Measurements of cross sections and charged pion spectra in proton-carbon interactions at 31 GeV/$c$

Interaction cross sections and charged pion spectra in $p+\mathrm{C}$ interactions at 31 GeV/$c$ were measured with the large-acceptance NA61/SHINE spectrometer at the CERN SPS. These data are required to improve predictions of the neutrino flux for the T2K long-baseline neutrino oscillation experiment in Japan. A set of data collected during the first NA61/SHINE run in 2007 with an isotropic graphite target with a thickness of 4% of a nuclear interaction length was used for the analysis. The measured $p+\mathrm{C}$ inelastic and production cross sections are 257.2 $\pm$ 1.9 $\pm$ 8.9 and 229.3 $\pm$ 1.9 $\pm$ 9.0 mb, respectively. Inclusive production cross sections for negatively and positively charged pions are presented as functions of laboratory momentum in ten intervals of the laboratory polar angle covering the range from 0 up to 420 mrad. The spectra are compared with predictions of several hadron production models.

Figure 1

The prediction from the T2K beam simulation: the $\{p,\theta \}$ distribution for positively charged pions weighted by the probability that their decay produces a muon neutrino passing through the SK detector.

Figure 2

The layout of the NA61/SHINE experiment at the CERN SPS (top view, not to scale). The chosen right-handed coordinate system is shown on the plot. The incoming beam direction is along the $z$ axis. The magnetic field bends charged particle trajectories in the $x\text{−}z$ (horizontal) plane. The drift direction in the TPCs is along the $y$ (vertical) axis.

Figure 3

Top: The beam spot as measured by BPD-3 after the $\overline{\text{V1}}$ cut described in the text. Bottom: The beam divergence in $x$ and $y$.

Figure 4

The beam momentum distribution measured by the reconstruction of beam particles in the TPCs. Only statistical errors are shown.

Figure 5

Top view (projection to the $x\text{−}z$ plane) of a $p+\mathrm{C}$ interaction as detected by the four NA61 TPCs and the ToF-F detector (for details see Sec. 2 and Fig. 2). The red lines correspond to the trajectories of tracks produced in the interaction and reconstructed using the TPC clusters indicated by yellow points. Stars correspond to the reconstructed ToF-F hits.

Figure 6

Invariant mass distribution of reconstructed $K_S^0$ candidates. The fitted mean value of the peak is given in the legend. The dashed histogram shows the simulated distribution, which is normalized to the data on the right side of the peak.

Figure 7

Track reconstruction efficiency for negatively charged particles as a function of momentum in the polar angle interval [100,140] mrad.

Figure 8

Specific energy loss in the TPCs for positively (top) and negatively (bottom) charged particles as a function of momentum. Curves show parametrizations of the mean $dE/dx$ calculated for different particle species.

Figure 9

The $dE/dx$ distributions for positively (full line) and negatively (dashed line) charged particles at 5 and 15 GeV/$c$ particle momenta; the momentum bin width is 0.4 GeV/$c$.

Figure 10

Top: Distribution of the difference between a particle’s time-of-flight measured independently by two overlapping scintillator bars of the ToF-F detector. The width of the distribution is about 160 ps, indicating a tof resolution of about 115 ps for a single measurement. Bottom: Mass squared, derived from the ToF-F measurement and the fitted path length and momentum, versus momentum $p$. The lines show the expected mass squared values for different particles.

Figure 11

Examples of two-dimensional $m^2$-$dE/dx$ plots for positively charged particles in three momentum intervals indicated in the panels. $2\sigma$ contours around fitted pion peaks are shown. The left and middle plots correspond to the $dE/dx$ crossover region while the right plot is at such a high momentum that the ToF-F resolution becomes a limiting factor. The combination of both measurements provides close to 100% purity in the pion selection over the whole momentum range.

Figure 12

Polar angle ($\theta$) vs azimuthal angle ($\phi$) distribution for reconstructed negatively charged particles in the momentum interval $0.5<p(\mathrm{GeV}/c)<5.0$.

Figure 13

Fraction of accepted particles as a function of momentum and polar angle, after the track acceptance cuts (see Sec. 5a) for negatively charged tracks (top), and after an additional ToF-F acceptance cut (see Sec. 5e) for positively charged tracks (bottom). The first polar angle bin, [0, 20] mrad, is fully covered by accepted particles up to 7.6 GeV/$c$.

Figure 14

The relative contribution of accepted primary $K^{-}$ and $\overline{p}$ to accepted primary negatively charged pions in different ($p$,$\theta$) intervals calculated within the venus model.

Figure 15

The relative contribution of accepted electrons and nonprimary negatively charged hadrons to accepted primary negatively charged pions in different ($p$,$\theta$) intervals calculated within the venus model. The low-momentum region where the ratio is larger than 3 is excluded.

Figure 16

Example of momentum dependence of the inverse correction factor and geometrical acceptance (top) and systematic errors (bottom) for the $h^{-}$ analysis for negatively charged pions in the polar angle interval [140,180] mrad. For details concerning systematic uncertainties, see Sec. 5g.

Figure 17

The $dE/dx$ distribution for positively charged particles in the momentum bin [0.7,0.8] GeV/$c$ and angular bin [180,240] mrad compared with the distribution calculated using the fitted relative abundances. A small systematic shift between the fit curves (Gaussian peaks centered on the Bethe-Bloch values) and data is observed. This effect results in a major contribution to the total systematic error in the particle identification procedure.

Figure 18

Example of the momentum dependence of the inverse correction factor and geometrical acceptance (top) and systematic errors (bottom) for the $dE/dx$ analysis for positively charged pions in the polar angle interval [140,180] mrad. The small differences between geometrical acceptance and global correction are due to the fact that pion loss and feed-down corrections, which are the most important ingredients of the global correction, cancel to a large extent. For details concerning systematic uncertainties see Sec. 5g.

Figure 19

Example of momentum dependence of the inverse correction factors (top), total inverse correction factor and geometrical acceptance (middle), and systematic errors (bottom) for the tof–$dE/dx$ analysis for positively charged pions in the polar angle interval [40,60] mrad. ${\epsilon }_{\mathrm{rec}}$ and ${\epsilon }_{ToF}$ are the efficiencies of the reconstruction and of the ToF-F, respectively. The feed-down correction accounts for pions from weak decays which are reconstructed as primary particles, while the pion loss accounts for pions lost due to decays or secondary interactions. For details concerning systematic uncertainties, see Sec. 5g. For the tof–$dE/dx$ analysis, within a given $\theta$ bin, in addition to the cut on the azimuthal angle, a momentum-dependent selection on the track topology was applied. The purpose of this cut is to select only regions with a flat acceptance along the whole momentum range.

Figure 20

Beam momentum dependence of the production cross section for $p+\mathrm{C}$ interactions. The NA61/SHINE result (filled square) is compared with previous measurements: Bellettini et al. (circle) [34], Carroll et al. (triangle) [35], and Denisov et al. (open squares) [36]. For the NA61/SHINE point, the error bar indicates statistical and systematic uncertainties added in quadrature. The result from Ref. [34] was recalculated by subtracting from the measured inelastic cross section a quasielastic contribution at 20 GeV/$c$ of $30.4\pm 1.9\left(\mathrm{sys}\right)$ mb.

Figure 21

Differential cross sections for ${\pi }^{-}$ meson production in $p+\mathrm{C}$ interactions at 31 GeV/$c$. The spectra are presented as a function of laboratory momentum ($p$) in different intervals of polar angle ($\theta$). Results obtained using three analysis methods are presented by different symbols: blue open circles, $h^{-}$ analysis; red open squares, $dE/dx$ analysis, and black full triangles tof–$dE/dx$ analysis. Error bars indicate only statistical uncertainties.

Figure 22

Differential cross sections for ${\pi }^{+}$ meson production in $p+\mathrm{C}$ interactions at 31 GeV/$c$. The spectra are presented as a function of laboratory momentum ($p$) in different intervals of polar angle ($\theta$). Results obtained using two analysis methods are presented by different symbols: red open squares, $dE/dx$ analysis, and black full triangles, tof–$dE/dx$ analysis. Error bars indicate only statistical uncertainties.

Figure 23

Laboratory momentum distributions of ${\pi }^{-}$ mesons produced in production $p+\mathrm{C}$ interactions at 31 GeV/$c$ in different intervals of polar angle ($\theta$). The spectra are normalized to the mean ${\pi }^{-}$ multiplicity in all production $p+\mathrm{C}$ interactions. Error bars indicate statistical and systematic uncertainties added in quadrature. The overall uncertainty ($2.3\%$) due to the normalization procedure is not shown. Predictions of hadron production models, fluka2008 (solid line), urqmd1.3.1 (dashed line), and venus4.12 (dotted line), are also indicated.

Figure 24

Laboratory momentum distributions of ${\pi }^{+}$ mesons produced in production $p+\mathrm{C}$ interactions at 31 GeV/$c$ in different intervals of polar angle ($\theta$). The spectra are normalized to the mean ${\pi }^{+}$ multiplicity in all production $p+\mathrm{C}$ interactions. Error bars indicate statistical and systematic uncertainties added in quadrature. The overall uncertainty ($2.3\%$) due to the normalization procedure is not shown. Predictions of hadron production models, fluka2008 (solid line), urqmd1.3.1 (dashed line), and venus4.12 (dotted line), are also indicated.

Figure 25

Relative uncertainties on the ${\pi }^{-}$ cross sections shown in the same binning as Fig. 23. Statistical (dotted line), systematic (dashed line), and total (solid line) uncertainties are indicated. The overall uncertainty due to the normalization procedure is not shown.

Figure 26

Relative uncertainties on the ${\pi }^{+}$ cross sections shown in the same binning as Fig. 24. Statistical (dotted line), systematic (dashed line), and total (solid line) uncertainties are indicated. The overall uncertainty due to the normalization procedure is not shown.

Figure 27

The momentum dependence of the ${\pi }^{+}$ to ${\pi }^{-}$ ratio. Errors are calculated taking into account only statistical uncertainties of the spectra plotted in Figs. 23 and 24. Predictions of hadron production models, fluka2008 (solid line), urqmd1.3.1 (dashed line), and venus4.12 (dotted line), are also indicated.