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 results on the total and elastic cross sections in proton-proton collisions at $\sqrt{s}=200$ GeV obtained with the Roman Pot setup of the STAR experiment at the Relativistic Heavy Ion Collider (RHIC). The elastic differential cross section was measured in the squared four-momentum transfer range $0.045 \leq -t \leq 0.135$ GeV$^2$. The value of the exponential slope parameter $B$ of the elastic differential cross section $d\sigma/dt \sim e^{-Bt}$ in the measured $-t$ range was found to be $B = 14.32 \pm 0.09 (stat.)^{\scriptstyle +0.13}_{\scriptstyle -0.28} (syst.)$ GeV$^{-2}$. The total cross section $\sigma_{tot}$, obtained from extrapolation of the $d\sigma/dt$ to the optical point at $-t = 0$, is $\sigma_{tot} = 54.67 \pm 0.21 (stat.) ^{\scriptstyle +1.28}_{\scriptstyle -1.38} (syst.)$ mb. We also present the values of the elastic cross section $\sigma_{el} = 10.85 \pm 0.03 (stat.) ^{\scriptstyle +0.49}_{\scriptstyle -0.41}(syst.)$ mb, the elastic cross section integrated within the STAR $t$-range $\sigma^{det}_{el} = 4.05 \pm 0.01 (stat.) ^{\scriptstyle+0.18}_{\scriptstyle -0.17}(syst.)$ mb, and the inelastic cross section $\sigma_{inel} = 43.82 \pm 0.21 (stat.) ^{\scriptstyle +1.37}_{\scriptstyle -1.44} (syst.)$ mb. The results are compared with the world data.
The B-slope of the exponential fit A*exp(-B*|t|) to the single differential proton-proton elastic cross-section in the t-range 0.045<|t|<0.135 GeV**2 at sqrt(s) = 200 GeV.
The total, elastic and inelastic cross-sections for proton-proton scattering at sqrt(s)=200 GeV, the elastic cross-section measured in the t-range 0.045<|t|<0.135 GeV^2 and the value of the differential cross-section extrapolated to |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.
K − p reactions have been studied at 13 different incident momenta between 1138 and 1434 MeV/ c . This interval corresponds to a mass of the K − p system varying from 1858 to 1993 MeV. About 300 000 photographs were taken in the 81 cm Saclay hydrogen bubble chamber exposed to a separated K − beam at the CERN proton-synchrotron. A total of about 44 000 events were analyzed, from which partial and differential cross sections were determined. Polarizations were obtained for the two-body reactions where the decay of the Λ or Σ hyperon allowed their measurement. Data for the two-body channels are presented here as well as for the main quasi-two-body reactions.
PARTIAL CROSS SECTIONS. DATA AT 1.305 TO 1.434 GEV/C FOR FINAL STATES K- P, K- P PI0 AND K- N PI+ COME FROM THE HAIFA GROUP, S. DADO ET AL.
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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.
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We have made measurements of polarization in π−p elastic scattering, with emphasis over the backward region, at 1.60 to 2.28 GeVc. The results indicate the absence of u-channel dominance in the backward region, as was observed in the case of π+p scattering. Comparisons have been made with predictions of various phase-shift analyses which show that the agreement is generally very poor in the backward region.
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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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The analyzing power A N of proton-proton, proton-hydrocarbon, and antiproton-hydrocarbon, scattering in the Coulomb-nuclear interference region has been measured using thhe 185 GeV/ c Fermilab polarized-proton and -antiproton beams. The results are found to be consistent with theoretical predictions within statistical uncertainties.
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Results are presented on π±p, K±p, and p±p elastic scattering measured with an apparatus having acceptance of 0.5<−t<2.5 (GeV/c)2 and 0.9<−t<11 (GeV/c)2 at 100 and 200 GeV/c, respectively. A diffractionlike dip is seen for the first time in the π−p t distribution at −t=4 (GeV/c)2. All meson-proton cross sections are found to be similar in the range 1<−t<2.5 (GeV/c)2, although some small systematic differences are observed. Cross sections for pp and p―p are compared with previous data.
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Results are presented on the measurement of 200-GeV/c π−p elastic scattering at −t from 0.8 to 11 (GeV/c)2. As −t is increased, dσdt falls by ∼6 decades to a prominent dip at 4 (GeV/c)2, followed by a second maximum and than a slow decrease with increasing −t.
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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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Backward elastic scattering of π± on protons has been measured for incident pion momenta between 30 and 90 GeV/c and 0≤−u≤0.5 (GeV/c)2. The u dependence of the cross sections is similar to that observed at lower momenta, and Regge models give acceptable fits to the data.
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Antiproton-proton elastic scattering has been measured at 100 GeV/c for 0.5<−t<2.5 (GeV/c)2 and at 200 GeV/c for 0.9<−t<4 (GeV/c)2. The data show that the −t≃1.4 (GeV/c)2 dip recently observed at 50 GeV/c persists to higher incident momenta. Proton-proton measurements made at the same beam momenta show similar structure.
CLEAR DIP OBSERVED AT -T=1.4 (GEV/C)**2.
Measurements of polarization in π+p elastic scattering have been made at 1.60, 1.80, 2.11, and 2.31 GeVc. The data cover the entire angular range, with emphasis on the backward region. Comparisons have been made with both u-channel and t-channel models, as well as with predictions of phase-shift analyses. While the agreement is generally poor in all cases, the best agreement is with some t-channel predictions.
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The polarization parameter for K + p elastic scattering has been measured at 1.60, 1.80, 2.11 and 3.31 GeV/ c incident momenta over the entire angular range with an emphasis on the backward region. The results in the extreme backward region appear to be small and consistent with zero.
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Total and differential cross sections for π−p elastic scattering are presented at 35 energies between 1400 and 2000 MeV.
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The angular distributions of the reactions K - p → K - p and K - p → K K 0 n have been measured at 23 incident K - momenta between 1.136 and 1.798 ifGeV/c using the bubble chamber technique. These data, together with other published data on the same reactions, including K - p polarisations, K̄N total cross sections, and measurements of Re ƒ(0)/ Im ƒ(0) , have been analysed in terms of partial-wave amplitudes. Resonance behaviour is confirmed for the P 03 partial wave at 1890 MeV. The resonance parameters of the F 15 (1915), F 17 (2030) and G 07 (2100) have been redetermined. No evidence has been found for new resonances coupling significantly to K K N in the energy region explored.
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Measurements of π±p backward elastic scattering have been made for incident pion momenta between 30 and 90 GeV/c and for 0<−u<0.5 (GeV/c)2. The momentum dependence of the cross sections is of a form expected from a simple Regge model, and the u dependence of the cross sections is similar to that observed at lower momenta.
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Differential cross sections in the t -range between 0.02 and 1.5 GeV 2 have been measured for the elastic scattering of particles and antiparticles on protons at 6.4, 10.4 and 14 GeV for K ± p and 10.4 GeV for π ± p and p ± p . Large statistics have been achieved and systematic uncertainties have been minimized. The relative systematic uncertainty between particle and antiparticle data is less than 0.5%. Accurate measurements of the position of the first crossover between particle and antiparticle differential cross sections have been performed. As the energy increases from 6.4 to 14 GeV the K ± p crossover moves to smaller values by 0.010 GeV 2 with a statistical error of 0.006 GeV 2 and a systematic uncertainty of 0.005 GeV 2 . The crossover positions at 10.4 GeV for π ± , K ± and p ± scale approximately with the interaction radii.
CROSSOVER POSITION IS -T = 0.209 +- 0.004 (DSYS = 0.003) GEV**2.
CROSSOVER POSITION IS -T = 0.209 +- 0.004 (DSYS = 0.003) GEV**2. SMALL ANGLE CROSS SECTIONS IN SMALLER T-BINS.
CROSSOVER POSITION IS -T = 0.211 +- 0.004 (DSYS = 0.0025) GEV**2.
Differential cross-sections for proton-proton elastic scattering have been measured covering the angular range from 50° to 90° c.m. at twelve incident momenta from 1.3 to 3.0 GeV/c. The angular distributions are quite smooth, but there is evidence of structure in the energy dependence of fixed-angle cross-sections at |t| ∼ 1 (GeV)2.
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The energy dependence of backward π+p elastic scattering has been measured for incident π momenta 2.0-6.0 GeV/c in steps of typically 100 MeV/c. Values are presented for both the differential cross section extrapolated to 180° and the slope of the backward peak as a function of momentum. In the s channel we see the effects of the established Δ++ resonances and evidence for the Δ(3230). Also, the data show the existence of a negative-parity Δ resonance with mass ∼2200 MeV/c2.
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Full angular distributions of the polarization parameter in elastic K+p scattering at 1.37, 1.45, 1.60, 1.71, 1.80, 1.89, 2.11, and 2.31 GeV/c are presented. These data were obtained in an experiment at the Zero Gradient Synchrotron using a polarized proton target with arrays of scintillation and Čerenkov counters to detect the scattered particles.
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The logarithmic slope of the differentical cross section for K ± p elastic scattering at 10 and 14 GeV, and for π ± p and p ± p at 10GeV has been measured. Rich structure is observed in the forward slope for all processes, which is well accounted for by the properties of a peripheral exchange amplitude for the nonexotic reactions, and by a peripheral component of the diffractive amplitude as clearly seen in the exotic processes, K ± p and pp.
GRAPH OF D(SIG)/DT.
SLOPE AS A FUNCTION OF T.
The backward angular distributions obtained in an experiment at the Zero Gradient Synchrotron of Argonne National Laboratory were used to systematically study the energy dependence of the 180° differential cross section for π+p elastic scattering in the center-of-mass energy region from 2159 to 3487 MeV. At each of 38 incident pion momenta between 2.0 and 6.0 GeV/c, a focusing spectrometer and scintillation counter hodoscopes were used to obtain differential cross sections for typically five pion scattering angles from 141° to 173° in the laboratory. Values for dσdΩ at 180° were then obtained by extrapolation. A resonance model and an interference model were used to perform fits to the energy dependence of dσdΩ (180°). Both models led to good fits to our data and yielded values for the masses, widths, parities, and the product of spin and elasticity for the Δ(2200), Δ(2420), Δ(2850), and Δ(3230) resonances. Our data confirm the existence of the Δ(3230) and require the negative-parity Δ(2200).
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The differential cross section for K ± p elastic scattering has been measured in the very low t region (0.003 < t < 0.2 GeV 2 ) in a wire chamber spectrometer experiment at 10.4 and 14 GeV/ c . The interference effect observed between the Coulomb and the nuclear interaction has been used to determine α, the ratio of real to imaginary part of the forward scattering amplitude. At 10.4 GeV/ c we measure α (K + p) = −0.21 ± 0.06 and α (K − p = 0.08 ± 0.04, and at 14 GeV/ c , α (K + p) = − 0.13 ± 0.03 and α (K − p) = 0.000 ± 0.04 in agreeement with the predictions of dispersion theory calculation.
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Angular distributions for π+p→π+p were measured for 13 incident-pion momenta from 4.4 to 6.0 GeV/c and for −t less than ∼0.1 (GeV/c)2. This experiment was performed at the Zero Gradient Synchrotron of Argonne National Laboratory, where a focusing magnetic spectrometer and a scintillation-counter hodoscope were used. In fitting the angular distributions the strong-interaction contribution was parameterized by an exponential form exp(bt); the Coulomb interference was also included. The resulting values of the slope parameter for |t|<∼0.1 (GeV/c)2 are presented for each incident beam momentum.
ENLARGED GRAPHS OF FIGURES SUPPLIED BY J. A. POIRIER.
SLOPE IS FROM FITTING EXP(SLOPE*T) TO FORWARD DIFFERENTIAL CROSS SECTION FOR -T < 0.1 GEV**2 APPROX AFTER ALLOWING FOR COULOMB INTERACTION.
The elastic differential cross section for pp scattering has been measured up to a momentum transfer of ‖ t ‖ = 3(GeV/ c ) 2 at 100 GeV/c and 200 GeV/c incident momenta. The 200 GeV/ c measurements shows a diffractive like dip at ‖ t ‖ = 1.5 GeV/ c while no such dip is seen in the 100 GeV/ c data.
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The differential cross section for π±, K±, and p± on hydrogen have been measured in the range 0.07<−t<1.6 (GeV/c)2. The dependence on momentum, momentum, transfer, and particle type are discussed.
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Elastic scattering of hadrons on protons has been measured at momenta of 50, 100, and 200 GeV/c. The meson-proton scattering is found to be independent of momentum and meson type for −t>0.8 (GeV/c)2. The momentum dependence of the pp dip at −t=1.4 (GeV/c)2 was investigated. Slope parameters are given.
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Elastic differential cross sections were measured at 6 energies between 2.3 and 6 BeVc for π++p and π−+p. The behavior of the secondary peak as a function of energy and charge is shown. Evidence for considerable resonance structure is seen in the angular distributions.
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The polarization parameter in elastic π−p scattering has been measured, at the Berkeley 184-in. synchrocyclotron, with the use of a polarized proton target. At 318-, 337-, and 390-MeV incident pion kinetic energy, the angular range from 70° to 180° in the center-of-mass system was covered. At 229 MeV, polarization measurements were made in the angular range 150° to 180°. Phase-shift analyses, using these and other published data, were made at the two lowest energies.
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