Measurements of the polarization parameters and angular distributions are reported for π±p elastic scattering at 100 GeV/c and for pp elastic scattering at 100- and 300-GeV/c incident momentum. The π±p data cover the kinematic range 0.18≤−t≤1.10 GeV2 and are in agreement with current Regge-model predictions. The pp data cover the kinematic range 0.15≤−t≤1.10 GeV2 and 0.15≤−t≤2.00 GeV2 at 100 and 300 GeV/c, respectively, and are found to be consistent with absorption-model predictions.
THESE ANGULAR DISTRIBUTIONS AND POLARIZATION PARAMETERS ARE TABULATED IN THE RECORD OF THE EARLIER BRIEF REPORT OF THIS EXPERIMENT USING PION BEAMS: I. P. AUER ET AL., PRL 39, 313 (1977).
THESE ANGULAR DISTRIBUTIONS AND POLARIZATION PARAMETERS ARE TABULATED IN THE RECORD OF THE EARLIER BRIEF REPORT OF THIS EXPERIMENT USING A PROTON BEAM: J. H. SNYDER ET AL., PRL 41, 781 (1978) AND PRL 41, 1256(E) (1978).
Measurements of the polarization parameter and angular distributions in pp elastic scattering at incident energies of 100 and 300 GeV are reported. The data cover the kinematic range 0.18<−t<2.0 GeV2. They are found to be consistent with absorption-model predictions.
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THE ANGULAR DISTRIBUTION IN THE PUBLISHED FIGURE IS NORMALIZED TO D(SIG)/DT AT -T = 0.55 GEV**2 FROM AKERLOF ET AL., PR D14, 2864 (1976).
The polarization parameter has been measured in K − p elastic scattering at eight incident beam momenta between 650 MeV/ c and 1071 MeV/ c throughout a center of mass angular range of −0.75 < cos θ ∗ < 0.85 . Experimental results and coefficients of Legendre polynomial fits to the data are presented and compared with other measurements and partial wave analysis.
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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.
In an experiment at the Argonne Zero-Gradient Synchrotron we have measured values of the polarization parameter P(t) in the elastic scattering of negative pions, positive pions, positive kaons, and protons on protons at several incident laboratory momenta from 2.50 to 5.15 GeVc, and for values of the momentum transfer variable −t from 0.2 to 2.0 (GeVc)2. The final results from p−p elastic scattering presented here extend our knowledge of the polarization to much larger values of −t than the results of previous measurements. Outstanding features revealed by these polarization data include (1) the development of a dip at about −t=0.7 (GeVc)2, with (2) a substantial secondary peak at larger values of −t and (3) the gradual diminution of the maximum polarization with increasing energy. It is possible to fit the t dependence of the experimental results with a simple model. The energy dependence of the polarized cross sections is also discussed.
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The polarization parameter in π±p elastic scattering has been measured at several momenta in the range 2.50-5.15 GeV/c pion laboratory momentum and covering the range in t approximately from -0.2 to -2.0(GeV/c)2. The data show positive polarization for π±p scattering, having a dip near t=−0.6 (GeV/c)2 and becoming relatively large at greater values of −t. The results for π+ and π− scattering are approximately equal in magnitude but of opposite sign. The data have been analyzed to separate the components, which are symmetric and antisymmetric with respect to pion charge, and to show both the t and s dependence of each part.
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The differential cross section for π+p elastic scattering has been measured at 13.8 GeVc for 0.7<|t|<3.8(GeVc)2. The cross section is found to be equal to that previously obtained for π−p elastic scattering, except in the region |t|=2.8 (GeVc)2, where the π+p data do not show the prominent dip observed in π−p scattering. Data have also been obtained for 13.8−GeVc K+p elastic scattering for 0.8<|t|<2.2 (GeVc)2.
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We studied 21 187 two-prong, two-prong-with-kink, and zero-prong-V events at incident kaon momentum of 1.33 GeVc using the 72-in. hydrogen bubble chamber at the Lawrence Radiation Laboratory and two scanning and measuring projectors in Urbana. We determined the total and partial cross sections for all contributing reactions. For the two-body final states, some production and polarization angular distributions were measured. The angular distributions are discussed in terms of exchanges in the kinematical channels s, t, and u assuming the simplest Feynman graphs. Elastic scattering is analyzed as a diffraction process.
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We report measurements of the polarization parameters in π+p and π−p elastic scattering at an incident momentum of 100 GeV/c. The results cover the range 0.18<~−t<~1.4 GeV2 and are in agreement with current Regge-model predictions.
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The differential cross section for π−−p elastic scattering has been measured at 13.8 and 22.6 GeV/c up to −t=5 (GeV/c)2. The dips in the angular distribution at −t≈0.8 and 2.8 (GeV/c)2 previously observed at lower momenta become less prominent at higher momentum. The −t=2.8 (GeV/c)2 dip is still observed at 13.8 GeV/c, but at 22.6 GeV/c it has become a sharp kink in the angular distribution. At large momentum transfers, dσdt at fixed t is still decreasing with increasing s, but at a slower rate in the 14- to 23-GeV/c region than at lower momenta.
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Differential cross sections for p−p elastic scattering are presented with scattering angles in the center-of-mass system greater than 35° to 50°. The data were obtained at incident laboratory momenta 0.857, 1.091, 1.210, 1.374, 1.405, and 1.501 GeV/c. This spans the region of the onset of Δ(1236) production and where a possible spin-singlet D-wave resonance is indicated in an analysis of earlier data.
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Interactions of 781-MeV π+ mesons with protons were investigated using the Brookhaven National Laboratory 14-in. hydrogen bubble chamber. A total of 2305 events was observed. The data were normalized to a total cross section of 22.2 mb, giving partial cross sections σ(π+p→π+p)=9.5±0.5 mb, σ(π+p→π+pπ0)=9.3±0.5 mb, σ(π+p→π+π+n)=2.15±0.17 mb, and a multiple-pion-production cross section of 1.15±0.17 mb. The elastic angular distribution was obtained and is dσdω=(0.25±0.03)+(0.90±0.11)cosθc.m.+(2.57±0.24)cos2θc.m.+(0.19±0.22)cos3θc.m.−(1.73±0.34)cos4c.m.. The kinetic-energy and angular distributions of the outgoing particles in single-pion production are given. The data are compared with other experiments in this energy region and their relevance to the shoulder in the π+p total cross section near 830 MeV is discussed.
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A total of 1589 two-prong events were observed in an exposure of the Brookhaven National Laboratory 14-in. bubble chamber at the Cosmotron. The fit to the elastic angular distribution requires terms through cos4θc.m.. The ratio of the inelastic cross sections σ(π−p→π−π+n)σ(π−p→π−π0p) is 3.75±0.46. The π−p→π−π+n reaction is dominated by formation of the π−n isobar and an enhancement in the di-pion mass spectrum previously reported by Kirz. The π−p→π−π0p reaction shows no structure in the effective-mass spectra.
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In an experiment on K--proton interactions in a hydrogen bubble chamber, the cross sections and angular distributions have been studied for elastic and charge-exchange scattering, and charged sigma hyperon production in the momentum range 90-300 MeV/c. Good agreement is found with previous cross sections except for the charge-exchange channel where the new values are 60% larger. The production distributions of the charged sigma hyperons and the polarisation of the Sigma + hyperon clearly indicate that P waves are present down to about 150 MeV/c, much lower than previously reported.
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Results are reported based on a study of π − p interactions at 147 GeV/ c in the FERMILAB 30-inch Proportional Wire Hybrid Bubble Chamber System. We have measured the topological cross sections and separated two-prong elastic and inelastic channels. In addition, we have extracted leading particle cross sections using the increased momentum resolution of the downstream proportional wire chambers. We have compared our results with experiments and predictions of a simple fragmentation hyphothesis.
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In a special run of the LHC with $\beta^\star = 2.5~$km, proton-proton elastic-scattering events were recorded at $\sqrt{s} = 13~$TeV with an integrated luminosity of $340~\mu \textrm{b}^{-1}$ using the ALFA subdetector of ATLAS in 2016. The elastic cross section was measured differentially in the Mandelstam $t$ variable in the range from $-t = 2.5 \cdot 10^{-4}~$GeV$^{2}$ to $-t = 0.46~$GeV$^{2}$ using 6.9 million elastic-scattering candidates. This paper presents measurements of the total cross section $\sigma_{\textrm{tot}}$, parameters of the nuclear slope, and the $\rho$-parameter defined as the ratio of the real part to the imaginary part of the elastic-scattering amplitude in the limit $t \rightarrow 0$. These parameters are determined from a fit to the differential elastic cross section using the optical theorem and different parameterizations of the $t$-dependence. The results for $\sigma_{\textrm{tot}}$ and $\rho$ are \begin{equation*} \sigma_{\textrm{tot}}(pp\rightarrow X) = \mbox{104.7} \pm 1.1 \; \mbox{mb} , \; \; \; \rho = \mbox{0.098} \pm 0.011 . \end{equation*} The uncertainty in $\sigma_{\textrm{tot}}$ is dominated by the luminosity measurement, and in $\rho$ by imperfect knowledge of the detector alignment and by modelling of the nuclear amplitude.
The measured total cross section. The systematic uncertainty includes experimental and theoretical uncerainties.
The measured total cross section. The systematic uncertainty includes experimental and theoretical uncerainties.
The rho-parameter, i.e. the ratio of the real to imaginary part of the elastic scattering amplitude extrapolated to t=0. The systematic uncertainty includes experimental and theoretical uncerainties.
We report here the results from an experiment to obtain differential cross sections for K−p elastic scattering in the laboratory momentum region from 1.4 to 1.9 GeV/c. These data span the region of a bump in the K−p total cross section at an energy of 2.05 GeV. Approximately 20000 elastic events were obtained at each of four momenta with an angular coverage of 0.9≥cosθc.m.≥−0.9. The data are intended to aid in phase-shift analyses of the resonances causing the bump in the total cross section and to study dip structures at constant values of the Mandelstam variables t and u.
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LEGENDRE POLYNOMIAL COEFFICIENTS.
FROM INTEGRATING LEGENDRE POLYNOMIAL FIT TO D(SIG)/DOMEGA. QUOTED ERRORS INCLUDE NORMALIZATION AND FITTING UNCERTAINTIES.
Differential cross sections for π+p elastic scattering in the momentum region 1.2 to 2.3 GeV/c are presented for the center-of-mass angular range 0.9>cosθ>−0.9. Typically, 50 000 events were obtained at each of 16 momenta using magnetostrictive-readout wire spark chambers to detect the particles scattered from a liquid hydrogen target. The results are compared to those of the CERN-71 phase-shift analysis. The well-known dips at t≅−0.7 (GeV/c)2 and at u′=−0.2 (GeV/c)2 are observed. In addition, structure is seen at constant u′=−1.3 (GeV/c)2. The results of a pion attenuation study in iron are also presented.
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We report on an experiment to obtain differential cross sections for K+p elastic scattering in the vicinity of the possible exotic baryon, the Z1*(1900). The differential cross sections are based on typically 70 000 selected events in the angular region −0.9≤cosθc.m.≤0.9 at each of 22 momenta from 0.865 to 2.125 GeV/c. The data are intended for use in partial-wave analysis to search for the Z1*.
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About 3700 two-prong and 5600 four-prong events of 10-GeV/c pp interactions in the Saclay 81-cm hydrogen bubble chamber have been measured and analyzed. The reliability of the identification of the different final states has been checked using Monte Carlo-generated events. For the channels accessible to analysis, cross sections and invariant-mass distributions are given. The c.m. angular distributions and the mean values of the transverse momentum for all final-state particles are shown and discussed. Production of Δ++(1236) accounts for about 30% of the cross section σ(pp→pnπ+)=4.1±0.4 mb. About 50% of the cross section σ(pp→ppπ+π−)=2.4±0.2 mb can be accounted for by Δ++ production. Production of nucleon isobars at 1450, 1520, and 1730 MeV and their subsequent decay into pπ+π− are investigated. Their cross sections, t dependences, and branching ratios are determined, using a one-pion-exchange model (OPEM) for calculating the background distributions. The production of resonances decaying into pπ− at 1236, 1500, and 1690 MeV is seen, and cross sections are given. Resonance production in the ppπ+π−π0 and pnπ+π+π− reactions is studied using background curves calculated with a model based on simple parametrizations of the c.m. momentum distributions. The production of nucleon isobars accounts for nearly 100% of these reactions. For the reactions pp→ppω, ppη, and ppf0, the cross sections found are 0.16±0.03, 0.16±0.07, and 0.10±0.04 mb, respectively, corrected for unobserved decay modes. It is shown that most of the gross features of the pion-production reactions can be explained by the OPEM with the form factors of Ferrari and Selleri.
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A measurement of the total $pp$ cross section at the LHC at $\sqrt{s}=7$ TeV is presented. In a special run with high-$\beta^{\star}$ beam optics, an integrated luminosity of 80 $\mu$b$^{-1}$ was accumulated in order to measure the differential elastic cross section as a function of the Mandelstam momentum transfer variable $t$. The measurement is performed with the ALFA sub-detector of ATLAS. Using a fit to the differential elastic cross section in the $|t|$ range from 0.01 GeV$^2$ to 0.1 GeV$^2$ to extrapolate to $|t|\rightarrow 0$, the total cross section, $\sigma_{\mathrm{tot}}(pp\rightarrow X)$, is measured via the optical theorem to be: $$\sigma_{\mathrm{tot}}(pp\rightarrow X) = 95.35 \; \pm 0.38 \; ({\mbox{stat.}}) \pm 1.25 \; ({\mbox{exp.}}) \pm 0.37 \; (\mbox{extr.}) \; \mbox{mb},$$ where the first error is statistical, the second accounts for all experimental systematic uncertainties and the last is related to uncertainties in the extrapolation to $|t|\rightarrow 0$. In addition, the slope of the elastic cross section at small $|t|$ is determined to be $B = 19.73 \pm 0.14 \; ({\mbox{stat.}}) \pm 0.26 \; ({\mbox{syst.}}) \; \mbox{GeV}^{-2}$.
The measured total cross section, the first systematic error accounts for all experimental uncertainties and the second error for the extrapolation t-->0.
The nuclear slope of the differential eslastic cross section at small |t|, the first systematic error accounts for all experimental uncertainties and the second error for the extrapolation t-->0.
The Optical Point dsigma/(elastic)/dt(t-->0), the total elastic cross section and the observed elastic cross section within the fiducial volume. The first systematic error accounts for all experimental uncertainties and the second error for the extrapolation t-->0.
A measurement of the total $pp$ cross section at the LHC at $\sqrt{s}=8$ TeV is presented. An integrated luminosity of $500$ $\mu$b$^{-1}$ was accumulated in a special run with high-$\beta^{\star}$ beam optics to measure the differential elastic cross section as a function of the Mandelstam momentum transfer variable $t$. The measurement is performed with the ALFA sub-detector of ATLAS. Using a fit to the differential elastic cross section in the $-t$ range from $0.014$ GeV$^2$ to $0.1$ GeV$^2$ to extrapolate $t\rightarrow 0$, the total cross section, $\sigma_{\mathrm{tot}}(pp\rightarrow X)$, is measured via the optical theorem to be: $\sigma_{\mathrm{tot}}(pp\rightarrow X) = {96.07} \; \pm 0.18 \; ({{stat.}}) \pm 0.85 \; ({{exp.}}) \pm 0.31 \; ({extr.}) \; {mb} \;,$ where the first error is statistical, the second accounts for all experimental systematic uncertainties and the last is related to uncertainties in the extrapolation $t\rightarrow 0$. In addition, the slope of the exponential function describing the elastic cross section at small $t$ is determined to be $B = 19.74 \pm 0.05 \; ({{stat.}}) \pm 0.23 \; ({{syst.}}) \; {GeV}^{-2}$.
The measured total cross section, the first systematic error accounts for all experimental uncertainties and the second error for the extrapolation t-->0.
The nuclear slope of the differential eslastic cross section at small |t|, the first systematic error accounts for all experimental uncertainties and the second error for the extrapolation t-->0.
The total elastic cross section and the observed elastic cross section within the fiducial volume.
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