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

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

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.

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.

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 .

Results are presented onK+p elastic scattering and on the reactionK+p→K+pπ+π− at 70 GeV/c. For the

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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.

Results are presented on π + p and K + p elastic scattering at 250 GeV/ c , the highest momentum so far reached for positive meson beams. The experiment (NA22) was performed with the european hybrid spectrometer. The π + p elastic cross section stays constant with energy while the K + p cross section increases.

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).

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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.

The coherent elastic reaction K + d → K + d and the break-up reaction K + d → K + pn are studied in a K + d experiment at 4.6 GeV/ c which the CERN 2 m bubble chamber. Partial and differential cross sections are given and the slopes of the differential cross sections are determined. The results for the reaction K + d → K + p(n s ), where n s denotes the spectator neutron, are compared with those of the reaction K + p → K + p on free protons. Combining our data with existing data on the reactions K + d → K 0 pp and K + p → K + p, parameters of the elastic K + -nucleon scattering at 4.6 GeV/ c are determined in the framework of the Glauber model. The D-wave of the deuteron and spin-flip effects are taken into account.

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.

The total cross section difference Δα L (pp) for proton-proton scattering with beam and target polarized longitudinally parallel and antiparallel, respectively, has been measured using the polarized proton beam from SATURNE II and a frozen spin polarized proton target. The beam polarization was reversed from pulse to pulse, and at each energy Δα L was measured for both signs of target polarization. The data below 800 MeV confirm the previously observed structures. The cross section difference is found to change by 8.0 ± 0.5 mb between 520 MeV and 760 MeV. At the higher energies the results show no indication for similar structures or for a change of the sign of Δα L .

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

Results on the elastic K − π − scattering have been obtained from a study of the K − π − system in 15 000 events of the type K − p→K − π − p π + at a K − beam momentum of 4.25 GeV/ c . The on-mass-shell values of the spherical harmonic moments of the K − π − scattering angular distribution and the K − π − elastic cross section have been obtained by extrapolation to the pion pole. From these values we determined the s- and p-wave phase shifts δ 0 3 and δ 1 3 as a function of the effective mass of the K − π − system between threshold and 1.25 GeV/ c 2 . The value of | δ 0 3 | is smaller than 17° for all mass values and the existence of a p-wave cannot be neglected. At m K − π − = 1.18 GeV/ c 2 there are two solutions for the phase shifts. On the average, the cross section of the K − π − elastic scattering over the region of the effective mass considered amounts to approximately 2.5 mb.

Measurements of the total cross section have been performed at the ISR with c.m. energies between 23.5 GeV and 62.5 GeV. Two independent experimental methods have been applied, a measurement of total interaction rate and of small angle elastic scattering. Both experiments give consistent results showing that the total cross section increases by (11.8±1.5) % over the ISR energy range. This experiment has also measured the slope of the forward diffraction peak in elastic scattering at small momentum transfer. The elastic cross section shows the same relative rise as the total cross section, and the ratio λ of elastic to total cross section approaches a constant value of λ =0.178±0.003.

From an experiment done with the CERN Omega spectrometer, triggered by a fast forward proton device, we present results on the differential cross section d σ d u for π − p backward elastic scattering. The d σ d u distribution agrees with an A e Bu law. The compilation of existing results shows a discrepancy between results but the ( d σ d u ) u=0 data fit perfectly an s 2 α 0 −2 dependence, as predicted by a single Δδ Regge trajectory exchange. A search for the reaction π − p → d p , with a fast forward deuteron, which can be produced by a double-baryon exchange mechanism, gives cross-section upper limits of ∼1% of the backward elastic cross section.

Elastic scattering of 14.3 GeV/ c K − with protons has been analyzed in the | t | region between 0.005 and 0.550 (GeV/ c ) 2 . The ratio α between the real and the imaginary part of the elastic forward scattering amplitude is found to be α =+0.056 ± 0.052. The slope parameters A and B in the expression d σ /d| t | ∞ exp( At + Bt 2 ) are A = 8.47 ± 0.20 (GeV/ c ) −2 and B = 1.82 ± 0.52 (GeV/ c ) −4 .

The results presented in this paper were obtained from a 105 000 frame exposure of the FNAL Hybrid Proportional Wire Chamber-30 inch Bubble Chamber System, in a tagged beam of 147 GeV/ c negative particles. Elastic, total and topological cross sections were obtained for both π − p and K − p interactions. Comparisons with other data, taken with various beam particles over large momentum intervals, show good agreement with KNO scaling, and similarity in the scaling behavior of σ n for the different beam particles.

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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.

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.