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 $B = 19.73 \pm 0.14 \; ({\mbox{stat.}}) \pm 0.26 \; ({\mbox{syst.}}) \; \mbox{GeV}^{-2}$.

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 $B = 19.74 \pm 0.05 \; ({{stat.}}) \pm 0.23 \; ({{syst.}}) \; {GeV}^{-2}$.

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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).

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.

In a 35 000-picture exposure of the 30-in. hydrogen bubble chamber to a 300-GeV/c proton beam at the Fermi National Accelerator Laboratory, 10054 interactions have been observed. The measured total cross section is $40.68 \pm 0.55$ mb, the elastic cross section is $7.89 \pm 0.52$ mb, and the average charged-particle multiplicity for inelastic events is $8.S0 \pm 0.12$.

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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.

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Differential cross sections for elastic π−p scattering were measured at eight energies for positive pions and seven energies for negative pions. Energies ranged from 310 to 650 MeV. These measurements were made at the 3-GeV proton synchrotron at Saclay, France. A beam of pions from an internal BeO target was directed into a liquid-hydrogen target. Fifty-one scintillation counters and a matrix-coincidence system were used to measure simultaneously elastic events at 21 angles and charged inelastic events at 78 π−p angle pairs. Events were detected by coincidence of pulses indicating the presence of an incident pion, scattered pion, and recoil proton, and the results were stored in the memory of a pulse-height analyzer. Various corrections were applied to the data and a least-squares fit was made to the results at each energy. The form of the fitting function was a power series in the cosine of the center-of-mass angle of the scattered pion. Integration under the fitted curves gave values for the total elastic cross sections (without charge exchange). The importance of certain angular-momentum states is discussed. The π−−p data are consistent with a D13 resonant state at 600 MeV, but do not necessarily require such a resonant state.

Differential cross sections for the elastic scattering of positive pi mesons by protons were measured at the Berkeley Bevatron at pion laboratory kinetic energies between 500 and 1600 MeV. Fifty scintillation counters and a matrix coincidence system were used to identify incoming pions and detect the recoil proton and pion companions. Results were fitted with a power series in the cosine of the center-of-mass scattering angle, and total elastic cross sections were obtained by integrating under the fitted curves. The coefficients of the cosine series are displayed, plotted versus the laboratory kinetic energy of the pion. The most striking features of these curves are the large positive value of the coefficient of cos6θ*, and the large negative value of the coefficient of cos4θ*, both of which maximize in the vicinity of the 1350-MeV peak in the total cross section. These results indicate that the most predominant state contributing to the scattering at the 1350-MeV peak has total angular momentum J=72, since the coefficients for terms above cos6θ* are negligible at this energy. One possible explanation is that the 1350-MeV peak is the result of an F72 resonance lying on the same Regge-pole trajectory as the (32, 32) resonance near 195 MeV.

Differential cross sections for the elastic scattering of negative pi mesons on protons (π−−p→π−−p) were measured at the Berkeley Bevatron at five laboratory kinetic energies of the pion between 500 and 1000 MeV. The results were least-squares fitted with a power series in the cosine of the center-of-mass scattering angle, and total elastic cross sections for π−−p→π−−p were obtained by integrating under the fitted curves. The coefficients of the cosine series are shown plotted versus the incident pion laboratory kinetic energy. These curves display as a striking feature a large value of the coefficient of cos5θ* peaking in the vicinity of the 900-MeV resonance. This implies that a superposition of F52 and D52 partial waves is prominent in the scattering at this energy, since the coefficients for terms above cos5θ* are negligible. One possible explanation is that the F52 enhancement comes from an elastic resonance in the isotopic spin T=12 state, consistent with Regge-pole formalism, and the D52 partial-wave state may be enhanced by inelastic processes. At 600 MeV the values of the coefficients do not seem to demand the prominence of any single partial-wave state, although the results are compatible with an enhancement in the J=32 amplitude. A table listing quantum numbers plausibly associated with the various peaks and "shoulders" seen in the π±−p total cross-section curves is presented.

Cross sections and charged multiplicity distributions forK+p interactions at 70 GeV/c are presented and compared withK+p data at other energies. Comparisons are also made with available π+p,pp, andK−p data.

A detailed analysis is presented of the reactions pp→pp,pp→ppπ0 and pp→pπ+n. The production cross sections are found to be 11.47 ± 0.33 mb, 2.54 ± 0.16 mb, and 5.73 ± 0.35 mb, respectively. The t dependence of elastic scattering can be described by the form e7.9t over the range 0.05<−t<0.50 GeV2. The single-particle distributions for the single-pion production processes are presented. Further detailed analyses are presented which demonstrate that pion-exchange phenomenology, both elementary and Reggeized, can account for the gross features of the peripheral pp→pπ+n data for M(pπ+)<2.4 GeV. Isospin-12 isobars are produced by some other processes in the channel pp→pN*+, especially when the invariant mass of the pion with the unrelated proton is large. We discuss the properties of these isobars.

This report is based on about 10 500 pp collision events produced in the 81-cm Saclay hydrogen bubble chamber at CERN. Cross-section values for the different identified final states and resonances are given. The isobars N*1238, N*1420, N*1518, N*1688, N*1920, and N*2360 were identified and their production cross-section values were found via a best-fit analysis of different invariant-mass histograms. About 70% of the isobars are connected with the quasi-two-body reactions pp→N*N and pp→N*N*. The reaction pp→nN*1238(pπ+) with a cross section of 3.25±0.16 mb was analyzed in terms of a peripheral absorption model, which was found to be in good agreement with the data. Various decay modes of the N*1518 and N*1688 isobars were observed and their branching ratios determined. The branching ratio of nπ+ to pπ+π− was found to be 0.77±0.45 for N*1518 and 0.67±0.40 for N*1688. The branching ratio of N*1238(pπ+)π− to pπ+π− of N*1688 was estimated to be 0.74±0.14. Pion production turned out to be mainly due to decay of isobars. Production of meson resonances turned out to be less important; the reaction pp→ppω0→ppπ+π−π0 was identified with a cross-section value of 0.11±0.02 mb. Finally, the production of neutral strange particles with a cross section of 0.45±0.04 mb is descussed. Strong formation of Y*1385 is observed.

We report results from a measurement of antiproton-proton and proton-proton small-angle elastic scattering at √ s = 24.3 GeV in the range 0.001 ⩽ | t | ⩽ 0.06 (GeV/ c ) 2 . The measurement was performed at the CERN p p Collider by using silicon detectors to observe protons recoiling from a hydrogen cluster-jet target intercepting the stored p and p beams. Fits to the measured differential cross sections yield the ratio of the real to the imaginary part of the forward nuclear scattering amplitude ρ and the nuclear slope parameter b for both p p and pp. We find that the difference Δρ = ρ ( p p ) − ρ( pp ) = 0.031 ± 0.010 agrees with conventional fits and disagrees with the “odderon” fit designed to accommodate the recent UA4 measurement of ρ( p p) at 546 GeV.

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In an exposure of the 30-in. hydrogen bubble chamber to a 303−GeVc proton beam, 2245 interactions have been observed. The measured total cross section is 39.0±1.0 mb and the average charged particle multiplicity 〈nch〉=8.86±0.16.

Small angle elastic scattering events have been observed at the CERN Intersecting Storage Rings. Directions of both particles as well as the collision vertex are reconstructed with the help of four sets of spark chambers, two for each of the two arms. The elastic nature of the events is demonstrated by a collinearity requirement. We find values for the (diffraction) slope parameter in disagreement with the simple linear extrapolation of lower energy (Surpukov) data.

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.

We have measured the difference between the pp total cross-sections for parallel and anti-parallel longitudinal spin states at beam momenta of 3 and 6 GeV/ c . These results, combined with our previous measurements, at lower momenta, are useful in clarifying a striking structure appearing at around 1.5 GeV/ c . We have also measured for the first time, the spin-spin correlation parameter C LL ( t ) in pp elastic scattering at 6 GeV/ c . We observe evidence for an exchange with A 1 -like quantum-numbers.

Interactions of 2.08−BeVc positive pions with protons have been studied using the 20-in. hydrogen bubble chamber and the alternating gradient synchrotron at Brookhaven National Laboratory. Using 3000 elastic and 8000 inelastic events, the partial cross sections for elastic scattering and for meson production have been measured. The ρ+, ρ0, ω0, and η0 resonances are produced strongly and emerge predominantly in the forward direction in the center-of-mass system, suggesting a peripheral mechanism for their production. The possibility of explaining these reactions by specific particle-exchange models is investigated. More than 75% of the ρ0, ω0, and η0 are produced with the N33* (1238) isobar. The N* (1688) is produced in about one-third of the π+π+N final states. Cross sections for production of ρ+p, π+pω, N33*ω, π+pη, N33*η, π+pρ0, N33*ρ0, N15*π+, and N33*π0, are given. A1, B, φ, and X mesons are not observed.

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Differential cross sections for the elastic scattering of K + mesons on protons have been measured at 12 lab momenta between 130 and 755 MeV/ c using a hydrogen filled bubble chamber. The results are consistent with a repulsive S-wave nuclear force. A phase-shift analysis yielded the following values of the low-energy parameters: a S 1 2 =(0.309±0.002) fm , r S 1 2 =(0.032±0.02) fm a P 1 2 =(0.021±0.002) fm , a P 3 2 =(0.013±0.001) fm 3

We have measured the differential cross section for small angle p−p scattering from 25 to 200 GeV incident energy and in the momentum transfer range 0.015<|t|<0.080 (GeVc)2. We find that the slope of the forward diffraction peak, b(s), increases with energy and can be fitted by the form b(s)=b0+2α′ lns, where b0=8.3±1.3 and α′=0.28±0.13 (GeVc)−2. Such dependence is compatible with the data existing both at higher and lower energies. We have also obtained the energy dependence of the p−p total cross section in the energy range from 48 to 196 GeV. Within our errors which are ± 1.1 mb the total cross section remains constant.

Proton-proton and proton-deuteron elastic scattering has been measured for incident laboratory energy from 50 to 400 GeV; minimum |t| values were, for p−p, 0.0005 (GeV/c)2, and for p−d, 0.0008 (GeV/c)2. From the differential cross sections we have determined the ratios of the real to imaginary parts of the forward scattering amplitude, ρpp and ρpd, for p−p and p−d scattering. Using a Glauber approach and a sum-of-exponentials form factor we obtain ρpn for p−n scattering.

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 reactions π − p → p π − and π − p → p ϱ − ( ϱ − → π − π 0 ) at 10 GeV/ c with the proton in the forward direction in the c.m.s. are discussed on the basis of 953 elastic scattering events and 2240 events of the reaction π − p → p π − π 0 . The total backward cross sections are 0.52±0.10 and 1.52±0.28 μ b, respectively. In both cases the production mechanism is compatible with the dominance of the baryonic Δ δ Regge trajectory exchange. The ϱ − decay angular distributions are studied in the u -channel helicity frame and the spin density matrix elements are presented as functions of u .

Final results of our measurements of elastic proton-proton scattering at the CERN Intersecting Storage Rings (ISR) for c.m. energies √ s from 23 to 63 GeV and momentum transfers | t | from 0.8 to 10 GeV 2 are presented. Absolute differential cross sections have been obtained using the split-field magnet detector facility (SFM) at the five standard energies for integrated luminosities ranging from 0.3 to 4.9 (pb) −1 . The rising total cross section is found to define a scale for diffractive phenomena near the forward peak, including the position of the diffraction minimum near t = −1.4 GeV 2 . The cross section at the minimum is strongly energy dependent, approximately as the ratio of the real to imaginary part of the scattering amplitude in the forward direction. The phase of the scattering amplitude is found to change sign near the minimum. The component of diffraction scattering beyond the second maximum has a much weaker t -dependence than expected in simple eikonal or constituent pictures connecting this region to the forward peak. A further break in slope is observed near t = −6 GeV 2 . There is no evidence for another minimum for t values up to 10 GeV 2 .

Analyses have been made for 871 four-prong events and 463 two-prong events corresponding to multiple pion production, resulting from p−p interactions at 2 Bev in the BNL 20-in. hydrogen bubble chamber. Cross sections have been obtained for all the observable double and triple pion production processes; the branching ratios predicted by the extended isobar model are shown to be in fair agreement with the data, but there are significant differences. The c.m. momentum distributions are also in fair agreement with the predictions of the model, although there are ambiguities in the interpretation. The pion-nucleon Q values give clear evidence for the importance of the (32, 32) resonant state in multiple pion production, but consideration of this state alone does not provide an explanation of the features of double pion production. Some contribution from another state, possibly the I=12 nucleon isobar, is necessary. In double production, the c.m. angular distributions of the nucleons show backward-forward peaking suggestive of a one-pion exchange process. The angular distributions of the nucleons from triple production are almost isotropic.

3600 two-pronged events, obtained in p−p interactions at 2 Bev in the BNL 20-in. hydrogen bubble chamber, have been analyzed. Cross sections have been measured for elastic scattering, for the two modes of single-pion production, p+p→p+n+π+, p+p→p+p+π0, and for strange-particle production. The branching ratio for the two one-pion production reactions is σ(pnπ+)σ(ppπ0)=4.17±0.25. Momentum distributions and Q values indicate that single-pion production proceeds almost entirely through the (32, 32) resonant state. The data have been considered in terms of the extended isobar model and also a one-pion exchange model for production. The branching ratio and momentum distributions can be explained by including a small effect from the I=12 resonant state in addition to the dominant I=32 resonance. The c.m. angular distribution of the nucleons in single-pion production shows very marked backward-forward peaking indicating a one-pion exchange mechanism. Absolute differential cross sections as a function of laboratory kinetic energy have been calculated from Selleri's equation for the pnπ+ reaction. There is good agreement with the data for low four-momentum transfers [q2<0.15(Bev/c)2], but for higher momentum transfers the theoretical cross sections are larger than the experimental cross sections.

New experimental results are presented on proton-proton elastic scattering in the range of momentum transfer 4 GeV 2 < − t < 10 GeV 2 at the centre-of-mass energy of √ s = 53 GeV. The data have been obtained using the Split-Field Magnet detector at the CERN Intersecting Storage Rings. We observe another change of slope of the differential cross section near − t =6.5 GeV 2 .

New experimental results are presented on proton-proton elastic scattering in the range of momentum transfer 0.8GeV 2 < − t < 9 GeV 2 at a centre-of-mass energy of √ s = 53 GeV. The data are obtained sing the Split-Field- Magnet Detector at the CERN Intersecting Storage Rings. The cross section has well-known minimum at − t = (1.34±0.02) GeV 2 but no further minimum or change of slope is observed between 2 and 6.5 GeV 2 .

New experimental results are presented on proton-proton elastic scattering at centre-of-mass energies s =23 GeV and s =62 GeV . The data are obtained using the Split Field Magnet detector at the CERN Intersecting Storage Rings. The absolute differential cross-sections show an energy-dependent behaviour. The position of the diffraction minimum changes from t =(−1.44±0.02)GeV 2 at 23 GeV to (−1.26±0.03)GeV 2 at 62 GeV. The cross-section at the second maximum is increasing with s . The connection of these observations with the hypothesis of “geometrical scaling” is discussed.

Report on the investigation of interactions in π−p collisions at a pion momentum of 1.59 GeV/c, by means of the 50 cm Saclay liquid hydrogen bubble chamber, operating in a magnetic field of 17.5 kG. The results obtained concern essentially the elastic scattering and the inelastic scattering accompanied by the production of either a single pion in π−p→ pπ−π0 and nπ−π+ interactions, or by more than one pion in four-prong events. The observed angular distribution for the elastic scattering in the diffraction region, can be approximated by an exponential law. From the extrapolated value, thus obtained for the forward scattering, one gets σel= (9.65±0.30) mb. Effective mass spectra of π−π0 and π−π+ dipions are given in case of one-pion production. Each of them exhibits the corresponding ρ− or ρ0 resonances in the region of ∼ 29μ2 (μ = mass of the charged pion). The ρ peaks are particularly conspicuous for low momentum transfer (Δ2) events. The ρ0 distribution presents a secondary peak at ∼31μ2 due probably to the ω0 → π−π+ process. The branching ratio (ω0→ π+π−)/(ω0→ π+π− 0) is estimated to be ∼ 7%. The results are fairly well interpreted in the frame of the peripheral interaction according to the one-pion exchange (OPE) model, Up to values of Δ2/μ2∼10. In particular, the ratio ρ−/ρ0 is of the order of 0.5, as predicted by this model. Furthermore, the distribution of the Treiman-Yang angle is compatible with an isotropic one inside the ρ. peak. The distribution of\(\sigma _{\pi ^ + \pi ^ - } \), as calculated by the use of the Chew-Low formula assumed to be valid in the physical region of Δ2, gives a maximum which is appreciably lower than the value of\(12\pi \tilde \lambda ^2 = 120 mb\) expected for a resonant elastic ππ scattering in a J=1 state at the peak of the ρ. However, a correcting factor to the Chew-Low formula, introduced by Selleri, gives a fairly good agreement with the expected value. Another distribution, namely the Δ2 distribution, at least for Δ2 < 10 μ2, agrees quite well with the peripheral character of the interaction involving the ρ resonance. π− angular distributions in the rest frame of the ρ exhibit a different behaviour for the ρ− and for the ρ0. Whereas the first one is symmetrical, as was already reported in a previous paper, the latter shows a clear forward π− asymmetry. The main features of the four-prong results are: 1) the occurrence of the 3/2 3/2 (ρπ+) isobar in π−p → pπ+π−π− events and 2) the possible production of the ω0→ π+π−π0 resonance in π−p→ pπ−π+π−π0 events. No ρ’s were observed in four-prong events.

The reaction π−+p→π−+p has been studied in the 15-in. bubble chamber at the Princeton-Pennsylvania Accelerator. The elastic scattering cross section was determined to be 8.5 ± 0.2 mb. The forward peak fits to an exponential in t with a slope of 8.1 ± 0.2 (GeV/c)−2. The forward differential cross section dσdΩ(0)=17.9±0.7 mb/sr. A fit of the center-of-mass angular distribution to Legendre polynomials needed terms up to the 12th order, corresponding to the highest nonzero partial wave of L=6.

Proton-proton elastic scattering has been measured in the region 4.9<|t|<12.1 GeV2 at a beam momentum of 201 GeV/c. If the form exp(At) is fitted to the data, the exponent A gradually changes from 1.5 to 0.9 GeV−2 over our t range. The data are consistent with the form exp(−6.6p⊥). A comparison with intersecting storage ring results shows that in this kinematical region the slopes are about the same, but dσdt at fixed t is still dropping with energy.

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.

The absolute luminosity of the CERN Intersecting Storage Rings has been determined by the Van der Meer method. Combining the measurement with small angle proton-proton elastic events, we find σ elastic = (6.8±0.6)mb.

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.

The single-pion production reactions $pp\to d\pi^+$, $pp\to np\pi^+$ and $pp\to pp\pi^0$ were measured at a beam momentum of 0.95 GeV/c ($T_p \approx$ 400 MeV) using the short version of the COSY-TOF spectrometer. The implementation of a central calorimeter provided particle identification, energy determination and neutron detection in addition to time-of-flight and angle measurements. Thus all pion production channels were recorded with 1-4 overconstraints. The total and differential cross sections obtained are compared to previous data and theoretical calculations. Main emphasis is put on the discussion of the $pp\pi^0$ channel, where we obtain angular distributions different from previous experimental results, however, partly in good agreement with recent phenomenological and theoretical predictions. In particular we observe very large anisotropies for the $\pi^0$ angular distributions in the kinematical region of small relative proton momenta revealing there a dominance of proton spinflip transitions associated with $\pi^0$ $s$- and $d$-partial waves and emphasizing the important role of $\pi^0$ d-waves.

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.

Total and differential cross sections are presented for the reactions K − p → K − p and K − p → K o n at 13 points in the c.m. energy range 1915–2168 MeV. An energy-dependent partial-wave analysis is carried out on these data together with the polarisation measurements of Daum et al. [1] and the total cross section measurements [2] within this energy range. The well known Σ(1915), Σ(2030) and Λ(2100) are observed and their resonance parameters measured. Structure is also found in the D 05 and F 07 waves. An SU(3) analysis of the 5 2 + octet, 7 2 + decuplet and 7 2 − singlet gives generally good agreement between theory and experiment except that the elasticity of the Σ(1915) is experimentally rather larger than predicted.

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.

A simultaneous partial-wave analysis of the three final states K + p, K ∗ (892)N and KΔ(1236) is attempted using inelastic data with large statistics at 1.21, 1.29, 1.38 and 1.69 GeV/ c as well as existing data on the elastic reaction. The constraint of unitarity, which is almost saturated by these reactions, allows one to determine the size and relative phases of the dominant partial waves and to give some limits on the others. Their variation with energy is discussed, as well as the consistency of the different sets of elastic phase shifts with the inelastic data. We also compare the predictions of the duality hypothesis with the data.

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.

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 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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