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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We have measured the spin-spin correlation parameter CNN at 2, 3, 4, and 6 GeV/c over the |t| range of 0.1 to 2.0 (GeV/c)2 and have observed a striking energy and |t| dependence in CNN. Polarization data were simultaneously collected and are compared to previous results.
CNN PARAMETER MEASURED.
Toward the goal of experimentally determining pp elastic scattering amplitudes at 6 GeV/c, we have measured a linear combination of triple-spin correlation parameters and also a linear combination of spintransfer parameters over the |t| range between 0.2 and 1.0 (GeV/c)2. A horizontally polarized beam (S direction) was obtained by precessing the spin of the polarized beam from the Argonne Zero Gradient Synchrotron using a superconducting solenoid. The target protons were polarized vertically (N direction) and the polarization of the recoil protons was measured with a carbon polarimeter. The results are consistent with the amplitude corresponding to π exchange being almost real and positive.
KSS = (S00S) AND HSNS = (SN0S) MEASURED HERE CONTAIN SMALL ADMIXTURES OF THE OTHER SPIN-TRANSFER AND TRIPLE-SPIN CORRELATION PARAMETERS RESPECTIVELY DUE TO THE POLARIZED TARGET MAGNETIC FIELD - SEE TEXT. MEAN VALUE OF HSNS OVER THIS T-RANGE IS 0.098 +- 0.085. PARITY CONSERVATION REQUIRES THE VANISHING OF THE PARAMETERS KSN, HSNN, (000S) AND DNS, WHILE (000N) MUST AGREE WITH THE SINGLE SCATTERING POLARIZATION PARAMETER (0N00).
Using the polarized-beam facility at Argonne National Laboratory and a polarized proton target, simultaneous measurements of the spin parameter P and the spin correlation term CNN were made. Data were obtained and analyzed at beam momenta of 2, 3, 4, and 6 GeV/c in the momentum-transfer-squared interval 0.1≤|t|≤2.8 (GeV/c)2. A preliminary phase-shift analysis of the 2- and 3-GeV/c data is discussed and a comparison with predictions of a particular Regge-pole model at all four energies is made.
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We have made the first measurement of the spin-spin correlation parameter CSS in pp elastic scattering at 6 GeV/c over the |t| range from 0.05 to 1.5 (GeV/c)2. The measured CSS data points are all negative, and their absolute values increase with |t|. The results are compared with some existing attempts to describe the pp scattering process.
NUMERICAL VALUES OBTAINED FROM AUTHORS. MAGNETIC FIELD ALIGNMENT AND APERTURE EFFECTS MEAN THAT QUANTITY ACTUALLY MEASURED IS 0.98 CSS + 0.02 CNN - 0.12 CSL. SEE LATER NUMBERS IN THE RECORD OF I. P. AUER ET AL., PL 70B, 475 (1977).
The small-angle elastic scattering for pp at s=23.5, 30.7, and 52.8 GeV and for p¯p at s=52.8 GeV are measured. The data are normalized on Coulomb scattering. Using the optical theorem and the best estimate of the real part of the forward scattering amplitude, ρ(pp¯)=0.1, we obtain σtot(p¯p)=44.1±2.9 mb for the total cross section and b(p¯p)=13.6±2.2 GeV−2 for the nuclear slope parameter. This supports the dispersion relation prediction that σtot(p¯p) will start to rise above Elab≈200 GeV.
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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 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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We measured the analyzing power A out to P⊥2=7.1 (GeV/c)2 with high precision by scattering a 24-GeV/c unpolarized proton beam from the new University of Michigan polarized proton target; the target’s 1-W cooling power allowed a beam intensity of more than 2×1011 protons per pulse. This high beam intensity together with the unexpectedly high average target polarization of about 85% allowed unusually accurate measurements of A at large P⊥2. These precise data confirmed that the one-spin parameter A is nonzero and indeed quite large at high P⊥2; most theoretical models predict that A should go to zero.
Errors quoted contain both statistical and systematic uncertainties.
Toward the goal of experimentally determining the p-p elastic-scattering amplitudes at 6 GeV/c, we have measured a number of triple- and double-spin correlation parameters over the ‖t‖ range between 0.2 and 1.0 (GeV/c)2. These new data permit the first nucleon-nucleon amplitude determination in the multi-GeV energy range. Polarized beams from the Argonne Zero Gradient Synchrotron and polarized targets were utilized. The polarization of the recoil proton was measured with a carbon polarimeter. A total of 14 different spin observables were measured (five spin transfer, four depolarization, and five triple-spin correlation parameters). These have been combined with earlier results, resulting in a data set of typically 30 measurements of 20 different spin observables for each of six ‖t‖ values between 0.2 and 1.0 (GeV/c)2. A solution for the amplitudes has been found at each ‖t‖, and comparisons are presented with several different models. The spin-nonflip helicity amplitudes are found to be much larger than the spin-flip amplitudes.
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As part of a program to determine proton-proton elastic-scattering amplitudes, we have measured the spin-spin correlation parameter CNN at 6 GeV/c. Measurements were made over the |t| range of 0.08 to 1.4 (GeV/c)2 using a polarized beam and a polarized target at the Argonne National Laboratory Zero Gradient Synchrotron.
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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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Proton-antiproton and proton-proton elastic scattering have been measured in the four-momentum transfer range 0.001⩽| t |⩽0.06 GeV 2 for center-of-mass energy 52.8 GeV at the CERN Intersecting Storage Rings (ISR). Using the known pp total cross section, a simultaneous fit to the pp̄ and pp differential cross sections yields the pp̄ total cross section; in addition, we obtain the ratio of the real-to-imaginary part of the forward nuclear-scattering amplitude and the nuclear-slope parameter for both pp̄ and pp. Our results show conclusively that the pp̄ total cross section is rising at ISR energies and lend support to conventional theories in which the difference between the pp̄ and pp total cross section vanishes at very high energy.
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The π + p cross section for elastic scattering from hydrogen was measured at seven incident energies ranging from 20.8 to 95.9 MeV for an angular range from 60° to 145°. The experimental set-up is discussed in detail as well as the method used for data analysis. A table of results and a set of phase shifts are provided.
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Large-angle π±p elastic-scattering cross sections, measured between 2 and 9 GeV/c in fine intervals of incident momentum and scattering angle, are used to search for cross-section fluctuations occurring for small changes in the center-of-mass energy as suggested by Ericson and Mayer-Kuckuck and by Frautschi. Significant fluctuations are observed.
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Antiproton-proton and proton-proton small-angle elastic scattering was measured for centre-of-mass energies s =30.6, 52.8 and 62.3 GeV at the CERN Intersectung Storage Rings. In addition, proton-proton elastic scattering was measured at s =23.5 GeV . Using the optical theorem, total cross sections are obtained with an accuracy of about 0.5% for proton-proton scattering and about 1% for antiproton-proton scattering. The measurement of the interference of the Coulomb scattering and the hadronic scattering permits a determination of the ratio of the real-to-imaginary part of the forward hadronic scattering amplitude. Also presented are measurements of the hadronic slope parameter.
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Antiproton-proton and proton-proton small-angle elastic scattering have been measured for centre-of-mass energies √ s = 30.7 and 62.5 GeV at the CERN Intersecting Storage Rings (ISR). Antiproton-proton and proton-proton total cross sections are obtained using the optical theorem. The measurement of the Coulomb scattering and its interference with the nuclear scattering allows a determination of the ratio of the real-to-imaginary part of the forward nuclear scattering amplitude. Also presented are measurements for the nuclear slope parameter at √ s = 62.5 GeV. Our new results reinforce the conclusions drawn recently from our measurements at √ s = 52.8 GeV. In particular, the pp̄ total cross section is rising at ISR energies and should continue to rise well beyond these energies.
DATA REQUESTED FROM AUTHORS.
RESULTS OF FITS.
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A total of 24 360 events having two charged particles in the final state from π−+p interactions at an incident π− momentum of 2.7 GeVc have been analyzed. The final states π−π+n and π−π0p are found to be dominated by rho-meson production, and in addition, significant N*(1238) production is seen. The partial cross sections for the dominant resonant channels are σ=(pρ−)=(1.3±0.2) mb, σ(nρ0)=(2.3±0.2) mb, and σ[π−N*+(→pπ0)]=(0.5±0.2) mb. The production of the ρ− and ρ0 and the decay of the ρ− agree very well with the predictions of an absorption-modified one-pion-exchange model. The production angular distributions of the ρ0 and ρ− follow an exponential of the form Ae+Bt. The results from a least-squares fit give B(ρ−)=9.32±0.08 (GeVc)−2, B(ρ0)=10.26±0.06 (GeVc)−2. A similar analysis for the elastic-scattering events gave B(el)=7.77±0.05 (GeVc)−2. The ρ0 decay distributions are asymmetric and they have been analyzed using a simple model which includes S−P-wave interference. No clear evidence is seen for a T=0, J=0 resonance at a mass near that of the ρ. The N*(1238) resonance production is found to be in agreement with the ρ-exchange model of Stodolsky and Sakurai. Indication of other resonance production with small cross section is seen, such as A1 and A2 production in the multiple missing neutral events. The masses and widths of the ρ0 and ρ− as a function of the four-momentum transfer squared to the nucleon have been determined.
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We present the results on total channel cross-sections obtained in the Saclay 180 l HBC exposed to a separated K− beam at Nimrod. The cross-sections for each channel are given at 13 incident K− momenta between 1.26 and 1.84 GeV/c.
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We have analyzed the two-prong final states in π+p interactions at 3.9 GeVc. Our result for elastic scattering is σ (elastic) = 6.50±0.1 mb (statistical error only). We find the elastic slope to be 6.61±0.14 (GeVc)−2. We find the elastic forward cross section to be 40.0±1.4 mb(GeVc)2. We have applied a longitudinal-momentum analysis to the one-pion-production channel. We find the cross section for the reaction π++p→π++π0+p to be 2.30±0.06 mb and that for π++p→π++π++n to be 1.45±0.05 mb. For resonance-production cross sections in these channels we find Δ(1236)=0.60±0.07 mb, ρ(760)=0.86±0.06 mb, and diffraction dissociation = 1.69±0.11 mb. We find that we can satisfactorily fit all distributions in the one-pion-production channel without assuming any phase-space production. In the missing-mass channel we observe dominant Δ++(1236) production plus evidence for A2+ production.
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The K − p differential and total elastic cross-sections have been measured at 14.25 GeV/ c . The results have been compared with various Regge models.
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The analyzing power AN of proton-proton elastic scattering in the Coulomb-nuclear interference region has been measured using the 200-GeV/c Fermilab polarized proton beam. A theoretically predicted interference between the hadronic non-spin-flip amplitude and the electromagnetic spin-flip amplitude is shown for the first time to be present at high energies in the region of 1.5 × 10−3 to 5.0 × 10−2 (GeV/c)2 four-momentum transfer squared, and our results are analyzed in connection with theoretical calculations. In addition, the role of possible contributions of the hadronic spin-flip amplitude is discussed.
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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.
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