We report on a high statistics measurement of the total and differential cross sections of the process gamma gamma -> pi^+ pi^- in the pi^+ pi^- invariant mass range 0.8 GeV/c^2 < W < 1.5 GeV/c^2 with 85.9 fb^{-1} of data collected at sqrt{s}=10.58 GeV and 10.52 GeV with the Belle detector. A clear signal of the f_0(980) resonance is observed in addition to the f_2(1270) resonance. An improved 90% confidence level upper limit Br.(eta'(958) -> pi^+ pi^-) < 2.9 x 10^{-3} is obtained for P- and CP-violating decay of the eta'(958) meson using the most conservative assumption about the interference with the background.

We report a high-statistics measurement of differential cross sections for the process gamma gamma -> pi^0 pi^0 in the kinematic range 0.6 GeV <= W <= 4.0 GeV and |cos theta*| <= 0.8, where W and theta* are the energy and pion scattering angle, respectively, in the gamma gamma center-of-mass system. Differential cross sections are fitted to obtain information on S, D_0, D_2, G_0 and G_2 waves. The G waves are important above W ~= 1.6 GeV. For W <= 1.6 GeV the D_2 wave is dominated by the f_2(1270) resonance while the S wave requires at least one additional resonance besides the f_0(980), which may be the f_0(1370) or f_0(1500). The differential cross sections are fitted with a simple parameterization to determine the parameters (the mass, total width and Gamma_{gamma gamma}B(f_0 -> pi^0 pi^0)) of this scalar meson as well as the f_0(980). The helicity 0 fraction of the f_2(1270) meson, taking into account interference for the first time, is also obtained.

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Angular distributions of the target symmetry for the reaction γ + p → π 0 + p have been measured at the Bonn 2.5 GeV Electron Synchrotron at pion c.m. angles between 13° and 63° and photon energies of 1.0 and 1.1 GeV. The π 0 mesons were detected by their two decay photons with total absorption lead-glass Čerenkov counters. Butanol was used as target material in a continuous flow 3 He cryostat operating at 0.5 K and 25 kG. The π 0 counting rate from free protons in the butanol target was derived from the measurements of the differential cross section on hydrogen. The data are compared with data of other laboratories and the results of two recent partial-wave analyses.

The elastic scattering of 300-Mev negative pions from hydrogen was studied with the aid of a hodoscopic system with pulse-fed counters. Equation (1) gives the angular distribution for the elastic scattering under the hypothesis that the fundamental contribution to the scattering comes from the S and P waves.

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Results of measurements of differential cross sections for the elastic scattering of 11'- mesons of energies 240, 270, 307 and 333 Mev by hydrogen are given.

The results are given of the measurement of the differential cross sections of charge-exchange scattering of 240, 270, 307, and 333-Mev 1r- mesons on hydrogen.

Large-angle cross sections for γd→π0d are systematically measured in the photon energy range between 500 and 1000 MeV. A good fit is obtained by use of a Glauber-model calculation which includes the dibaryon resonances F33(2.26) and G41(2.51), but the fit has an unusual nature in the role of resonance and nonresonance contributions.

The yields and average transverse momenta of pions, kaons, and antiprotons produced at the Fermilab p¯p collider at s=300, 540, 1000, and 1800 GeV are presented and compared with data from the energies reached at the CERN collider. We also present data on the dependence of average transverse momentum 〈pt〉 and particle ratios as a function of charged particle density dNcdη; data for particle densities as high as six times the average value, corresponding to a Bjorken energy density 6 GeV/fm3, are reported. These data are relevant to the search for quark-gluon phase of QCD.

The differential cross sections at 180° for the reactions γ+p→π++n and γ+n→π−+p were measured using a magnetic spectrometer to detect π± mesons. In order to reduce the spread of energy resolution due to the nucleon motion inside the deuteron, a photon difference method was employed with a 50-MeV step for the reaction γ+n→π−+p. The data show structures at the second- and the third-resonance regions for both reactions. A simple phenomenological analysis was made for fitting the data, and the results are compared with those of previous analyses.

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Results are presented on the elastic scattering of photons by protons. The incident photon energy ranged from 0.55 GeV to 4.5 GeV, and the four-momentum transfer t ranged from 0.12 to 1.0 (GeV/c)2. The data at large angles, 60°<θ*<115°, are characterized by a pronounced excitation of the D13(1518) resonance, a shoulder in the 1688-MeV mass region, and a precipitous drop thereafter in the cross section as a function of incident energy. The low-t data are characterized by a diffraction slope of 5 (GeV/c)−2. The data are inconsistent with the predictions of the vector-dominance model if the latter is restricted to ρ0, ω, and φ vector mesons.

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The differential cross sections of π−p→γn at center-of-mass energy Ẽ=1363, 1337, and 1245 MeV are presented. The angular distributions are compared with recent γn→π−p experiments. Though the cross sections for π−p→γn are somewhat lower than those for the inverse reaction, when all uncertainties are considered, we find that our data are in acceptable agreement at all three energies with the inverse reaction determined from π−π+ ratio measurements, in support of time-reversal invariance. The agreement with bubble-chamber measurements at Ẽ=1363 and 1337 MeV is less satisfactory. The isotensor dip test applied to our data is inconclusive. Our measurements are compared with many multipole analyses, disagreeing with most, in particular with pure fixed- t dispersion relation calculations. We find no evidence, in the sense suggested by Donnachie, for the classification of the P11(1470) resonance in an SU(3) antidecuplet. The data are consistent with a small radiative decay of the P11(1470) resonance, as predicted by quark models.

Measurements of the deuteron elastic magnetic structure function B(Q2) are reported at squared four-momentum transfer values 1.20≤Q2≤2.77 (GeV/c)2. Also reported are values for the proton magnetic form factor GMp(Q2) at 11 Q2 values between 0.49 and 1.75 (GeV/c)2. The data were obtained using an electron beam of 0.5 to 1.3 GeV. Electrons backscattered near 180° were detected in coincidence with deuterons or protons recoiling near 0° in a large solid-angle double-arm spectrometer system. The data for B(Q2) are found to decrease rapidly from Q2=1.2 to 2 (GeV/c)2, and then rise to a secondary maximum around Q2=2.5 (GeV/c)2. Reasonable agreement is found with several different models, including those in the relativistic impulse approximation, nonrelativistic calculations that include meson-exchange currents, isobar configurations, and six-quark configurations, and one calculation based on the Skyrme model. All calculations are very sensitive to the choice of deuteron wave function and nucleon form factor parametrization. The data for GMp(Q2) are in good agreement with the empirical dipole fit.

The photoproduction of neutral pions from hydrogen has been studied by counting the recoil protons with a magnetic spectrometer and scintillation counters. The process has been studied between photon energies of 260 and 450 Mev and between center-of-momentum pion angles of 70° and 153°. The excitation functions show a resonance type shape with maxima at about 320 Mev. Angular distributions are analyzed in the form A+Bcosθ+Ccos2θ in the center-of-momentum system. The coefficient B, which gives the front-back asymmetry, is small at all energies; and the ratio −AC is 1.22±0.10 at all energies between 295 and 450 Mev. The maximum cross section at 90° in the c.m. system is 26×10−30 cm2/steradian for 320-Mev photons. The total cross section divided by the square of the c.m. photon wavelength has a maximum near 340 Mev, and drops by nearly a factor of two at 450 Mev. These results are consistent with magnetic dipole and electric quadrupole absorption leading to a resonant state of the pion-nucleon system of angular momentum 32 and isotopic spin 32.

This paper reports measurements of the differential cross section for photoproduction of neutral pions in hydrogen at energies 300, 400, and 450 Mev, at center-of-momentum angles of 70° to 150°. One decay photon from the neutral pion is observed in coincidence with the recoil proton, whose energy and angle are measured to define the photon energy. The results obtained by this method are in good agreement with more accurate measurements obtained recently by the method of observing only the recoil proton.

The excitation functions for positive pion production from hydrogen have been obtained in the energy region from 230 Mev to 450 Mev and at laboratory pion angles of 24°, 38°, 53°, 73°, 93°, 115°, 140°, and 160°. The pions are detected and identified by measuring their range and ionization in a scintillation counter telescope. The above data are analyzed to give the angular distributions in the center-of-momentum system, and a least-squares analysis made to determine coefficients in σ(θ)=A+Bcosθ+Ccos2θ. The total cross section shows a peak at 300 Mev of magnitude 2.20×10−28 cm2. The coefficient B passes through a maximum negative value at 250 Mev and then passes through zero at 325 Mev and remains positive up to the highest energy measured.

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Positive pions produced in a cold, high-pressure hydrogen gas target by the 500-Mev bremsstrahlung of the CalTech synchrotron, have been analyzed by a large magnetic spectrometer. The photoproduction cross section has been measured as a function of photon energy at laboratory angles of 12.5°, 30°, 51°, 73°, 104°, 140°, and 180°. The energy region covered depends somewhat on the angle, but is typically from 200 to 470 Mev. From these excitation curves the angular distribution of the photopions in the center of momentum system is obtained for various photon energies, and these angular distributions are analyzed in the form A+Bcosθ+Ccos2θ. The angular distribution has a backward maximum at low energies and a forward maximum at high energies, the coefficient B changing sign at about 340 Mev. The total cross section shows a striking maximum near 290 Mev, of magnitude 205×10−30 cm2, and falls off above the maximum faster than λ2.

Measurements of the differential cross section for the process γ+p→π0+p have been made at eight pion center-of-mass angles in the range 51-135° and for incident photon energies from approximately 600-1200 MeV. The bremsstrahlung photon beam used was obtained from the California Institute of Technology electron synchrotron. Both the recoil proton and one γ ray from the decay of the π0 were detected. The incident photon energy was determined by measuring the laboratory angle and time of flight of the recoil proton. The angular distributions obtained indicate that the third pion-nucleon resonance is predominantly a D(52) resonance excited by a magnetic quadrupole transition. It can also be concluded that any contribution to the π0 photoproduction cross section from a virtual vector-meson exchange process is probably negligible in the region of the second and third pion-nucleon resonances.

Absolute measurements of the elastic electron-proton cross section have been made with a precision of about 4% for values of the square of the four-momentum transfer, q2, in the range 6.0 to 30.0 F−2 and for electron scattering angles in the range 45° to 145°. To within the experimental errors, it is found that the charge and magnetic form factors of the proton have a common dependence on q2 when normalized to unity at q2=0, and that an accurate representation of the behavior of the form factor and that of the cross sections themselves can be given in terms of a three-pole approximation to the dispersion theory of nucleon form factors.

The differential cross section for the reaction γ+p→π++n was measured using the Caltech 1.5-GeV electron synchrotron. The positive pions were detected and momentum analyzed in a multichannel magnetic spectrometer and the data were recorded in the memory of a pulse-height analyzer. The energy resolution was improved over previous experiments and an attempt was made to minimize systematic errors. The data are presented in the form of energy distributions at 12 lab angles from 34° to 155°, and the range of lab proton energies extended from 500 to 1350 MeV. Data were not taken at all energies for each angle, since the maximum useful momentum of the spectrometer, 600 MeVc, restricted the maximum energy for lab angles less than or equal to 74°.

We report measurements of the differential cross section for photoproduction of π0 mesons from hydrogen, with the pion emerging near 0 deg, in the photon energy range 290 to 700 MeV. The results show no unusual behavior of the cross section in the forward direction. They are consistent with the angular distribution characteristic of a magnetic-dipole transition to a P32 state. The results agree reasonably well with theoretical predictions of Gourdin and Salin, but disagree with a prediction of DeTollis and Verganelakis. Least-squares fits in powers of cosθ have been made to the available angular distributions.

The forward charge-exchange differential cross section has been measured using two Čerenkov spectrometers at five energies of incident pions. The resulting cross-section values are 4.02 ± 0.22, 3.61 ± 0.13, 4.19 ± 0.13, 3.91 ± 0.12, 3.02 ± 0.14 mb/sr at incident pion energies 400, 450, 500, 550 and 600 MeV, respectively. These values are in a good agreement with dispersion-relation predictions.

The differential cross sections of the proton Compton scattering around the second resonance have been measured at a c.m. angle of 90° for incident photon energies between 450 MeV and 950 MeV in steps of 50 MeV, and at an angle of 60° for energies between 600 MeV and 800 MeV. The results show that the peak of the 2nd resonance agrees with that of the pion photoproduction process. We also calculated the proton Compton scattering based on unitarity and fixed- t dispersion relations. The calculation describes well the data of the cross section and the recoil proton polarization.

The reaction γ V p → p π + π − was studied in the W , Q 2 region 1.3–2.8 GeV, 0.3–1.4 GeV 2 using the streamer chamber at DESY. A detailed analysis of rho production via γ V p→ ϱ 0 p is presented. Near threshold rho production has peripheral and non-peripheral contributions of comparable magnitude. At higher energies ( W > 2 GeV) the peripheral component is dominant. The Q 2 dependence of σ ( γ V p→ ϱ 0 p) follows that of the rho propagator as predicted by VDM. The slope of d σ /d t at 〈 Q 2 〉 = 0.4 and 0.8 GeV 2 is within errors equal to its value at Q 2 = 0. The overall shape of the ϱ 0 is t dependent as in photoproduction, but is independent of Q 2 . The decay angular distribution shows that longitudinal rhos dominate in the threshold region. At higher energies transverse rhos are dominant. Rho production by transverse photons proceeds almost exclusively by natural parity exchange, σ T N ⩾ (0.83 ± 0.06) σ T for 2.2 < W < 2.8 GeV. The s -channel helicity-flip amplitudes are small compared to non-flip amplitudes. The ratio R = σ L / σ T was determined assuming s -channel helicity conservation. We find R = ξ 2 Q 2 / M ϱ 2 with ξ 2 ≈ 0.4 for 〈 W 〉 = 2.45 GeV. Interference between rho production amplitudes from longitudinal and transverse photons is observed. With increasing energy the phase between the two amplitudes decreases. The observed features of rho electroproduction are consistent with a dominantly diffractive production mechanism for W > 2 GeV.

Differential cross-section measurements for π − p → γ n, consisting of three angular distributions at 618, 676 and 718 MeV/ c , and the energy dependence at θ γ = 90° for seven incident pion momenta between 502 and 888 MeV/ c , are presented. Our data qualitatively support recent multipole analyses. Agreement with the Scheffler et al. results for the inverse reaction, γ n → π − p, using a ( π − -recoil p) coincidence technique is good excluding a large violation of time reversal invariance. The agreement with γ n → π − p data obtained using the R ( π − / π + ) ratio technique or a deuterium bubble chamber is only qualitative.

Differential cross sections for Compton scattering by the proton have been measured in the energy interval between 200 and 500 MeV at scattering angles of θ cms = 75° and θ cms = 90° using the CATS, the CATS/TRAJAN, and the COPP setups with the Glasgow Tagger at MAMI (Mainz). The data are compared with predictions from dispersion theory using photo-meson amplitudes from the recent VPI solution SM95. The experiment and the theoretical procedure are described in detail. It is found that the experiment and predictions are in agreement as far as the energy dependence of the differential cross sections in the Δ-range is concerned. However, there is evidence that a scaling down of the resonance part of the M 1+ 3 2 photo-meson amplitude by (2.8 ± 0.9)% is required in comparison with the VPI analysis. The deduced value of the M 1+ 3 2 - photoproduction amplitude at the resonance energy of 320 MeV is: |M 1+ 3 2 | = (39.6 ± 0.4) × 10 −3 m π + −1 .

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The rates for forward electroproduction of single charged pions from deutrium have been measured in the resonance region, at a virtual photon mass squared ≈−0.5( GeV/ c 2 ) 2 . Results are presented in the form of a π − to π + cross-section ratio.

The elastic differential cross section for the scattering of negative pions by hydrogen was measured at laboratory-system pion kinetic energies of 230, 290, 370, and 427 Mev. The elastically scattered pions were detected by a counter telescope which discriminated against recoil protons and inelastic pions on the basis of range. Differential cross sections were obtained at nine angles for each energy and were fitted by a least-squares program to a series of Legendre polynomials. At the three higher energies, D waves are required to give satisfactory fits to the data. The real parts of the forward-scattering amplitudes calculated from this experiment are in agreement with the predictions of dispersion theory. The results of this experiment, in conjunction with data from other pion-nucleon scattering experiments, support the hypothesis of charge independence at these higher energies.

The structure and size of the proton have been studied by means of high-energy electron scattering. The elastic scattering of electrons from protons in polyethylene has been investigated at the following energies in the laboratory system: 200, 300, 400, 500, and 550 Mev. The range of laboratory angles examined has been 30° to 135°. At the largest angles and the highest energy, the cross section for scattering shows a deviation below that expected from a point proton by a factor of about nine. The magnitude and variation with angle of the deviations determine a structure factor for the proton, and thereby determine the size and shape of the charge and magnetic-moment distributions within the proton. An interpretation, consistent at all energies and angles and agreeing with earlier results from this laboratory, fixes the rms radius at (0.77±0.10) ×10−13 cm for each of the charge and moment distributions. The shape of the density function is not far from a Gaussian with rms radius 0.70×10−13 cm or an exponential with rms radius 0.80×10−13 cm. An equivalent interpretation of the experiments would ascribe the apparent size to a breakdown of the Coulomb law and the conventional theory of electromagnetism.

The bremsstrahlung beam of the Cornell Bev electron synchrotron has been used to study the reaction γ+p→π0+p over the photon energy range 250 Mev to 1 Bev, and for center-of-mass pion angles between 20° and 70°. The recoil protons, of energies between 10 and 60 Mev, were identified and their energies determined using a range telescope of eight thin plastic scintillators enclosed in a vacuum chamber with the thin liquid hydrogen target. Correlated pulse-height information was obtained by photographing an oscilloscope display and was used to sort out the protons from mesons and electrons. Corrections were made for the background of photoprotons from the Mylar target cup, the energy loss of the protons in the liquid hydrogen, absorption and scattering in the counter telescope, and the variation of beam intensity profile with energy. Compared with previous experiments and extrapolations the results show a somewhat smaller forward differential cross section above 400 Mev. The angular distributions obtained from a least-squares fit to all existing data indicate a d32 assignment for the 760-Mev resonance level. Other implications of the data are also discussed.

The ratio of the yields of negative and positive pions photoproduced in deuterium has been measured at six photon energies between 500 and 1000 Mev and at seven angles between 20° and 160° in the center-of-momentum system of the photon and target nucleon. Pions were selected with a magnetic spectrometer and identified using momentum and specific ionization in a scintillation counter telescope. The spectator model of the deuteron was used to identify the photon energy. Statistical errors assigned to the π−π+ ratio range between five and fifteen percent. The results of the present experiment join smoothly with the low-energy π−π+ ratios obtained by Sands et al. At high energies the π−π+ ratio varies from 0.5 at forward angles and energies near 900 Mev to 2.5 at 160° c.m. and energies 600 to 800 Mev. The cross sections for π− photo-production from neutrons have been derived from the π−π+ ratio and the CalTech π+ photoproduction data. The angular distributions for π− production are considerably different from those for π+; there is, for example, a systematic increase at the most backward angles. The energy dependence of the total cross section for π− is similar to that for π+, although the second resonance peak occurs at a slightly lower energy, and at 900 and 1000 Mev the π− cross section is smaller by a factor 1.6. A comparison is made of the cross sections for π+ photoproduction from hydrogen and deuterium, although the accuracy of this comparison is not high.

Recoil protons from the process γ+p→p+π0 have been detected by nuclear emulsions placed within a hydrogen-gas target and used to measure the differential cross section for production of neutral pions. In this manner protons of energies as low as 5 Mev can be detected at laboratory angles corresponding to emission of a pion at center-of-momentum (c.m.) angles as low as 26°. This experiment thus supplements that of Oakley and Walker which is in the same range of photon energies (240-480 Mev), but is restricted to pion c.m. angles greater than about 70° owing to higher minimum detectable proton energy. Common experimental points provide intercomparison of absolute values. Angular distributions are analyzed in the form dσdΩ=A+Bcosθ+Ccos2θ in the c.m. system. The combined Oakley-Walker and present data give the average value of the ratio AC as -1.60±0.10 in the energy range from 260 to 450 Mev. The coefficient B, which gives the front-back asymmetry, passes through zero below the resonance energy of 320 Mev and is positive at higher energies. These results are consistent with magnetic dipole absorption leading to a state of the pion-nucleon system of angular momentum 32, together with a finite amount of S-wave interference.

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This paper reports experimental findings on the Dirac (F1) and Pauli (F2) form factors of the proton. The form factors have been obtained by using the Rosenbluth formula and the method of intersecting ellipses in analyzing the elastic electron-proton scattering cross sections. A range of energies covering the interval 200-1000 Mev for the incident electrons is explored. Scattering angles vary from 35° to 145°. Values as high as q2≅31 f−2 (q=energy−momentumtransfer) are investigated, but form factors can be reliably determined only up to about q2=25 f−2. Splitting of the form factors is confirmed. The newly measured data are in good agreement with earlier Stanford data on the form factors and also with the predictions of a recent theoretical model of the proton. Consistency in determining the values of the form factors at different energies and angles gives support to the techniques of quantum electrodynamics up to q2≅25 f−2. At the extreme conditions of this experiment (975 Mev, 145°) the behavior of the form factors may be exhibiting some anomaly.

The process γ+p→π0+p has been studied by detecting recoil protons from a liquid hydrogen target which was bombarded by the bremsstrahlung beam of the California Institute of Technology electron synchrotron. The angle and momentum of the recoil protons were measured by a magnetic spectrometer-three scintillation counter coincidence system. The process has been studied between photon laboratory energies of 490 and 940 Mev and between pion center-of-mass angles of 31.5° and 147°. Protons which arose from meson pair production were significant at forward laboratory angles. A correction for this contamination is discussed. The results of these measurements show two interesting features. One is that the total cross section, which falls very rapidly above the 32−32 resonance energy near 320 Mev, reaches a minimum at about 600 Mev, and then increases to a broad maximum near 800 or 900 Mev. The other striking feature of the data is that the shape of the angular distribution seems to change rather suddenly near 900 Mev.

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The ratio of π - to π + electroproduction cross sections from deuterium has been measured in the resonance region, at a four-momentum transfer squared close to −1.0 (GeV/ c ) 2 . Results in the forward direction are presented and a comparison is made with predictions based on SU(6) W and the Melosh transformation.

We have measured the production cross section for K s 0 in e + e − annihilation from 3.6 to 5.0 GeV center of mass energy. A substantial increase of the K s 0 yield is observed around 4 GeV in qualitative agreement with the charm hypothesis.

The differential cross section has been measured for the reaction γ +p→ π o + p at the Bonn 2.5 GeV electron synchrotron in the energy range from 0.55 to 2.2 GeV at a c.m.angle of 120 degrees.

The preliminary results of measurements of differential cross-sections for the photo-production of neutral pions from protons are given. The data fall in the range 60–125 degrees in pion c.m. angle and 350 to 850 MeV in photon energy.

The differential cross section for the reaction γp → π 0 p at forward angles has been measured in the energy region between 350 MeV and 1175 MeV. A phenomenological multiple analysis was carried out on the present data together with other data.