Large-angle production of charged pions with 3--12.9 GeV/$c$ incident protons on nuclear targets

Large-angle production of charged pions with 3–12.9 GeV/ $c$ incident protons on nuclear targets

M. G. Catanesi et al. (HARP Collaboration)

Phys. Rev. C 77, 055207 – Published 15 May 2008

Abstract

Measurements of the double-differential $π^{\pm}$ production cross section in the momentum range $100 ⩽ p ⩽ 800$ MeV/ $c$ and angle range $0.35 ⩽ θ ⩽ 2.15$ rad in proton-beryllium, proton-carbon, proton-aluminium, proton-copper, proton-tin, proton-tantalum, and proton-lead collisions are presented. The data were taken with the large-acceptance HARP detector in the T9 beam line of the CERN PS. The pions were produced by proton beams in a momentum range from 3 to 12.9 GeV/ $c$ hitting a target with a thickness of 5% of a nuclear interaction length. Tracking and identification of the produced particles was performed by using a small-radius cylindrical Time Projection Chamber (TPC) placed inside a solenoidal magnet. Incident particles were identified by an elaborate system of beam detectors. Results are obtained for the double-differential cross sections $d^{2} σ / (d p d θ)$ at six incident proton beam momenta [3, 5, 8, and 8.9 GeV/ $c$ (Be only) and 12 and 12.9 GeV/ $c$ (Al only)]. They are based on a complete correction of static and dynamic distortions of tracks in the HARP TPC, which allows the complete statistics of the collected data set to be used. The results include and supersede our previously published results and are compatible with these. Results are compared with the GEANT4 and MARS Monte Carlo simulation.

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Received 27 December 2007

DOI:https://doi.org/10.1103/PhysRevC.77.055207

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Vol. 77, Iss. 5 — May 2008

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Images

Figure 1
Schematic layout of the HARP detector. The convention for the coordinate system is shown in the lower right corner. The three most downstream (unlabeled) drift chamber modules are only partly equipped with electronics and are not used for tracking. The detector covers a total length of 13.5 m along the beam axis and has a maximum width of 6.5 m perpendicular to the beam.
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Figure 2
Effect of dynamic distortions on a track in the HARP TPC for a $p$ -Be interaction sample at 5 GeV/ $c$ , as a function of the event number in the spill before corrections (left) and after dynamic distortion corrections (right). The symbols show the average extrapolated distance from the incoming beam particle trajectory for $π^{-}$ (filled squares) and $π^{+}$ (filled circles).
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Figure 3
Full spill analysis of $Q / p_{T}$ for the highest statistics data sample: $p$ -Be at 8.9 GeV/ $c$ before corrections (left) and after corrections (right). Six curves are drawn, each for the next 50 events in the spill. One notices that the distributions in the right panel are not distinguishable.
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Figure 4
As a momentum benchmark, after the dynamic distortion correction, the closed box shows the average momentum observed for protons selected using their range (reaching the second RPC) and $d E / d x$ . Closed circles show protons selected within a high $d E / d x$ region; open circles show $π^{-}$ selected with $d E / d x$ ; open boxes show $π^{+}$ selected with $d E / d x$ . The angle of the particles is restricted in a range with $\sin θ \approx 0.9$ . The variation in the uncorrected sample was $\approx 5 %$ for the high- $p_{T}$ samples. The corrected data stay stable well within 3%. The low- $p_{T}$ data remain stable with or without correction.
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Figure 5
Stability of the TPC calibration. (Left) $d E / d x$ versus settings for pions with $300 ⩽ p ⩽ 500$ MeV/ $c$ . (Right) Mean momentum for protons with a $d E / d x$ between 7 and 8 MIP versus setting. Settings go from low $A$ to high $A$ including beam momenta from 3 to 12.9 GeV/ $c$ .
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Figure 6
Double-differential cross sections for $π^{+}$ production (left) and $π^{-}$ production (right) in $p$ -Be interactions as a function of momentum displayed in different angular bins (shown in mrad in the panels). In the figure, the symbol legend 9 refers to 8.9 GeV/ $c$ nominal beam momentum. The error bars represent the combination of statistical and systematic uncertainties.
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Figure 7
Double-differential cross sections for $π^{+}$ production (left) and $π^{-}$ production (right) in $p$ -C interactions as a function of momentum displayed in different angular bins (shown in mrad in the panels). The error bars represent the combination of statistical and systematic uncertainties.
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Figure 8
Double-differential cross sections for $π^{+}$ production (left) and $π^{-}$ production (right) in $p$ -Al interactions as a function of momentum displayed in different angular bins (shown in mrad in the panels). In the figure, the symbol legend 13 refers to 12.9 GeV/ $c$ nominal beam momentum. The error bars represent the combination of statistical and systematic uncertainties.
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Figure 9
Double-differential cross sections for $π^{+}$ production (left) and $π^{-}$ production (right) in $p$ -Cu interactions as a function of momentum displayed in different angular bins (shown in mrad in the panels). The error bars represent the combination of statistical and systematic uncertainties.
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Figure 10
Double-differential cross sections for $π^{+}$ production (left) and $π^{-}$ production (right) in $p$ -Sn interactions as a function of momentum displayed in different angular bins (shown in mrad in the panels). The error bars represent the combination of statistical and systematic uncertainties.
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Figure 11
Double-differential cross sections for $π^{+}$ production (left) and $π^{-}$ production (right) in $p$ -Ta interactions as a function of momentum displayed in different angular bins (shown in mrad in the panels). The error bars represent the combination of statistical and systematic uncertainties.
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Figure 12
Double-differential cross sections for $π^{+}$ production (left) and $π^{-}$ production (right) in $p$ -Pb interactions as a function of momentum displayed in different angular bins (shown in mrad in the panels). The error bars represent the combination of statistical and systematic uncertainties.
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Figure 13
Ratio of the $π^{-}$ production cross sections measured without and with corrections for dynamic distortions in $p$ -Be interactions at 8.9 GeV/ $c$ , as a function of momentum for different angular bins (shown in mrad in the panels). The error band in the ratio takes into account momentum error and the error on the efficiency; the other errors are correlated. The errors on the data points are statistical.
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Figure 14
Ratio of the $π^{+}$ production cross sections measured without and with corrections for dynamic distortions in $p$ -Be interactions at 8.9 GeV/ $c$ , as a function of momentum for different angular bins (shown in mrad in the panels). The error band in the ratio takes into account momentum error and the error on the efficiency; the other errors are correlated. The errors on the data points are statistical.
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Figure 15
Ratio of the $π^{-}$ production cross sections measured without and with corrections for dynamic distortions in $p$ -Ta interactions at 8 GeV/ $c$ , as a function of momentum for different angular bins (shown in mrad in the panels). The error band in the ratio takes into account momentum error and the error on the efficiency; the other errors are correlated. The errors on the data points are statistical.
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Figure 16
Ratio of the $π^{+}$ production cross sections measured without and with corrections for dynamic distortions in $p$ -Ta interactions at 8 GeV/ $c$ , as a function of momentum for different angular bins (shown in mrad in the panels). The error band in the ratio takes into account momentum error and the error on the efficiency; the other errors are correlated. The errors on the data points are statistical.
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Figure 17
The dependence on the beam momentum of the $π^{-}$ (right) and $π^{+}$ (left) production yields in $p$ -Be, $p$ -C, $p$ -Al, $p$ -Cu, $p$ -Sn, $p$ -Ta, and $p$ -Pb interactions averaged over the forward angular region ( $0.350 ⩽ θ < 1.550$ rad) and momentum region $100 ⩽ p < 700$ MeV/ $c$ . The results are given in arbitrary units, with a consistent scale between the left and right panels. Data points for different target nuclei and equal momenta are slightly shifted horizontally with respect to each other to increase their visibility.
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Figure 18
From top-left panel to bottom-right, the ratio of the differential cross sections for $π^{-}$ and $π^{+}$ production in $p$ -Be, $p$ -C, $p$ -Al, $p$ -Cu, $p$ -Sn, $p$ -Ta, and $p$ -Pb interactions as a function of the secondary momentum integrated over the forward angular region (shown in mrad). In the figure, the symbol legends 13 and 9 refer to 12.9 and 8.9 GeV/ $c$ nominal beam momentum, respectively.
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Figure 19
The dependence on the atomic number $A$ of the pion production yields in $p$ -Be, $p$ -Al, $p$ -C, $p$ -Cu, $p$ -Sn, $p$ -Ta, and $p$ -Pb interactions averaged over the forward angular region ( $0.35 ⩽ θ < 1.55$ rad) and momentum region $100 ⩽ p < 700 MeV / c$ . The results are given in arbitrary units, with a consistent scale between the left and right panels. The vertical scale used in this figure is consistent with the one in Fig. 17.
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Figure 20
Predictions of the $π^{+}$ (closed symbols) and $π^{-}$ (open symbols) yields for different designs of the NF focusing stage. Integrated yields (left) and the integrated yields normalized to the kinetic energy of the proton (right) for $p$ -Ta and $p$ -Pb interactions. The circles indicate the integral over the full HARP acceptance ( $100 < p < 700$ MeV/ $c$ and $0.35 < θ < 1.55 rad$ ), the squares are integrated over $0.35 < θ < 0.95 rad$ , and the diamonds are calculated for the smaller angular range and $250 < p < 500$ MeV/ $c$ . Although the units are indicated as “arbitrary,” for the largest region the yield is expressed as $d^{2} σ / d p d Ω$ in mb/(GeV/ $c$ sr). For the other regions the same normalization is chosen, but now scaled with the relative bin size to show visually the correct ratio of number of pions produced in these kinematic regions. The full error bar shows the overall (systematic and statistical) error; the inner error bar shows the error relevant for the point-to-point comparison. For the latter error only the uncorrelated systematic uncertainties were added to the statistical error.
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Figure 21
Total systematic error (gray solid line) and main components: black short-dashed line for absorption and tertiary interactions, black dotted line for track efficiency and target pointing efficiency, black dot-dashed line for $π^{0}$ subtraction, black solid line for momentum scale plus resolution and angle scale, and gray short-dashed line for PID for two typical targets (Be and Ta).
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Figure 22
Comparison of HARP double-differential $π^{+}$ ( $π^{-}$ ) cross sections for $p$ -C at 3 GeV/ $c$ with GEANT4 and MARS Monte Carlo predictions, using several generator models (see text for details).
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Figure 23
Comparison of HARP double-differential $π^{+}$ cross sections for $p$ -C at 5 GeV/ $c$ with GEANT4 and MARS Monte Carlo predictions, using several generator models (see text for details).
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Figure 24
Comparison of HARP double-differential $π^{-}$ cross sections for $p$ -C at 5 GeV/ $c$ with GEANT4 Monte Carlo predictions, using several generator models (see text for details).
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Figure 25
Comparison of HARP double-differential $π^{+}$ cross sections for $p$ -C at 8 GeV/ $c$ with GEANT4 and MARS Monte Carlo predictions, using several generator models (see text for details).
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Figure 26
Comparison of HARP double-differential $π^{-}$ cross sections for $p$ -C at 8 GeV/ $c$ with GEANT4 and MARS Monte Carlo predictions, using several generator models (see text for details).
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Figure 27
Comparison of HARP double-differential $π^{\pm}$ cross sections for $p$ -C at 12 GeV/ $c$ with GEANT4 and MARS Monte Carlo predictions, using several generator models (see text for details).
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Figure 28
Comparison of HARP double-differential $π^{\pm}$ cross sections for $p$ -Ta at 3 GeV/ $c$ with GEANT4 and MARS Monte Carlo predictions, using several generator models (see text for details).
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Figure 29
Comparison of HARP double-differential $π^{+}$ cross sections for $p$ -Ta at 5 GeV/ $c$ with GEANT4 and MARS Monte Carlo predictions, using several generator models (see text for details).
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Figure 30
Comparison of HARP double-differential $π^{-}$ cross sections for $p$ -Ta at 5 GeV/ $c$ with GEANT4 and MARS Monte Carlo predictions, using several generator models (see text for details).
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Figure 31
Comparison of HARP double-differential $π^{+}$ cross sections for $p$ -Ta at 8 GeV/ $c$ with GEANT4 and MARS Monte Carlo predictions, using several generator models (see text for details).
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Figure 32
Comparison of HARP double-differential $π^{-}$ cross sections for $p$ -Ta at 8 GeV/ $c$ with GEANT4 and MARS Monte Carlo predictions, using several generator models (see text for details).
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Figure 33
Comparison of HARP double-differential $π^{\pm}$ cross sections for $p$ -Ta at 12 GeV/ $c$ with GEANT4 and MARS Monte Carlo predictions, using several generator models (see text for details).
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Physical Review C

covering nuclear physics