The inclusive reactions h+p→ φ +X, (h= π ±, ,K ± ,p ± ), are studied for 0⪅ x F ⪅0.3 and p ⊥ ⩽ 1 GeV at 93 and and 63 GeV incident momentum. Differential cross sections d σ /d p ⊥ 2 and dσ /d x F are presented and are compared with predictions of the naive parton model.
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A study is presented of the reactions K + p→(K + ω )p at 8.25 and 16 GeV/ c and K − p→(K − ω )p at 10 and 16 GeV/ c and comparison is made with K + results at 10 GeV/ c and K − at 7.3 GeV/ c . The (K + ω) and (K − ω) mass spectra both present a strong enhancement very near threshold, while a second peak at ∼1.7 GeV is evident only with incident K − at the lower energies. The threshold peak has very weak energy dependence and is mostly due to the 1 + S state which is produced conserving s -channel helicity. It is suggested that this is another decay mode of the resonance Q 1 (1290) known to decay mainly into Kϱ. The ratio of the Q 1 coupling constants to the Kω and Kϱ decay channels, R ω = g K ω 2 / g K ϱ 2 is determined to be 0.21±0.04. The enhancement at 1.7 GeV is predominantly, but not exclusively, due to the 2 − state. While the K + and K − induced reactions give basically similar results, small differences are observed that can be qualitatively explained in the framework of the Deck model.
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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.
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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.
EARLIER RESULTS GIVEN IN 'A'.
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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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In this paper a comparison of the general features of the reactions K ± p→Q ± p (1) at incident momentum 8.25 GeV/ c is presented. The relevant data derive from events yielding four-constraint fits to the reactions K ± p→K ± π + π − p in exposures of the CERN 2m HBC to RF-separated K + and K − beams. The (K ππ ) effective mass distributions, production angular distributions in the Q region (1.2⩽ M (K ππ )⩽1.5 GeV) and corresponding decay angular distributions are exhibited, and background effects due to N ∗ and Δ production are systematically studied. In particular, it is found that the distributions d σ /d t ′ and d σ /d t for reactions (1) are adequately described by exponential functions over the interval 0.05–0.35 GeV 2 , and exhibit a cross-over effect for momentum transfer squared −0.1 GeV 2 . For both reactions a flattening of d σ /d t ′ for t ′ < 0.05 GeV 2 is observed. By studying the Chew-Low plots and the effects of the different cuts it was found that this flattening cannot be attributed to amplitudes with net s -channel helicity flip different from zero, at least at these energies.
ABOUT 7 PCT RELATIVE NORMALIZATION UNCERTAINTY FOR K+ AND K- SAMPLES.
FITS TO D(SIG)/DT AND D(SIG)/DTP FOR Q+ AND Q- PRODUCTION TO DETERMINE CROSS-OVER POSITIONS. DATA HAVE MASS CUTS TO SELECT K*0 AND REMOVE DEL++ AND DEL0. MIN IS THE MINIMUM VALUE OF -T FOR THE RELEVANT (K PI PI) MASS.
We present our final data on the production of the baryons p, Λ, Λ , Σ 0 , Σ 0 , Σ − , Σ + , Ω + , and of the baryon resonances Δ ++ (1232), Σ ∗± (1385), Σ ∗± (1385) in K + p interactions at 70 GeV/ c . Results are given on total and semi-inclusive cross sections, transverse momentum distributions and Feynman- x spectra. The data are compared with measurements at 32 GeV/ c and other energies. The predictions of the LUND fragmentation model for low- p T hadron-hadron collisions are examined and found to offer a reasonably successful description of the data.
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Inclusive and semi-inclusive cross sections and distributions of γ's and π0's inK+p interactions at 70 GeV/c are presented. The results are compared to other experiments and to the Lund model for low-pT hadron collisions.
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The reaction K + p → p + X is studied at a beam momentum of 16 GeV/ c using the events where a slow proton with momentum p lab < 1.2 GeV/ c is identified by its bubble density. The inclusive spectra presented and compared with those obtained in K + p interactions at 32 GeV/ c and K − p interactions at 14.3 GeV/ c . The prominent features associated with a triple-Regge formula are found to be consistent with the data. It is shown that the Δ ++ (1236) production strongly affects the shape of the inclusive spectra and the results of the triple-Regge fit. After removal of events associated with Δ ++ (1236) production, the data are consistent with the dominance of an ffR coupling.
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The production and decay of the quasi-two-body final states KΔ(1232) and K ∗ (892)N produced in K + d interactions below 1.5 GeV/ c have been studied in a bubble chamber experiment.
RESONANCE CROSS SECTIONS COMPUTED BY MULTIPLYING THE PRODUCTION PERCENTAGES GIVEN BY THE INTERFERENCE MODEL BY THE CHANNEL CROSS SECTIONS GIVEN IN G. GIACOMELLI ET AL., NP B37, 577 (1972).
DIFFERENTIAL CROSS SECTIONS FROM DEUTERIUM DATA, NORMALIZED TO THE EXPERIMENTAL INTEGRATED CROSS SECTIONS QUOTED IN T 2.
LEGENDRE COEFFICIENTS FROM DEUTERIUM DATA.
We present results on inclusive φ meson production in K + p interactions at 70 GeV/ c in the kaon fragmentation x >0.2 region. Comparison with other data on φ meson production in K ± and p induced reactions provides evidence that the strange valence-quark fragmentation or recombination processes play the dominant role in the K ± → φ transitions. Arguments are presented that the kaon valence strange s -quark carries a much higher momentum fraction than the u-quark. Evidence for the previously observed narrow φπ + state at mass ∼2.1 GeV is discussed.
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Inclusive and semi-inclusive production of Λ and\(\bar \Lambda\) inK+p interactions is studied at an incident momentum of 70 GeV/c. Cross sections and single particle distributions are presented and compared with data at lower energies. Scaling is observed between 32 and 70 GeV/c in the Feynmanx variable in the target and the beam fragmentation regions for Λ and\(\bar \Lambda\) inclusive production respectively. An increase of Λ (\(\bar \Lambda\)) production is observed in the beam (target) fragmentation regions, whereas the data at 70 and 32 GeV/c are reasonably close in the central region. The dependence of the Λ(\(\bar \Lambda\)) polarization as a function ofx is measured and found to be in general agreement with the results at 32 GeV/c. The (Λ\(\bar \Lambda\)) pair production cross section increases significantly from 32 to 70 GeV/c. The Λ and\(\bar \Lambda\) production associated with an identified proton is also studied.
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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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Energy, charge and strangeness flow inK+p interactions at 32 and 70 GeV/c, and π+p interactions at 32 GeV/c are studied in terms of the angular variable λ=|x|/pT. The data ondQ/dλ anddE/dλ show only a weak indication of scale breaking between 32 and 70 GeV/c. For inclusive “non-diffractive”, inclusive “diffractive” and exclusive “non-diffractive” jets, the fraction of charge in any angular region ΔΩ away from the central region is found to be proportional to the energy fraction in the same interval. The data ondQ/dE versus λ are compatible with some versions of dual-sheet models and agree also with the LUND Monte-Carlo model. The data are also compared with\(v(\bar v)p\) interactions in BEBC. In exclusive channels the average ratiodQ/dS=0.78±0.04 is consistent, in the framework of fragmentation models, with a larger probability for the fragmentation of the\(\bar s\)-valence quark than theu-valence quark in theK+-meson.
CHARGE FLOW IN NONDIFFRACTIVE PROTON-LIKE AND KAON-LIKE JETS.
CHARGE FLOW IN NONDIFFRACTIVE PROTON-LIKE AND KAON-LIKE JETS.
CHARGE FLOW IN NONDIFFRACTIVE PROTON-LIKE AND KAON-LIKE JETS.
The inclusive production of protons with laboratory momentum less than 1.2 GeV/ c is studied in the reacion K + p → pX at 32 GeV/ c . A comparison with the 16 GeV/ c data shows ahat the total cross section remains practically constant while the structure function shows a clear energy dependence. The data are compatible with a tripls-Regge expansion and with factorization. About 40% of the events include a K 0 in the final state. The analysis of the K 0 pX sample indicates a sizeable contribution of beam fragmentation and abundant K 890 ∗ and Δ ++ production.
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The inclusive production of resonances is systematically studied in K + p interactions at 32 GeV/ c . Total production cross sections are given for three baryon resonances, five vector and three 2 + tensor mesons. We also compare the central and fragmentation components of the total production cross sections with quark model predictions.
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Total and semi-inclusive cross sections, longitudinal and transverse momentum distributions and spin density matrix elements of theK*+(892) andK*0(892) produced in the inclusive reactionsK+p→K*+(892)+X andK+p→K*0(892)+X at 32 GeV/c are studied in detail. The inclusive spectra of theK*(892) and their decay products are compared with pion and neutral kaon production. TheK*+(892) andK*+(892) are dominantly produced by kaon fragmentation processes. The dependence of average transverse momentum <pT> vs.x for resonances has been investigated for the first time.
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Inclusive and semi-inclusive distributions of γ's and π 0 's in the reactions K + p → γ + X and K + p → π 0 + X at 32 GeV/ c are presented and discussed. When compared to the inclusive π − production, the π 0 cross section is found to be significantly higher in low | x | and p T regions. The data are compared with other experiments and quark fusion model predictions.
No description provided.
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ESTIMATED FROM GAMMA AND 2GAMMA SPECTRA.
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Data on Λ and\(\bar \Lambda \) polarization inK±p interactions at 32 GeV/c are presented. A comparison is made between the results of these two experiments as well as with the data at lower energies. The contribution of the different production mechanisms to the Λ(\(\bar \Lambda \)) polarization are discussed.
Data are presented on figures only. DATA NOT ENCODED.
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DD IVENTS SELECTED BY THE RAPIDITY GAP METHOD.
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Results are presented on inclusive production of resonant and non-resonant particle systems produced inK+p interactions at 32 GeV/c. We compareK*+(892),\(\bar \Sigma ^{ *- } \)(1385), Σ*±(1385), and ϱ0 inclusivex-spectra with the ones of non-resonantKs0π±,\(\bar \Lambda \pi ^ -\), Λπ± and π+π− pairs at the same effective mass. Resonance-particle pairsK*+π±, Σ*+π−, and\(\bar \Sigma ^{ *- } \pi ^ -\) are also studied together with non-resonant tripletsKs0π±, Λπ+π−,\(\bar \Lambda \pi ^ -\pi ^ -\). The invariantx-spectra of resonant particle pairs decrease less rapidly withx then the corresponding non-resonant pairs. Comparison with quark-recombination predictions indicates that the particles, resonances and multiparticle systems are probably created off a single valence quark or diquark instead of carrying all possible valence-quarks.
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THESE DATA ARE TABULATED IN THE RECORD OF THE PUBLISHED VERSION.
DIVIDE BY 20 TO GET MB/GEV**2.
FROM QUADRATIC EXPONENTIAL FITS TO D(SIG)/DT FOR -T = 0 TO 1.4 GEV**2. SYSTEMATIC ERRORS INCLUDED.
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The production properties ofKs0,\(\bar \Lambda\) andK+p interactions at 32 GeV/c are investigated using the final statistics of the experiment. We present total and semi-inclusive cross sections and aver-age multiplicities. Estimates are given of the diffractive dissociation contributions to total and differential cross sections. Thex-,pT−, and transverse mass dependence of inclusive and semi-inclusive distributions is discussed as well as properties of “prompt”Ks0's. The ratio of “prompt”K890+ (K8900) to “prompt”K0 cross sections is measured to be 1.03±0.12 (0.98±0.17). From a comparison of\(\bar \Lambda\) production inK±p interactions at 32 GeV/c, we estimate a strange sea-quark suppression of 0.26 ±0.02. The double differential cross sections ofKs0's is studied as a function of Feynman-x andpT2, and a Triple-Regge fit performed. The data are compared in detail to versions of the Lund-model for low-pT hadronic collisions.
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Inclusive production of Δ ++ (1232) with >| t p, Δ ++>|<0.6 (GeV/ c ) 2 is studied in 32 GeV/ c K + p interactions. A systematic comparison with the reaction K + p→pX for >| t p,p>| < 0.6 (GeV/ c ) 2 is made. The production properties of the Δ ++ (1232), of associated π + , π − and K 0 production and of the recoiling system X 0 are investigated in detail. The polarization of the Δ ++ and the energy dependence of the total K + π − cross sections, determined by a Chew-Low extrapolation, are presented and discussed.
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Inclusive cross sections and longitudinal momentum distributions are presented for γ rays produced in K − p and K + p interactions at 32 GeV/c in the 4.5 m Mirabelle hydrogen bubble chamber at the Serpukhov accelerator. The average longitudinal and transverse momentum of neutral pions and the average π 0 multiplicity ▪ 〈 n π 0〉 are estimated. It is found that 〈 n π 0〉 is an increasing function of the number of charged prongs.
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No description provided.
Results are presented on two-particle inclusive production inK+p interactions at 32 GeV/c. We study thex1,2=x1+x2 dependence of invariant structure functions of (ππ)-pairs and compare them to single particle inclusive distributions in the fragmentation regions. Distributions of particles observed at Feynmanx2 in association with various “trigger” particles or systems atx1 in the same hemisphere are dicussed in terms of the reduced variable\(\tilde x_2= x_2 /(1 - |x_1 |)\). We further present absolute production rates and production ratios of π+'s and π−'s associated with π±,Ks0, Λ,\(\bar \Lambda \),K*+ (890), (Ks0π+), and (π+ π−)-triggers, and compare them with qualitative predictions of the quark recombination model. Forwardbackward correlations between (Ks0π±), (Ks0,p), (Λ, π−),\((\bar \Lambda \pi ^ \pm)\), and (p, π−) pairs are also discussed.
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Final data on topological cross sections are presented. Inclusive single particle distributions for the reactionsK+p→ π±X at 32 GeV/c are discussed and compared with data at lower energies. Early scaling in the fragmentation regions is confirmed, while cross sections in th central region continue to rise with energy even faster than inpp interactions. Thex-andpT-dependence of the π+/π− ratio inK+p interactions is discussed and a comparison of reactionsK+p→ π±X andK−p→ π±X at 32 GeV/c is made in the context of constituent models. We also present transverse momentum distributions, show prominent seagull effects and study how they are influenced by resonance production.
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We present inclusive ¶ and K *0 (892) cross sections and Feynman x -spectra in K + p collisions at 250 GeV/ c . In the K + fragmentation region, x > 0.2, the ratio of ¶ to K *0 (892) is used to estimate the strangeness suppression factor λ , with the result γ =0.17 ± 0.02 (stat ± 0.01 (syst). We see no evidence for an energy dependence of λ in the CM energy range 7.8 ≤ s ≤21.7 GeV.
RESULTS AT 32 AND 70 GEV INCLUDED FOR COMPARISON.
RESULTS AT 32 AND 70 GEV INCLUDED FOR COMPARISON.
RESULTS AT 32 AND 70 GEV INCLUDED FOR COMPARISON.
Inclusive data are presented on ϱ 0 ,ϱ + and ω produced in k + p interactions at 250 GeV/ c , for ϱ + and ω for the first time in K + p experiment. In the forward CM hemisphere, the ϱ + , ϱ 0 and ω differential production rates are equal within errors, and remarkably similar to muon-inelastic scattering data on ϱ 0 and ω at 280 GeV/ c .
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We report on a study of inclusiveπ0 and η meson production inπ+p andK+p interactions at 250 GeV/c beam momentum. The Feynman-x spectrum ofπ0 is very similar in shape and normalization to that of negatively charged particles produced in the same experiment. The results are compared with data at other energies and with FRITIOF model predictions. This model overestimates the η cross section by a factor of 2.5. It reproduces theπ0 cross section correctly, but predicts a too hardπ0x distribution.
Data from Gamma Detectors only.
Data from Gamma Detectors only.
Data from RCBC only.
Results on the multiplicity structure of diffractively excited meson and proton systems in À+/K+p interactions at 250 GeV/c are presented for diffractive masses up to about 9 GeV. The energy dependence of the average charge multiplicity and the shape of the multiplicity distribution in terms of KNO-scaling and negative binomial distribution are investigated. The diffractive systems are compared toe+e−,lh and non-diffractivehh final states as suggested by modern approaches of the Pomeron-hadron collision. Systematic differences are found between diffractive meson and proton systems but also between diffraction and the reactions compared to.
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The inclusive production of neutral kaons is studied inK+p and π+p interactions at 250 GeV/c. Total and semi-inclusive cross sections and average kaon multiplicities are presented and compared with the data at lower energies. The longitudinal and transverse momentum distributions and their energy dependence are analyzed. The results are interpreted in the framework of recent parton models.
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Inclusive production of direct soft photons is studied inK+p andK+π interactions at 250 GeV/c. Total cross sections, Feynman-x and transverse momentum distributions of direct γ's are presented. The measured cross sections are several times larger than expected from QED inner bremsstrahlung, indicating the presence of an anomalous soft photon source. The model of Lichard and Van Hove, based on the “cold quark-gluon plasma” picture, agrees with the data.
Results extrapolated below p(gamma) = m(pi0)/2.
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Quasi-elastic scattering with central dipion cluster production is studied in π+p andK+p interactions at 250 GeV/c. The cross section of double pomeron exchange is obtained as σDPE(π+p →π+(π+π−)p)=24 ±5 µb and σDPE(K+p→K+(π+π−)p)=19 ±5 µb. The low energy pomeron-pomeron cross section is estimated for the first time.
Numerical values supplied by W. Kittel.
Numerical values supplied by W. Kittel.
Numerical values supplied by W. Kittel.
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We present data on the production of the baryons Λ,\(\bar \Lambda \),p and of the baryon resonances Σ*+ (1385) and Δ++ (1232) inK+p and π+p interactions at 250 GeV/c. Results are given on total and semi-inclusive cross sections, Feynman-x spectra, transverse momentum distributions and Λ polarization. The data are compared with measurements at lower energies, with deep inclastic lepton nucleon data and with predictions of quark-parton models. The models underestimate Λ production in the central c.m. region, a feature also seen in recent heavy-ion data. This failure can be cured in JETSET 6.3 by adjustment of the di-quark break-up probability.
No description provided.
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A detailed analysis of the inclusive production of the vector mesonsφ,K*+,0(892)\(\bar K*^0 (892),\rho ^{ + ,0} ,\omega \) and the tensor mesonsK2*0)(1430) andf2(1270) inK+p interactions at 250 GeV/c is presented The data are compared with results at lower energies and with various quark-parton models. The production ofρ0,K*0(892) and\(\bar K*^0 (892)\) increases at the same rate as a function ofs, is concentrated in the central region and is not reproduced by the models. Production of the tensor mesonsf2(1270) andK2*0(1340) is suppressed relative toρ0 andK*0(892) by a factor of about 3.
No description provided.
No description provided.
Topological cross section for events containing K*(892)0 production.
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Data on the reactions (K+/π+)p→(K+/π+)pπ+π- and (K+/π+)p→(K+/π+)p2π+2π-, obtained with the European Hybrid Spectrometer, are presented and compared with data at lower energies. The contribution of beam and target diffractive dissociation and double Pomeron exchange, and porperties of these reactions are discussed.
No description provided.
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Elastic scattering of 32.1 GeV/ c K + on protons has been measured in a bubble chamber experiment. Results are presented in the momentum transfer interval 0.06–1.40 GeV 2 and compared with data at different energies. An effective Regge trajectory is calculated using K + p elastic data from 10 to 175 GeV/ c .
No description provided.
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.
KP AND PP CROSSOVER POINTS AT -T = 0.19 +- 0.04 AND 0.11 +- 0.02 GEV**2 (AVERAGE VALUES) RESPECTIVELY.
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.
No description provided.
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Cross sections and charged multiplicity distributions for π+p,K+p andpp interactions at 250 GeV/c are presented and compared to each other as well as to earlier (for π+p andK+p lower energy) data. Consistently, the meson-proton (M+p) data have narrower multiplicity distributions and higher average multiplicity thanpp data. Up to our energy, generalized KNO functions describe the energy dependence of the shape of the multiplity distribution with one parameter forM+p and one forpp collisions. If interpreted in terms of negative binomials, the parameter 1/k tends to be slightly lower forM+p than forpp data. For both types of hadron-hadron collision, 1/k is larger than fore+e− andlp collisions.
No description provided.
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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.
No description provided.
No description provided.
ERRORS IN ELASTIC CROSS SECTIONS INCLUDE SYSTEMATIC ERRORS.
Data are presented on inclusive π0 production in the forward c.m. hemisphere (xF>0.025) in π+p,K+p andpp interactions at 250 GeV/c. These data are compared to results at other energies and interpreted in terms of quark-parton models.
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A detailed study ofJ/ψ hadronic production has been performed in a high statistics experiment (more than 1.5 106J/ψ observed in their dimuon decay mode). Data have been taken with incident π±,K±,p±, on hydrogen and platinum targets, at 150, 200 and 280 GeV/c. We find from the observed nuclear dependance of the cross sections, that about 18% of theJ/ψ are produced diffractively. Using known structure functions of the quarks in the nucleon and in the pion, we derive estimations for the gluon structure functions.
No description provided.
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No description provided.