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 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.
The nuclear slope parameter B from a fit of the form exp(-Bt-Ct^2-Dt^3). The systematic uncertainty includes experimental and theoretical uncerainties.
We have measured the cross section at 180° for K + p and K + n elastic scattering in the momentum range 1.0 to 1.5 GeV/ c . The K + n cross section was measured on deuterium and the K + p on hydrogen and deuterium. We were thus able to measure directly the difference between free nucleon (proton) scattering and bound nucleon (proton) scattering at large angles. This difference was found to be small and within our experimental accuracy the K + p(n) cross section should be equal to the K + p (free) cross section at 180°. We found no evidence for an s -channel resonance Z ∗ in either the K + p or K + n system. A comparison of our data and those of other groups with theoretical predictions is given.
DEUTERIUM TARGET. U IS ABOUT 0.1 GEV**2.
HYDROGEN AND DEUTERIUM TARGET DATA ARE IN GOOD AGREEMENT. THESE CROSS SECTIONS ARE A WEIGHTED AVERAGE.
The differential elastic scattering cross section for 2.7 GeV c antiprotons on protons has been studied using film from the 20″ BNL hydrogen bubble chamber. The diffraction pattern based on a total sample of 7300 events shows a sharp forward maximum, a first diffraction minimum, and a second maximum. The forward diffraction peak is fitted by ( d σ d t ) elastic =[325 ± 6 mb ( GeV c ) 2 ] exp [−13.3 ± 0.2( GeV c ) −2 t and the total elastic cross section is found to be 25.6 ± 0.6 mb. The first and second diffraction peaks are fitted by the optical model formula for a “black” disc. d σ d t ∼ [j 1 (2k R sin 1 2 θ)] 2 (1 + a cos θ) 2 where R = 1.2 fm and a = −5.
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The TOTEM experiment has made a precise measurement of the elastic proton-proton differential cross-section at the centre-of-mass energy sqrt(s) = 8 TeV based on a high-statistics data sample obtained with the beta* = 90 optics. Both the statistical and systematic uncertainties remain below 1%, except for the t-independent contribution from the overall normalisation. This unprecedented precision allows to exclude a purely exponential differential cross-section in the range of four-momentum transfer squared 0.027 < |t| < 0.2 GeV^2 with a significance greater than 7 sigma. Two extended parametrisations, with quadratic and cubic polynomials in the exponent, are shown to be well compatible with the data. Using them for the differential cross-section extrapolation to t = 0, and further applying the optical theorem, yields total cross-section estimates of (101.5 +- 2.1) mb and (101.9 +- 2.1) mb, respectively, in agreement with previous TOTEM measurements.
The elastic differential cross-section as determined in this analysis using the ''optimised'' binning.
At the LHC energy of $\sqrt s = 7\,{\mathrm { TeV}}$ , under various beam and background conditions, luminosities, and Roman Pot positions, TOTEM has measured the differential cross-section for proton-proton elastic scattering as a function of the four-momentum transfer squared t. The results of the different analyses are in excellent agreement demonstrating no sizeable dependence on the beam conditions. Due to the very close approach of the Roman Pot detectors to the beam center (≈5σ(beam)) in a dedicated run with β* = 90 m, |t|-values down to 5·10(−)(3) GeV(2) were reached. The exponential slope of the differential elastic cross-section in this newly explored |t|-region remained unchanged and thus an exponential fit with only one constant B = (19.9 ± 0.3) GeV(−)(2) over the large |t|-range from 0.005 to 0.2 GeV(2) describes the differential distribution well. The high precision of the measurement and the large fit range lead to an error on the slope parameter B which is remarkably small compared to previous experiments. It allows a precise extrapolation over the non-visible cross-section (only 9%) to t = 0. With the luminosity from CMS, the elastic cross-section was determined to be (25.4 ± 1.1) mb, and using in addition the optical theorem, the total pp cross-section was derived to be (98.6 ± 2.2) mb. For model comparisons the t-distributions are tabulated including the large |t|-range of the previous measurement (TOTEM Collaboration (Antchev G. et al), EPL, 95 (2011) 41001).
The measured differential elastic cross section.
The measured differential elastic cross section in the high |T| region. where it originally appeared as a plot, but was not tabulated.
The fitted slope parameter for the elastic cross section fitted over 4 |T| ranges.
The c.m. angular distribution of π+p elastic scattering at 1.6 GeV/c shows a strong forward diffraction peak decreasing exponentially with a slopeA + = (6.9±0.5) GeV−2 comparable to thatA − = (7.2±0.5) GeV−2 observed in a previous experiment for π-p elastic scattering at the same incident momentum. The behaviour of the π+ and the π− angular distributions is quite different beyond the diffraction peak. The π+p total elastic cross-section is found to be Σ01 = (16.70±0.45) mb.
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Elastic scattering, single-pion and deuteron production have been investigated. The cross-section for elastic scattering is σelastic = (13.5±0.3) mb. The angular distribution has been fitted to dσ/d|t|=(dσ/d|t|)0 e −bt in the region of low values oft. The best fit givesb=(6.7±0.5) (GeV/c)−2 and (dσ/d|t|)0=(91±5) mb(GeV/c)−2. The cross-sections for ppπ0, pnπ+ reactions are respectively (2.6±0.3) mb and (9.7±0.4) mb. These reactions are dominated by the (3/2, 3/2) nucleonpion isobar production and by forward backward collimation of the nucleons. The production rates for the isobars ++1238 , +1238 , +1500 have been estimated, taking into account the experimental peripheral behaviour of the interaction. In the pnπ+ reaction they are (50±2)%; (10±3)%; (4±3)%. In the ppπ+ reaction the production of ++1238 is estimated to be (45±10)%. The dπ+ and dπ+π+π- reaction cross-sections are respectively (0.03±0.01) mb, and (0.04±0.01) mb.
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An extensive investigation of antiproton-proton interactions at 5.7 GeV/c without strange-particle production was carried out using a hydrogen bubble chamber. Cross-sections for different channels are given and discussed. The reliability of the analysis was checked using artificially generated events. The cross-sections for elastic scattering, for all processes involving annihilation, and for all other inelastic processes are respectively σel=(16.3±0.6)mb,σannlbil=(22.5±2.0)mb, σinel=(24.8±2.0)mb. TheN * 1:38 is present both in the single and multiple pion production channels. For the reaction MediaObjects/11539_2007_Article_BF02720569_f1.jpg a cross-section of (1.05±0.21) mb was obtained. Cross-sections forN * 1238 production in other channels are also given. Some indication of the presence ofI=1/2 isobars was found in the nucleon-pion and the nucleon-two-pion systems. The inelastic nonannihilation reactions were found to be strongly peripheral. The one-pion exchange model including either a form factor or corrections for absorption was applied to the reaction MediaObjects/11539_2007_Article_BF02720569_f2.jpg . Neither version of the model could correctly account for all features of the reaction. The average number of pions in the annihilation was found to be 7.3±0.6. The presence of an asymmetry in the angular distribution of the charged pions was confirmed at this energy; it is due mostly to high-energy pions. The production of ρ and ω mesons was observed in various annihilation channels. Rates of up to 80% for ρ production and up to 15% for ω production were obtained by fitting phase-space and Breit-Wigner curves to the effective-mass distributions of different channels.
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The differential cross-section for elastic scattering π−+p has been determined on the basis of 1 421 events observed in a propane bubble chamber. The angular distribution presents a backward bump (θ>90°) of (31.5±1.3)%. The amplitude at 0° obtained extrapolating the angular distribution by means of a least squares fit is compared with the value obtained from the dispersion relations and the optical theorem. New values of the pion proton cross-sections were taken into account for the dispersion relation integrals. Using the same best fit of the angular distribution a value for the interaction radius is obtained from considerations based on the diffraction scattering part.
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Inclusive e\pmp single and double differential cross sections for neutral and charged current deep inelastic scattering processes are measured with the H1 detector at HERA. The data were taken at a centre-of-mass energy of \surds = 319GeV with a total integrated luminosity of 333.7 pb-1 shared between two lepton beam charges and two longitudinal lepton polarisation modes. The differential cross sections are measured in the range of negative fourmomentum transfer squared, Q2, between 60 and 50 000GeV2, and Bjorken x between 0.0008 and 0.65. The measurements are combined with earlier published unpolarised H1 data to improve statistical precision and used to determine the structure function xF_3^gammaZ. A measurement of the neutral current parity violating structure function F_2^gammaZ is presented for the first time. The polarisation dependence of the charged current total cross section is also measured. The new measurements are well described by a next-to-leading order QCD fit based on all published H1 inclusive cross section data which are used to extract the parton distribution functions of the proton.
The Neutral Current Reduced Cross Section for E- P interactions with a beam polarisation of -25.8 % for Q^2 values of 120, 150, 200, 250 and 300 GeV^2.
The Neutral Current Reduced Cross Section for E- P interactions with a beam polarisation of -25.8 % for Q^2 values of 400, 500, 650, 800 and 1000 GeV^2.
The Neutral Current Reduced Cross Section for E- P interactions with a beam polarisation of -25.8 % for Q^2 values of 1200, 1500, 2000, 3000 and 5000 GeV^2.
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