Results are presented from experiment WA7 at the CERN SPS, which has measured the elastic differential cross sections of π ± p, K ± p, p p and pp at incident momen ta of 20, 30 and 50 GeV/ c . The measurements cover the momentum transfer range 0.5 < | t | < 8 (GeV/ c ) 2 , corresponding to c.m. scattering angles between 10° and 50°. The experimental set-up, trigger logic and data analysis are described. The experimental results are compared with existing meson-proton and nucleon-proton data at lower and higher energies covering the medium- and large-| t | region. Some prominent models and their predictions for elastic scattering at WA7 energies and beyond are reviewed, with emphasis on geometrical scaling, factorizing eikonal models, lowest-order QCD and other dynamical exchange-type models. Results for p p two-body annihilation into π − π + and K − K + at 30 and 50 GeV/ c , obtained in parallel with the elastic p p data, are also presented.
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Measurements of the differential elastic cross sections for π − p scattering at incident momenta of 20 and 50 GeV c and π + p at 50 GeV c in the momentum transfer range 0.7 < |t|; < 8.0 ( GeV c ) 2 are presented. The data are compared with various models of elastic scattering.
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A description is given of an experiment to study elastic scattering of π ± , K ± and p on protons at c.m. scattering angles from 45° to 100° at incident laboratory momenta 20 GeV/ c and 30 GeV/ c . The corresponding t range is from −6.2 (GeV/ c ) 2 to −28 (GeV/ c ) 2 . There are no previous observations for these reactions in this t range. High intensity and large geometrical acceptance were required in order to measure the low cross sections. The experiment used a double-arm spectrometer. MWPCs were used for reconstruction, and threshold and differential Čerenkov counters for identification. Scintillation counters, Čerenkov counters and a hadron calorimeter were used in the trigger. The trigger logic utilized specially designed matrices and a hard wired microprocessor. The π − p elastic scattering cross sections follow approximately the dimensional counting rule from 3.5 GeV/ c .and up to 30 GeV/ c . The cross sections decrease by seven orders of magnitude in this energy range. The data is compared to quark models. None of these models give a comprehensive description of the results. However, some modifications to these models improve their consistency with the data.
EARLIER RESULTS GIVEN IN 'A'.
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EARLIER RESULTS GIVEN IN 'A'.
Elastic cross-section measurements are presented for π ± −p at 20 GeV/ c and π − −p at 30 GeV/ c incident momenta in the large angle region (50° to 90° in the c.m. system). The data are compared with published lower energy elastic cross sections. A test is made of the dimensional counting rules for π ± −p elastic scattering and some indication of a deviation from this rule is observed in the π − −p case. A comparison is also made with the predictions of the constituent interchange model. Although the broad features of the predictions are confirmed, there are some important discrepancies. Finally, the predictions of the model due to Preparata and Soffer are also compared with the new data.
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THE UPPER LIMIT QUOTED WHEN NO EVENTS OBSERVED IS THE CROSS SECTION CORRESPONDING TO ONE DETECTED EVENT.
THE UPPER LIMIT QUOTED WHEN NO EVENTS OBSERVED IS THE CROSS SECTION CORRESPONDING TO ONE DETECTED EVENT.
We have measured the elastic cross section for pp, p¯p, π+p, π−p, K+p, and K−p scattering at incident momenta of 70, 100, 125, 150, 175, and 200 GeV/c. The range of the four-momentum transfer squared t varied with the beam momentum from 0.0016≤−t≤0.36 (GeV/c)2 at 200 GeV/c to 0.0018≤−t≤0.0625 (GeV/c)2 at 70 GeV/c. The conventional parametrization of the t dependence of the nuclear amplitude by a simple exponential in t was found to be inadequate. An excellent fit to the data was obtained by a parametrization motivated by the additive quark model. Using this parametrization we determined the ratio of the real to the imaginary part of the nuclear amplitude by the Coulomb-interference method.
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INCLUDING DATA FROM PREVIOUS WORK OF THIS GROUP.
The results presented in this paper were obtained from a 105 000 frame exposure of the FNAL Hybrid Proportional Wire Chamber-30 inch Bubble Chamber System, in a tagged beam of 147 GeV/ c negative particles. Elastic, total and topological cross sections were obtained for both π − p and K − p interactions. Comparisons with other data, taken with various beam particles over large momentum intervals, show good agreement with KNO scaling, and similarity in the scaling behavior of σ n for the different beam particles.
THESE CROSS SECTIONS ARE NOT NORMALIZED TO ANY OTHER ABSOLUTE MEASUREMENT. THE ERRORS INCLUDE SOME SYSTEMATIC ERRORS.
THE FORWARD CROSS SECTION AGREES WELL WITH THE OPTICAL POINT FROM TOTAL CROSS SECTION MEASUREMENTS.
THESE CROSS SECTIONS ARE NOT NORMALIZED TO ANY OTHER ABSOLUTE MEASUREMENT.
Analyzing powers for π−p elastic scattering have been measured at TRIUMF using the CHAOS spectrometer and a spin-polarized target. These data were collected at a bombarding energy of Tπ=279MeV and cover an angular range of 53<~θc.m.π<~180°. There is good agreement between these data and the latest partial wave analysis from the VPI/GWU group.
Analysing power measurement.
Analyzing powers for πp elastic scattering at bombarding energies below the Δ(1232) resonance were measured at TRIUMF using the CHAOS spectrometer and a polarized spin target. This work presents π− data at six incident energies of 57, 67, 87, 98, 117, and 139 MeV, and a single π+ data set at 139 MeV. The higher energy measurements cover an angular range of 72°<~θc.m.<~180° while the lower energies were limited to 101°<~θc.m.<~180°. There is a high degree of consistency between this work and the predictions of the VPI/GWU group’s SM95 partial wave analysis.
Analysing power measurements for a 139 GeV PI+ beam (standard track).
Analysing power measurements for a 139 GeV PI- beam (standard track).
Analysing power measurements for a 117 GeV PI- beam (standard track).
Analyzing powers for πp elastic scattering were measured using the CHAOS spectrometer at energies spanning the Δ(1232) resonance. This work presents π+ data at the pion kinetic energies 117, 130, 139, 155, 169, 180, 193, 218, 241, and 267 MeV and π− data at 87, 117, 193, and 241 MeV, covering an angular range of 50°<~θc.m.<~180° at the higher energies and 90°<~θc.m.<~180° at the lower energies. Unique features of the spectrometer acceptance were employed to reduce systematic errors. Single-energy phase shift analyses indicate the resulting S11 and S31 phases favor the results of the SM95 phase shift analysis over that of the older KH80 analysis.
Measurement of the PI+ analysing power at 117 MeV.. The data were collected in the conventional mode and may be independently floated within the systematic error.
Measurement of the PI+ analysing power at 139 MeV.. The data were collected in the conventional mode and may be independently floated within the systematic error.
Measurement of the PI- analysing power at 87 MeV.. The data were collected in the conventional mode and may be independently floated within the systematic error.
Polarization in π−p elastic scattering, with emphasis in the region around the secondary dip and also θc.m.=90°, has been measured at 2.93 and 3.25 GeV/c. We observe an interesting sign change in this angular region.
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Angular distributions of the analyzing powers for π+p→ and π−p→ elastic scattering have been measured in a single-scattering experiment employing a polarized proton target. Measurements were obtained for pion energies of 98, 139, 166, 215, and 263 MeV. The addition of these data to the existing πp database significantly reduces the uncertainties in all S and P phase shifts for πp reactions over the delta resonance.
Measured values of the analyzing power for PI+ P elastic scattering at incident kinetic energy 98 MeV.
Measured values of the analyzing power for PI+ P elastic scattering at incident kinetic energy 139 MeV.
Measured values of the analyzing power for PI+ P elastic scattering at incident kinetic energy 166 MeV.
We have measured the polarization for elastic scattering in the reaction π−p→π−p at 2.93 and 3.25 GeV/c using a polarized proton target and multiwire proportional chambers (MWPC's) with emphasis on large-angle scattering. Events were selected by fast scintillation-counter logic. Beam trajectories were measured with four MWPC's and the scattered-particle angles were measured with one or two MWPC's; elastic events were determined by coplanarity and angle-angle correlations. The polarization is in agreement with previous measurements below |t|=2.0 (GeV/c)2, and crosses from negative to positive near the secondary dip in the differential cross section dσdt. In the backward region, an energy dependence appears with the polarization being large and negative at 2.93 GeV/c and consistent with zero at 3.25 GeV/c.
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The polarization parameter has been measured for π − p elastic scattering in the backward region at 3.5 GeV/ c incident momentum. The experimental set-up consisted of a polarized target in a spectrometer magnet, hodoscopes and wire spark chambers. Data are presented for the range −0.95< u ⩽−0.19 GeV 2 . An isospin analysis has been carried out to separate the I u = 1 2 and I u = 3 2 contributions.
BACKWARD SCATTERING.
Polarization in π − p elastic scattering, with emphasis over the backward region, has been measured at 2.93 and 3.25 GeV/ c . We observe large changes in polarization compared with existing data above and below these energies. Our data may be useful in determining the properties of resonances and in understanding baryon exchanges.
THESE DATA, TOGETHER WITH THE FORWARD SCATTERING POLARIZATION MEASUREMENTS, ARE TABULATED IN THE RECORD OF P. AUER ET AL., PRL 37, 83 (1976).
We have measured the polarization in π − backward elastic scattering at 2.22, 2.46, 2.71 and 3.50 GeV/ c incident momenta, in the u -range−1.0 ≦ u ≦0.1 (GeV/ c ) 2 . The experiment used a polarized proton target and detected both pions and protons. We have found large discrepancies between the new data and the result of even the latest phase-shift analysis.
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Data are presented on elastic πp and Kp scattering for values of −t up to 2.5 and 3.5 (GeV/c)2 at incident momenta of 100 and 200 GeV/c, respectively. All of the cross sections are found to be nearly identical, although there is some momentum dependence of the π+p data; a small systematic difference observed between pion and kaon data cannot be explained by geometrical scaling.
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The angular distributions of K + p and π + p backward elastic scattering have been measured at 5.2 and 6.9 GeV/ c . Backward π - p and K - p elastic scattering were studied at 6.9 GeV/ c . Backward peaks are observed in K + p scattering with an energy dependence of the form s −4 .
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We present results of measurements of the differential cross sections for the following elastic-scattering reactions: (i) π + p at 5.2 and 7.0 GeV/ c in the range −1 < u < 0.02 (GeV/ c ) 2 , (ii) π − p at 7.0 GeV/ c in the range −0.7 < u < 0.05 (GeV/ c ) 2 , (iii) K + p at 5.2 and 7.0 GeV/ c in the ranges −1 < t < −0.01 (GeV/ c ) 2 and −1 < u < 0 (GeV/ c ) 2 , and K − p at 7.0 GeV/ c in the range −1 < u < 0 (GeV/ c ) 2 .
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SIDE GEOMETRY.
Analyzing powers of pion-proton elastic scattering have been measured at PSI with the Low Energy Pion Spectrometer LEPS as well as a novel polarized scintillator target. Angular distributions between 40 and 120 deg (c.m.) were taken at 45.2, 51.2, 57.2, 68.5, 77.2, and 87.2 MeV incoming pion kinetic energy for pi+ p scattering, and at 67.3 and 87.2 MeV for pi- p scattering. These new measurements constitute a substantial extension of the polarization data base at low energies. Predictions from phase shift analyses are compared with the experimental results, and deviations are observed at low energies.
Analyzing power for PI+ P elastic scattering at incidient kinetic energy 87.2 MeV from the data set 1.
Analyzing power for PI+ P elastic scattering at incidient kinetic energy 68.4 MeV from the data set 1.
Analyzing power for PI+ P elastic scattering at incidient kinetic energy 57.2 MeV from the data set 1.
The spin rotation parameter R has been measured at CERN, for π ± p at 6 GeV c and for π − p at 16 GeV c , with t ranging from −0.19 to −0.51 ( GeV c ) 2 . The parameter A was measured for π − p at 6 GeV c in the interval between t =−0.19 and minus;0.41 ( GeV c ) 2 . The averaged values are the following; R (+6) =−0.08±0.04, R (−6) =−0.23±0.05 and R (−16) =−0.23±0.05. The values obtained for A are close to +1.
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We have measured π±p and pp elastic differential cross sections in the range |cosθc.m.|<0.35 for incident momenta from 2 to 9.7 GeV/c for π−p and pp and from 2 to 6.3 GeV/c for π+p. We find that the fixed-c.m.-angle πp differential cross sections cannot be described as simple functions of s. The data are compared to the energy and angular dependence predicted by the constituent model of Gunion, Brodsky, and Blankenbecler.
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A comprehensive measurement of the differential cross section for π±p and pp elastic scattering has been made at large center-of-mass angles. π−p and pp scattering were measured with incident laboratory momenta ranging from 2 to 9.5 GeV/c. π+p scattering was measured with momenta from 2 to 6.3 GeV/c. Scattering angles were in the range −0.3≲cosθc.m.≲0.4. The results of the experiment are compared to constituent models and statistical models.
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Differential cross sections for π±p, K±p, pp, and p¯p elastic scattering were measured at 3, 3.65, 5, and 6 GeVc for momentum transfers from 0.03 to 1.5 GeV2 using the Argonne effective mass spectrometer. Particular attention was paid to the relative particle-antiparticle normalization. The crossover points are consistent with no energy dependence, average values being 0.14 ± 0.03, 1.190 ± 0.005, and 0.160 ± 0.007 GeV2 for π's, K's, and protons, respectively.
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