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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Measurements of π±p, K±p, pp, and p¯p elastic scattering are presented for incident momenta of 3, 3.65, 5, and 6 GeVc and momentum transfers typically 0.03 to 1.8 GeV2. The angle and momentum of the scattered particle were measured with the Argonne Effective Mass Spectrometer for 300 000 events, yielding 930 cross-section values with an uncertainty in absolute normalization of ±4%. Only the K+ and proton data show any significant change in slope of the forward diffraction peak with incident momentum. The particle-antiparticle crossover positions are consistent with no energy dependence, average values being 0.14 ± 0.03, 0.190 ± 0.006, and 0.162 ± 0.004 GeV2 for π' s, K' s, and protons, respectively; these errors reflect both statistics and the ±1.5% uncertainty in particle-antiparticle relative normalization. Differences between particle and antiparticle cross sections isolate interference terms between amplitudes of opposite C parity in the t channel; these differences indicate that the imaginary part of the odd-C nonflip-helicity amplitude has a J0(r(−t)12) structure for −t<0.8 GeV2, as predicted by strong absorption models. The cross-section differences for K± and proton-antiproton are in qualitative agreement with the predictions of ω universality, the agreement improving with increasing energy. The corresponding quark-model predictions relating the π± and K± differences failed by more than a factor of 2. We have combined our π± cross sections with other data to better determine the πN amplitudes in a model-independent way; results of this analysis are presented.
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The differential cross sections for the elastic scattering of π+, π−, K+, K−, p, and p¯ on protons have been measured in the t interval -0.04 to -0.75 GeV2 at five momenta: 50, 70, 100, 140, and 175 GeV/c. The t distributions have been parametrized by the quadratic exponential form dσdt=Aexp(B|t|+C|t|2) and the energy dependence has been described in terms of a single-pole Regge model. The pp and K+p diffraction peaks are found to shrink with α′∼0.20 and ∼0.15 GeV−2, respectively. The p¯p diffraction peak is antishrinking while π±p and K−p are relatively energy-independent. Total elastic cross sections are calculated by integrating the differential cross sections. The rapid decline in σel observed at low energies has stopped and all six reactions approach relatively constant values of σel. The ratio of σelσtot approaches a constant value for all six reactions by 100 GeV, consistent with the predictions of the geometric-scaling hypothesis. This ratio is ∼0.18 for pp and p¯p, and ∼0.12-0.14 for π±p and K±p. A crossover is observed between K+p and K−p scattering at |t|∼0.19 GeV2, and between pp and p¯p at |t|∼0.11 GeV2. Inversion of the cross sections into impact-parameter space shows that protons are quite transparent to mesons even in head-on collisions. The probability for a meson to pass through a proton head-on without interaction inelastically is ∼20% while it is only ∼6% for an incident proton or antiproton. Finally, the results are compared with various quark-model predictions.
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The ratio of π+p to pp elastic scattering is found to be smoothly varying over the range −t=0.03 to 0.4 GeV2. It is well fitted by a single exponential, indicating the forward behavior must be quite similar for the two reactions.
ACTUALLY THE DATA ARE THE EXPONENTIAL SLOPE OF THE RATIO OF D(SIG)/DT FOR THE TWO REACTIONS.
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).
The P parameter for π + p scattering at 236.3 MeV has been measured between 50° and 146° c.m. with very low background using a butanol polarized proton target. The resulting D phases are in fair agreement with dispersion relation values.
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