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.
Elastic π−+p differential cross-section data are presented at the incident-pion momenta 1.72, 1.89, 2.07, 2.27 and 2.46 GeV/c. Resonant behaviour in the coefficients of a Legendre polynomial expansion indicates G- or H-wave resonance. Further analysis using an energy-dependent parametrization of G- and H-waves shows the results to be compatible with the 7−/2 assignment for the , but equally acceptable solutions are obtained with the inclusion of an additional 9+/2 resonance contribution.
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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.
Accelerating polarized protons to 22 GeV/c at the Brookhaven Alternating Gradient Synchro- tron required both extensive hardware modifications and a difficult commissioning process. We had to overcome 45 strong depolarizing resonances to maintain polarization up to 22 GeV/c in this strong-focusing synchrotron. At 18.5 GeV/c we measured the analyzing power A and the spin-spin correlation parameter Ann in large- P⊥2 proton-proton elastic scattering, using the polarized proton beam and a polarized proton target. We also obtained a high-precision measurement of A at P⊥2=0.3 (GeV/c)2 at 13.3 GeV/c. At 18.5 GeV/c we found that Ann=(-2±16)% at P⊥2=4.7 (GeV/c)2, where it was about 60% near 12 GeV at the Argonne Zero Gradient Synchrotron. This sharp change suggests that spin-spin forces may have a strong and unexpected energy dependence at high P⊥2.
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2.2 GeV point taken from Brown et al., PR D31(85) 3017.
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We measured the analyzing power A and the spin-spin correlation parameter Ann in medium-P⊥2 proton-proton elastic scattering, using a polarized-proton target and the 18.5-GeV/c Brookhaven Alternating-Gradient Synchrotron polarized-proton beam. We found sharp dips in both A and Ann, which occur at different P⊥2 values. The unexpected sharp structure in the spin-spin force occurs near P⊥2=2.3 (GeV/c)2 where the elastic cross section has no apparent structure.
Errors contain both statistics and systematics.
We measured the analyzing power A and the spin-spin correlation parameter Ann, in large-P⊥2 proton-proton elastic scattering, using a polarized-proton target and the polarized-proton beam at the Brookhaven Alternating-Gradient Synchrotron. We also used our polarimeter to measure A at small P⊥2 at 13 GeV with good precision and found some deviation from the expected 1Plab behavior. At 18.5 GeV/c we found Ann=(−2±16)% at P⊥2=4.7 (GeV/c)2. Comparison with lower-energy data from the Argonne Zero-Gradient Synchrotron shows a sharp and surprising energy dependence for Ann at large P⊥2.
POL is error weighted average of polarized beam and target measurements.
POL is error-weighted average of polarized beam and target measurements.
POL is error-weighted average of polarized beam and target measurement.
The spin analyzing power A in 28-GeV/c proton-proton elastic scattering was measured at P⊥2=6.5 (GeV/c)2 using a polarized proton target and a high-intensity unpolarized proton beam at the Brookhaven National Laboratory Alternating Gradient Synchrotron. The result of (24±8)% confirms that the analyzing power is large and rising in the large-P⊥2 region.
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Using the new Brookhaven Alternating Gradient Synchrotron polarized proton beam and our polarized proton target, we measured the spin-spin correlation parameter Ann in 16.5-GeV/c proton-proton elastic scattering. We found an Ann of (6.1±3.0)% at P⊥2=2.2 (GeV/c)2. We also measured the analyzing power A in two independent ways, providing a good test of possible experimental errors. Comparing our new data with 12-GeV Argonne Zero Gradient Synchrotron data shows no evidence for strong energy dependence in Ann in this medium-P⊥2 region.
ERROR CONTAINS BOTH SYSTEMATIC AND STATISTICAL UNCERTAINTY.
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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The analyzing power in 28 GeV/c proton/proton elastic scattering was measured at P2∥=5.95 and 6.56 (GeV/c)2 using a polarized proton target and an unpolarized proton beam at the Brookhaven National Laboratory AGS. Results indicate that the analyzing power, A, is rising sharply with P2∥.
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The analyzing power A in 28-GeV/c proton-proton elastic scattering was measured with a polarized proton target and a high-intensity unpolarized proton beam at the Brook-haven National Laboratory alternating-gradient synchrotron. The P⊥2 range of 2.85 to 5.95 (GeV/c)2 was covered with good precision. A small dip of about -3.5% was found near P⊥2=3.5 (GeV/c)2 where a 24-GeV/c CERN experiment had reported a deep dip of about -16% with large errors. In the previously unexplored large-P⊥2 region near 6 (GeV/c)2 these new large-error points suggest that A may be rising.
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A measurement of the proton-proton elastic differential cross section at 50 GeV/ c incident momentum in the momentum transfer range 0.8<| t |<4.0 (GeV/ c ) 2 is presented. The data are compared to pp data at lower and higher energies, and to some model predictions.
NUMERICAL VALUES OF DATA SUPPLIED BY D. IMRIE. ERROR CONTAINS BOTH STATISTICAL AND SYSTEMATICS EXCEPT THE OVERALL NORMALIZATION ERROR.
Measurements of the K - p and K + p elastic differential cross sections at 20 and 50 GeV/ c , respectively, have been made in the momentum transfer range 0.7 < ∥ t ∥ < 8.0 GeV/ c .
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The analyzing power, A, was measured in proton-proton elastic scattering with use of a polarized proton target and 28-GeV/c primary protons from the alternating-gradient synchrotron. Over the P⊥2 range of 0.5 to 2.8 (GeV/c)2, the data show interesting structure. There is a rather sharp dip at P⊥2=0.8 (GeV/c)2 corresponding to the break in the elastic differential cross section at the end of the diffraction peak.
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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'.
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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We measured the differential cross section for proton-proton elastic scattering at 6 GeV/c, with both initial spins oriented normal to the scattering plane. The analyzing power A shows significant structure with a large broad peak reaching about 24% near P⊥2=1.6 (GeV/c)2. The spin-spin correlation parameter Ann exhibits more dramatic structure, with a small but very sharp peak rising rapidly to about 13% at 90°c.m.. This sharp peak may be caused by particle-identity effects.
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A measurement of the polarization parameter P 0 in pp elastic scattering has been made at 24 GeV/ c over the range of momentum transfer squared 0.7 < | t | < 5.0 (GeV/ c ) 2 . The structure of P 0 has changed compared to typical lower energy data. The second peak is suppressed and a dip has appeared at | t | = 3.6 (GeV/ c ) 2 .
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Proton-proton elastic scattering using 201- and 400-GeV/c extracted beams at Fermilab has been measured in the region 4.9<−t<14.4 GeV2. Contrary to predictions of diffraction models, there is no sign of a second dip or "break," and the slope A in the fit exp(At) is smaller than predicted. It drops from 1.5 to 0.8 GeV−2 over our t range. The shape of the t distribution can be fitted by the power law dσdt∝t−8.4 which is close to a quantum-chromodynamics (QCD) prediction of t−8. At fixed t the 201-GeV/c cross sections are about 2.3 times those at 400 GeV/c which is compatible with the QCD and constituent-interchange-model prediction that dσdt∝s−10 at fixed ts.
LOW T.
HIGH T.
LOW T.
None
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The energy dependence of the spin-parallel and spin-antiparallel cross sections for p↑+p↑→p+p at 90°c.m. was measured for beam momenta between 6 and 12.75 GeV/c. The ratio (dσdt)parallel:(dσdt)antiparallel at 90° is about 1.2 up to 8 GeV/c and then increases rapidly to a value of almost 4 near 11 GeV/c. Our data indicate that this ratio may depend only on the variable P⊥2, and suggests that the ratio may reach a limiting value of about 4 for large P⊥2.
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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.
Measurement was made of dσdt for n↑+p↑→n+p at P⊥2=0.8 and 1.0 (GeV/c)2 at 6 GeV/c. The 6-GeV/c 53%-polarized neutrons from the 12-GeV/c polarized deuteron beam at the Argonne zero-gradient synchroton were scattered from our 75%-polarized proton target. Both spins were oriented perpendicular to the scattering plane. We found large unexpected spin-spin effects in n−p elastic scattering which are quite different from the p−p spin-spin effects.
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We measured dσdt for p↑+p↑→p+p from P⊥2=4.50 to 5.09 (GeV/c)2 at 11.75 GeV/c. We used a 59%-polarized proton beam and a 71%-polarized proton target with both spins oriented perpendicular to the scattering plane. In these large-P⊥2 hard-scattering events, spin effects are very large and the ratio (dσdt)↑↑:(dσdt)↑↓ grows rapidly with increasing P⊥2, reaching a value of 4 at 90° (c.m.). Thus, hard elastic scattering, which is presumably due to the direct scattering of the protons' constituents, may only occur when the two incident protons' spins are parallel.
THE ERRORS INCLUDE STATISTICAL AND SYSTEMATIC ERRORS ADDED IN QUADRATURE. THE PARALLEL/ANTIPARALLEL SPIN CROSS SECTION RATIO IS (1+CNN)/(1-CNN).
Proton-proton elastic scattering at 400 GeV/c has been measured in the region 5.4<−t<14.4 GeV2 with no sign of a second dip or "break." If the data are fitted by exp(At), the slope A decreases from 1.5±0.1 to 0.7±0.2 GeV−2 over the range. At fixed t the 400-GeV/c cross sections are about 0.6 times those at 200 GeV/c in this t range. At fixed θc.m.=15°, dσdt∝s−n where n=9.7±0.3.
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