The differential cross sections for K − p and p p elastic scattering have been measured over the range of four-momentum transfer squared 0.18<− t <3.3 (GeV/ c ) 2 . The K − p data decrease smoothly as a function of − t , whereas, the p p data shows a break at − t = 0.6 (GeV/ c ) 2 followed by a fast drop to − t ≅ 1.6 (GeV/ c ) 2 where the differential cross section levels off and stays constant out to − t = 3 (GeV/ c ) 2 .
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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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We present results on .~--p seattering at kinetic energies in the laboratory of 516, 616, 710, 887 and 1085MeV. The data were obtained by exposing a liquid hydrogen bubble chamber to a pion beam from the Saelay proton synchrotron Saturne. The chamber had a diameter of 20 cm and a depth of 10 cm. There was no magnetic field. Two cameras, 15 em apart, were situated at 84 cm from the center- of the chamber. A triple quadrnpole lens looking at an internal target, and a bending magnet, defined the beam, whose momentum spread was less than 2%. The value of the momentum was measured by the wire-orbit method and by time of flight technique, and the computed momentum spread was checked by means of a Cerenkov counter. The pictures were scanned twice for all pion interactions. 0nly those events with primaries at most 3 ~ off from the mean beam direction and with vertices inside a well defined fiducial volume, were considered. All not obviously inelastic events were measured and computed by means of a Mercury Ferranti computer. The elasticity of the event was established by eoplanarity and angular correlation of the outgoing tracks. We checked that no bias was introduced for elastic events with dip angles for the scattering plane of less than 80 ~ and with cosines of the scattering angles in the C.M.S. of less than 0.95. Figs. 1 to 5 show the angular distributions for elastic scattering, for all events with dip angles for the scattering plane less than 80 ~ . The solid curves represent a best fit to the differential cross section. The ratio of charged inelastic to elastic events, was obtained by comparing the number of inelastic scatterings to the areas under the solid curves which give the number of elastic seatterings.
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The backward angular distributions obtained in an experiment at the Zero Gradient Synchrotron of Argonne National Laboratory were used to systematically study the energy dependence of the 180° differential cross section for π+p elastic scattering in the center-of-mass energy region from 2159 to 3487 MeV. At each of 38 incident pion momenta between 2.0 and 6.0 GeV/c, a focusing spectrometer and scintillation counter hodoscopes were used to obtain differential cross sections for typically five pion scattering angles from 141° to 173° in the laboratory. Values for dσdΩ at 180° were then obtained by extrapolation. A resonance model and an interference model were used to perform fits to the energy dependence of dσdΩ (180°). Both models led to good fits to our data and yielded values for the masses, widths, parities, and the product of spin and elasticity for the Δ(2200), Δ(2420), Δ(2850), and Δ(3230) resonances. Our data confirm the existence of the Δ(3230) and require the negative-parity Δ(2200).
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A study of 205-GeV/c π−p interactions has been made with a 48 800-picture exposure in the bare Fermilab 30-inch hydrogen bubble chamber. The average number of charged particles produced per inelastic interaction is 7.99±0.06. The elastic cross section is 3.18±0.13 mb and the total cross section is 24.19±0.44 mb. The inclusive cross sections for neutral-particle production are: σ(γ)=171.3±15.3 mb, σ(KS0)=3.64±0.61 mb (x<0.3), σ(Λ)=1.71±0.34 mb (x<0.3), and σ(Λ¯)=0.59±0.23 mb (x<0.1). The average number of π0's produced per inelastic collision is consistent with a linear rise with the number of charged particles, and about equal to the number of produced π− or π+. The average number of K0's, Λ's, and Λ¯'s is consistent with very little dependence on the number of charged particles. General characteristics of neutral-particle production are presented and compared with other experiments. For each topology the produced neutral energy is ∼13 of the incident energy.
THE ERRORS INCLUDE THOSE DUE TO VARIOUS CORRECTIONS.
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The interactions of 775 MeV (kinetic energy) π−-mesons in a hydrogen bubble chamber have been studied. Total and partial crosssections have been determined with the following results: σ (total) = (39.0±1.6) mb, σ (elastic)=(14.8±0.7) mb, σ (π− + p → all neutrals) = (9.0 ± 0.5) mb, σ (π− + p = π− + π+ + n) = (9.8 ± 0.5) mb, and σ (π− + p = π− + p + π0) = (4.8 ± 0.3) mb. The elastic-scattering angular distribution has been fitted with a Legendre polynomial series terminated at the fifth order. Various angular and effective-mass distributions of single-π production are presented and discussed in terms of the Olsson-Yodh and O.P.E. models.
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Elastic π−+p differential cross-section data are presented at the incident-pion momenta 1.72, 1.89, 2.07, 2.27 and 2.46 GeV/c. Resonant behaviour in the coefficients of a Legendre polynomial expansion indicates G- or H-wave resonance. Further analysis using an energy-dependent parametrization of G- and H-waves shows the results to be compatible with the 7−/2 assignment for the , but equally acceptable solutions are obtained with the inclusion of an additional 9+/2 resonance contribution.
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A bubble chamber investigation of π−+p elastic scattering at 1 200 MeV (K.E.) is reported. The total and differential cross-sections are determined. By extrapolation of the angular distribution, the 0° cross-section is derived and compared with the results obtained with the help of the dispersion relations and the optical theorem. The forward peak is investigated in terms of diffraction scattering and a value for the optical radius is derived.
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The interactions of 720 MeV negative pions with protons were investigated using pictures from the 35 cm Saclay hydrogen bubble chamber. Partial cross-sections were determined with the following results: σ(elastic)=13.2±0.5) mb, σ(π−pπ0)=(5.25±0.30) mb, σ(π−π+n)=()7.17±0.35) mb σ (neutrals)=(9.9±0.7) mb, σ (2π production)=(1.03±0.13) mb. The elastic-scattering angular distribution was fitted with a fifth-order polynomial in cos θ* π which shows the effect of a significantF 5/2-D 5/2 interference contribution and predicts a value for (dσ/dΩ) (0°) in agreement with dispersion theory. For both single-π production channels, the two-body effective mass plots and c.m. angular distributions are presented, discussed and compared with the predictions from phase-space, the Olsson-Yodh isobar model and the pole model of isobar production. TheN *(3/2, 3/2) isobar is seen to play an important role in the ππN final states, but the agreement of the data with the existing isobar models and their assumptions is not satisfactory. A comparison of the different two-pion production cross-sections π−pπ−π+, π−pπ0π0 and π−π+nπ0 suggests a strong contribution of π−p→η0n to the π−π+nπ0 final state. An upper limit for σ(π−p→η0n) of (3.0±0.4) mb was obtained.
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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.
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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.
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Single-pion production in π−−p interactions has been studied at 905, 960, and 1100 MeV. Comparison with the isobar and one-pion-exchange (OPE) mechanisms of pion production shows that, below 1 BeV, pion production occurs primarily through the formation of an intermediate excited state of the nucleon (isobar), while at higher energies the influence of the ρ resonance in the ππ system becomes increasingly important. There is some evidence for an I=2 state in the events at the lower energies.
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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 $8.S0 \pm 0.12$.
QUOTED ERRORS INCLUDE EFFECTS OF CORRECTIONS.
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We report on a measurement of the mass of the Z 0 boson, its total width, and its partial decay widths into hadrons and leptons. On the basis of 25 801 hadronic decays and 1999 decays into electrons, muons or taus, selected over eleven energy points between 88.28 GeV and 95.04 GeV, we obtain from a combined fit to hadrons and leptons a mass of M z =91.154±0.021 (exp)±0.030 (LEP) GeV, and a total width of Γ z =2.536±0.045 GeV. The errors on M z have been separated into the experimental error and the uncertainty due to the LEP beam energy. The measured leptonic partial widths are Γ ee =81.2±2.6 MeV, Γ μμ =82.6± 5.8 MeV, and Γ ττ =85.7±7.1 MeV, consistent with lepton universality. From a fit assuming lepton universality we obtain Γ ℓ + ℓ − = 81.9±2.0 MeV. The hadronic partial width is Γ had =1838±46 MeV. From the measured total and partial widths a model independent value for the invisible width is calculated to be Γ inv =453±44 MeV. The errors quoted include both the statistical and the systematic uncertainties.
Measured values of e+ e- --> e+ e- cross section.
Corrected cross section. Corrections are for t-channel effects and loss of acollinear events near the boundary of the acceptance.
A comparison is made of the low-mass three-meson systems (πππ), (Kππ), (π K K ) and ( K K K ) diffractively produced in the reaction meson + proton → three mesons + proton. Several striking similarities and a few important differences are observed: (i) the reactions are consistent with the assumption that the three mesons decay entirely into a 0 − meson and a 0 + , 1 − or 2 + resonance; (ii) the three-meson mass spectra have a peak ≈ 250 MeV above the effective threshold M eff of the dominant decay mode and then fall off approximately as (mass) −3 ;(iii) the average spin 〈 J 〉 = 0.55 + 1.1 Q eff , where Q eff = M - M eff ; (iv) the average orbital angular momentum 〈 l 〉 increases according to 〈 l 〉 = 0.75 Q eff ; (v) the three-meson states are produced dominantly in unnatural spin-parity states and no evidence for their being resonant is found; (vi) the only natural spin-parity states found are the well-established 2 + resonances A 2 and K ∗ (1420); they have similar properties to the non-resonant unnatural parity states except for a dip at t = 0 in the dσ/d t distributions; (vii) both the unnatural and natural spin-parity states are produced mostly by an exchange of natural parity; (viii) there is evidence for two types of production mechanism with different polarization properties, one approximately conserving helicity in the t -channel and the other in the s -channel.
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A multidimensional analysis of the reaction π − p → π − p π + π − at 3.93 GeV/ c is presented. Its results are compared to those obtained with conventional methods and its limitations are discussed.
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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.
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We report a measurement of the p p total cross section at √ s =1.8 TeV using a luminosity-independent method. Our result is σ T =72.1±3.3 mb ; we also derive the total elastic cross section σ el =16.6±1.6 mb. A value is obtained for the total single diffraction cross section of 11.7±2.3 mb.
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We present measurements of the αα elastic scattering differential cross section at √ s = 126 GeV in the range 0.05 ⩽ ‖ t ‖
ERRORS ARE STATISTICAL ONLY.
EXPONENTIAL FIT TO CROSS SECTION BELOW T = 0.075 GEV**2.
The cross section for the K L 0 p elastic scattering has been measured for the first time. The incident momentum and momentum transfer ranges are 3 ⩽ p ⩽ 13 GeV/ c , 0.1 ⩽ | t | ⩽ 1.3 GeV 2 . The results are compared to those of other experiments related to ours by isotopic spin conservation, finding agreement with some and discrepancies with others. The differential cross sections have been parametrized in the form A e bt . The coefficients show little or no dependence on energy, with A ≅ 9.8 mb · GeV −2 and b ≅ 4.7 GeV −2 . The effective linear trajectory has been determined and gives α 0 = 0.95 ± 0.15, α ′ = −0.35 ± 0.48 GeV −2 , in good agreement with dominance by pomeron exchange.
CROSS SECTIONS DEDUCED FROM THE 46 PCT OF EVENTS WHICH YIELD UNIQUE SOLUTIONS.
<RAW> CROSS SECTIONS DEDUCED FROM A STATISTICAL TREATMENT OF ALL EVENTS.
<SMOOTHED> CROSS SECTIONS DEDUCED FROM A STATISTICAL TREATMENT OF ALL EVENTS.
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