cross section values in Table 7 have been applied to the NUANCE MC predictions. The grey area represents the total systematic uncertainty in the MC.

Figure 14

Reconstructed muon angle for the SciBar 1-track, 2-track, and 3-track samples after the fit in antineutrino-mode running for NUANCE. The $K^{+}$ production weight and the cross section values in Table 7 have been applied to the NUANCE MC. The grey area represents the total systematic uncertainty in the MC.

Figure 15

Reconstructed muon angle for the SciBar 1-track, 2-track, and 3-track samples in neutrino-mode running for data and NEUT MC. The background contributions from $K^{-}$ and $K_L^0$ are very small but included in the MC histogram. The grey area represents the total systematic uncertainty in the MC.

Figure 16

Reconstructed muon angle for the SciBar 1-track, 2-track, and 3-track samples in antineutrino-mode running for data and NEUT MC. The background contributions from $K^{-}$ and $K_L^0$ are small but included in the MC histogram. The grey area represents the total systematic uncertainty in the MC.

Figure 17

Correlation matrix associated with the systematic and statistical uncertainties for the neutrino and antineutrino angular distributions for NEUT.

Figure 18

Reconstructed muon angle for the SciBar 1-track, 2-track, and 3-track samples in neutrino-mode running for data and the NEUT MC. The $K^{+}$ production weight and the cross section central values in Table 11 have been applied to the NEUT predictions. The grey area represents the total systematic uncertainty in the MC.

Figure 19

Reconstructed muon angle for the SciBar 1-track, 2-track, and 3-track samples in antineutrino-mode running for data and NEUT MC. The $K^{+}$ production weight and the cross section central values in Table 11 have been applied to the NEUT predictions. The grey area represents the total systematic uncertainty in the MC.