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.

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).

Proton-proton elastic scattering has been measured by the TOTEM experiment at the CERN Large Hadron Collider at {\surd}s = 7 TeV in dedicated runs with the Roman Pot detectors placed as close as seven times the transverse beam size (sbeam) from the outgoing beams. After careful study of the accelerator optics and the detector alignment, |t|, the square of four-momentum transferred in the elastic scattering process, has been determined with an uncertainty of d t = 0.1GeV p|t|. In this letter, first results of the differential cross section are presented covering a |t|-range from 0.36 to 2.5GeV2. The differential cross-section in the range 0.36 < |t| < 0.47 GeV2 is described by an exponential with a slope parameter B = (23.6{\pm}0.5stat {\pm}0.4syst)GeV-2, followed by a significant diffractive minimum at |t| = (0.53{\pm}0.01stat{\pm}0.01syst)GeV2. For |t|-values larger than ~ 1.5GeV2, the cross-section exhibits a power law behaviour with an exponent of -7.8_\pm} 0.3stat{\pm}0.1syst. When compared to predictions based on the different available models, the data show a strong discriminative power despite the small t-range covered.

The differential cross sections for elastic π − p, K − p , p p and π + p, pp scattering at 39 and 44.5 GeV/ c , respectively, have been measured in the interval of momentum transfer squared 0.15 ≤ ovbt | ≤ 2 (GeV/ c ) 2 .

We report on a measurement of elastic differential cross sections for p±p, π±p, and K±p at 100 and 200 GeV/c in the range 0.03<|t|<0.10 (GeV/c)2. Our data display a simple exponential dependence which is consistent with other measurements in this t region or with extrapolations from higher t.

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.

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.

Elastic Σ − p and π − p cross section have been measured at 17.2 GeV/ c in the t interval −0.12, −0.38 (GeV/ c ) 2 . The Σ − p slope is b = 8.12 ± 0.35 (GeV/ c ) −2 .

The differential cross section of π+p elastic scattering has been measured in two high-statistics bubble-chamber exposures at laboratory beam momenta of 3.7 and 7.1 GeV/c. A new feature suggested by these data is a dip in dσdu at −u≃3 GeV2. This dip corresponds well to the third zero of J0(b−u′), where ℏcb=1 fm. The effective u-channel Regge trajectory computed for these two energies has a slope of 0.22 ± 0.26.

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.

Data on 6.2 GeV/ c π − p and K − p elastic scattering cross sections are presented in the range 0.3 < − t < 10.7 (GeV/ c ) 2 .

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.

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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Angular distributions of π + and K + p elastic scattering have been measured for an incident beam momentum of 10.0 GeV/ c . For π + p elastic scattering almost the complete angular distribution was measured. The angular distribution of proton-proton elastic scattering was measured for an incident momentum of 9.0 GeV/ c in the interval of the four-momentum transfer squared from 0.7 (GeV/ c ) 2 to 5.0 (GeV/ v ) 2 . For π + p elastic scattering the structures at − t = 2.8 (GeV/ c ) 2 and − t = 4.8 (GeV/ c ) 2 are less pronounced than at lower momenta. The cross section for scattering at 90° in the c.m. system is of the order of 1 nb/GeV/ c ) 2 . For K + p elastic scattering is a break in the angular distribution around − t = 3 (GeV/ c ) 2 . The differential cross sections for proton-proton elastic scattering decrease smoothly with increasing momentum transfers.

A comparison of K±p and p±p elastic scattering is made for incident energy 50 to 175 GeV. Average values of 0.19±0.04 and 0.11±0.02 GeV2 were found for the invariant-momentum-transfer values of the Kp and pp crossover points, respectively.

The Fermilab hybrid 30-in. bubble-chamber spectrometer was exposed to a tagged 147-GeV/c positive beam containing π+, K+, and p. A sample of 3003 K+p, 19410 pp, and 20745 π+p interactions is used to derive σn, 〈n〉, f2cc, and 〈nc〉D for each beam particle. These values are compared to values obtained at other, mostly lower, beam momenta. The overall dependence of 〈n〉 on Ea, the available center-of-mass energy, for these three reactions as well as π−p and pp interactions has been determined.

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Elastic diffraction scattering of π − , K − and p on protons has been measured at 25 and 40 GeV/c at the Serpukhov Proton Accelerator. Differential elastic cross sections and diffraction slopes are presented in the momentum-transfer interval 0.07–0.80 (GeV/ c ) 2 and compared with existing data at lower energies.

K − p elastic scattering at 10 GeV/ c is studied on ∼3600 bubble chamber events. The elastic cross section is found to be σ el = (3.20 ± 0.14)mb and the ratio σ el σ tot = (0.142 ± 0.006) , that is below the upper limit of 0.185 suggested in a model by Van Hove. The value of the forward differential cross section is consistent with zero real part to the scattering amplitude. The slope of d σ d t is similar to that for π ± and greater than that of K + , with no evidence for shrinkage of the diffraction peak. No events of backward scattering were observed. The Regge-pole model of Phillips and Rarita gives a good fit to the data.

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Bubble chamber film of 10 GeV/ c K − p interactions was scanned automatically by an H.P.D. to look for small angle scatters in the | t |-range from 0.008 to 0.1 GeV 2 . Combining the 1800 events so obtained with 22 000 elastic events obtained from normal scanning (| t | > 0.06 GeV 2 ), the real part of the elastic scattering amplitude was found to be (+25 ± 10)% of the imaginary part. Evidence is found for a change in slope in the differential cross-section distribution, from 9.8 ± 0.6 GeV −2 in the | t |-range below 0.1 GeV 2 to 7.1 ± 0.2 GeV −2 in the range 0.12 < | t | ⩽ 0.4 GeV 2 .

Results are presented on elastic scattering of 10.1 GeV/ c K − mesons on protons, based on a sample of 16 261 kinematically-fitted bubble-chamber events. The differential cross section is given over the | t |- range of 0.06 to 2.5 GeV 2 and is fitted with the expressions a e bt , A e Bt + Ct 2 and ( P e Qt + Re St ) over various intervals of t . The results are compared with those of other experiments at nearby energies. Upper limits of | α | < 0.28 and σ B < 0.4 μ b (both at a 90% confidence level) are given for the ratio of real to imaginary part of the forward-scattering amplitude and the backward-elastic-scattering cross section, respectively.

We have measured π+p, π−p, and pp elastic scattering at an incident-beam momentum of 200 GeV/c in the region of −t, four-momentum transfer squared, from 0.021 to 0.665 (GeV/c)2. The data allow an investigation of the t dependence of the logarithmic forward slope parameter b≡(ddt)(lndσdt). In addition to standard parametrization, we use functional forms suggested by the additive quark model to fit the measured dσdt distributions. Within the context of this model we estimate the size of the clothed quark in the pion and proton. Limits on the elastic-scattering amplitude derived from unitarity bounds are checked, and no violations are observed.

The differential cross sections for the elastic scattering of π+, π−, K+, K−, p, and p¯ on protons have been measured in the t interval -0.04 to -0.75 GeV2 at five momenta: 50, 70, 100, 140, and 175 GeV/c. The t distributions have been parametrized by the quadratic exponential form dσdt=Aexp(B|t|+C|t|2) and the energy dependence has been described in terms of a single-pole Regge model. The pp and K+p diffraction peaks are found to shrink with α′∼0.20 and ∼0.15 GeV−2, respectively. The p¯p diffraction peak is antishrinking while π±p and K−p are relatively energy-independent. Total elastic cross sections are calculated by integrating the differential cross sections. The rapid decline in σel observed at low energies has stopped and all six reactions approach relatively constant values of σel. The ratio of σelσtot approaches a constant value for all six reactions by 100 GeV, consistent with the predictions of the geometric-scaling hypothesis. This ratio is ∼0.18 for pp and p¯p, and ∼0.12-0.14 for π±p and K±p. A crossover is observed between K+p and K−p scattering at |t|∼0.19 GeV2, and between pp and p¯p at |t|∼0.11 GeV2. Inversion of the cross sections into impact-parameter space shows that protons are quite transparent to mesons even in head-on collisions. The probability for a meson to pass through a proton head-on without interaction inelastically is ∼20% while it is only ∼6% for an incident proton or antiproton. Finally, the results are compared with various quark-model predictions.