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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We report final results on the polarization parameter P in elastic scattering of π − , K − and antiprotons at 40 GeV/ c incident momentum. The energy dependence of P (t) in π − p above 10 GeV/ c is well fitted by P (t) α s αR(t)-α P (t) where α R (t) are the effective Regge and Pomeron trajectories respectively. The data in K − p are compatible with exchange degeneracy. The results inp¯p show an important structure for |t|> 0.3 (GeV/c) 2 demonstrating the existence of a large helicity flip amplitude.
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The polarization parameter P has been measured for elastic π + p, K + p and pp scattering at 45 GeV/c. Four-momentum transfer ranges from −0.08 to −1.1 (GeV/) 2 for pp, and from −0.08 to −0.9 (GeV/) 2 for π + p and K + p. The energy dependence of the polarization P ( t ) in π + p and in K + p above 6 GeV/c incident momentum is compatible with interference between pomeron and Regge poles. On the other hand, the polarization in p p elastic scattering decreases faster than ordinary Regge model predictions. This result can be explained by interference between non flip and flip amplitudes of the pomeron, leading to negative values for the polarization.
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The spin rotation parameter R has been measured for elastic π − p scattering at 40 GeV/ c , at four momentum transfers t ranging from −0.19 to −0.52 (GeV/ c ) 2 . The average value within this interval is R π − p = -0.200± 0.023. The resulting constraints on the πN scattering amplitudes are discussed. The experiments also yields an average value for K − p scattering, R K − p scattering, R K − p = -0.16±0.16.
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The spin rotation sf R in pp and π + p elastic scattering at 45 GeV/c has been measured at the Seppukhov accelarator, for z . sfnc ; t |; ranging from 0.2 to 0.5 (GeV/) 2 . The results are presented, together with previous R measurements at lower energies. The equality of the values for R in proton-proton and pion-proton scattering, within the experimental errors, is a test of factorization of the residues in the pomeron exchange.
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The differential cross section has been measured at 30, 50, 80, 100, 120 and 140 GeV/ c for 0.002 < | t | < 0.04 ( GeV / c ) 2 . The results show that the π − p real part goes from negative to positive values below 80 GeV/ c . The slope parameter in the t -region measured is significantly higher than what has been found − t = 0.2 (GeV/ c ) 2 .
FROM FIT TO D(SIG)/DT AND SIGMA TOTAL FOR -T = 0.002 TO 0.04 (0.02 AT 30 GEV/C AND 0.03 AT 140 GEV/C) GEV**2.
The differential cross section of π − p scattering has been measured in the energy region 100–345 GeV and in the t -range 0.002<| t |< 0.04 (GeV/ c ) 2 . The real part of the π − p scattering amplitude has been extracted from the data. The results show that the real part continues to increase with energy. The energy dependence of the slope parameter has also been determined. The shrinkage found expressed in terms of the slope of the pomeron trajectory is2 α ′ p =0.23±0.04 (GeV/ c ) −2 . This agrees with the energy dependence found at larger| t |-values.
RE(AMP)/IM(AMP) (REAL/IMAG) AND SLOPE PARAMETERS DEDUCED FROM A FIT TO D(SIG)/DT IN T HE COULOMB INTERFERENCE REGION (-T = 0.002 TO 0.04 GEV**2).
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.
THESE CROSS SECTIONS ARE NOT NORMALIZED TO ANY OTHER ABSOLUTE MEASUREMENT. THE ERRORS INCLUDE SOME SYSTEMATIC ERRORS.
THE FORWARD CROSS SECTION AGREES WELL WITH THE OPTICAL POINT FROM TOTAL CROSS SECTION MEASUREMENTS.
THESE CROSS SECTIONS ARE NOT NORMALIZED TO ANY OTHER ABSOLUTE MEASUREMENT.
Analyzing powers for πp elastic scattering were measured using the CHAOS spectrometer at energies spanning the Δ(1232) resonance. This work presents π+ data at the pion kinetic energies 117, 130, 139, 155, 169, 180, 193, 218, 241, and 267 MeV and π− data at 87, 117, 193, and 241 MeV, covering an angular range of 50°<~θc.m.<~180° at the higher energies and 90°<~θc.m.<~180° at the lower energies. Unique features of the spectrometer acceptance were employed to reduce systematic errors. Single-energy phase shift analyses indicate the resulting S11 and S31 phases favor the results of the SM95 phase shift analysis over that of the older KH80 analysis.
Measurement of the PI+ analysing power at 117 MeV.. The data were collected in the conventional mode and may be independently floated within the systematic error.
Measurement of the PI+ analysing power at 139 MeV.. The data were collected in the conventional mode and may be independently floated within the systematic error.
Measurement of the PI- analysing power at 87 MeV.. The data were collected in the conventional mode and may be independently floated within the systematic error.
Angular distributions of the analyzing powers for π+p→ and π−p→ elastic scattering have been measured in a single-scattering experiment employing a polarized proton target. Measurements were obtained for pion energies of 98, 139, 166, 215, and 263 MeV. The addition of these data to the existing πp database significantly reduces the uncertainties in all S and P phase shifts for πp reactions over the delta resonance.
Measured values of the analyzing power for PI+ P elastic scattering at incident kinetic energy 98 MeV.
Measured values of the analyzing power for PI+ P elastic scattering at incident kinetic energy 139 MeV.
Measured values of the analyzing power for PI+ P elastic scattering at incident kinetic energy 166 MeV.
Analyzing powers of pion-proton elastic scattering have been measured at PSI with the Low Energy Pion Spectrometer LEPS as well as a novel polarized scintillator target. Angular distributions between 40 and 120 deg (c.m.) were taken at 45.2, 51.2, 57.2, 68.5, 77.2, and 87.2 MeV incoming pion kinetic energy for pi+ p scattering, and at 67.3 and 87.2 MeV for pi- p scattering. These new measurements constitute a substantial extension of the polarization data base at low energies. Predictions from phase shift analyses are compared with the experimental results, and deviations are observed at low energies.
Analyzing power for PI+ P elastic scattering at incidient kinetic energy 87.2 MeV from the data set 1.
Analyzing power for PI+ P elastic scattering at incidient kinetic energy 68.4 MeV from the data set 1.
Analyzing power for PI+ P elastic scattering at incidient kinetic energy 57.2 MeV from the data set 1.
We report our first measurements of the polarization in the elastic scattering of negative pions from polarized protons at an incident pion momentum of 40 GeV/ c . The momentum-transfer region covered was 0.08 < | t | < 1.3 (GeV/ c ) 2 . The angular distribution of the polarization exhibits a first minimum of ∼ − 5% and the well-known zero around t ≈ − 0.6 (GeV/ c ) 2 . The energy variation of the first minimum (at around t = − 0.2) may be expressed in a simple form, P avr = −(0.48±0.06) s −0.52±0.05 .
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We have measured the polarization parameter in π−p elastic scattering at laboratory momenta of 1180, 1250, and 1360 MeV/c in the angular interval 65°<θc.m.<115°. The results were used to show that the polarized target used in these (and other similar) experiments was uniformly polarized. These measurements were also used to resolve pre-existing experimental discrepancies in the determination of the polarization parameter, and to clarify the behavior of scattering amplitudes in this energy range. We show that local measurements of this type are important in resolving discrete ambiguities affecting the energy continuation of the amplitudes. An important by-product of this experiment is the development of a fast method of reconstructing particle trajectories and fitting the elastic events, which could have a significant impact for future high-statistics experiments.
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Analyzing powers for πp elastic scattering at bombarding energies below the Δ(1232) resonance were measured at TRIUMF using the CHAOS spectrometer and a polarized spin target. This work presents π− data at six incident energies of 57, 67, 87, 98, 117, and 139 MeV, and a single π+ data set at 139 MeV. The higher energy measurements cover an angular range of 72°<~θc.m.<~180° while the lower energies were limited to 101°<~θc.m.<~180°. There is a high degree of consistency between this work and the predictions of the VPI/GWU group’s SM95 partial wave analysis.
Analysing power measurements for a 139 GeV PI+ beam (standard track).
Analysing power measurements for a 139 GeV PI- beam (standard track).
Analysing power measurements for a 117 GeV PI- beam (standard track).
The ratio of π+p to pp elastic scattering is found to be smoothly varying over the range −t=0.03 to 0.4 GeV2. It is well fitted by a single exponential, indicating the forward behavior must be quite similar for the two reactions.
ACTUALLY THE DATA ARE THE EXPONENTIAL SLOPE OF THE RATIO OF D(SIG)/DT FOR THE TWO REACTIONS.
Differential cross sections for π − p and pp elastic scattering have been measured at incident momenta ranging from 30 to 345 GeV and in the t range 0.002 (GeV/ c ) 2 ⩽ | t | ⩽ 0.04 (GeV/ c ) 2 . From the analysis of the data, the ratio ϱ ( t = 0) of the real to the imaginary parts of the forward scattering amplitude was determined together with the logarithmic slope b of the diffraction cone.
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The differential cross sections for elastic π − p, K − p , p p and π + p, pp scattering at 39 and 44.5 GeV/ c , respectively, have been measured in the interval of momentum transfer squared 0.15 ≤ ovbt | ≤ 2 (GeV/ c ) 2 .
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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.
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ERRORS IN ELASTIC CROSS SECTIONS INCLUDE SYSTEMATIC ERRORS.
Differential cross sections for the elastic scattering of negative pions from hydrogen have been measured over a limited range of squared four-momentum transfer (t) in the vicinity of t≃−3 (GeV/c)2 for incident pion momenta of 2.51, 2.76, and 3.01 GeV/c. These measurements confirm the existence of a minimum in the differential cross section in this region of incident momentum and scattering angle. The minimum occurs at a smaller value of t [t≃−2.6 (GeV/c)2] than has been observed at higher momenta.
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Hoping to find resonant structures in the momentum dependence of π − p elastic scattering we have measured the differential cross section for this reaction at c.m. angles near 90°. An intense pion beam (≈ 10 7 π /s) has been used, together with a high incident momentum resolution (d P / P ≈ 2 × 10 −4 ), to scan the region of laboratory momenta from 5.75 to 13.02 GeV/ c (c.m. energy from 3.42 to 5.03 GeV). The sensitivity attained by the experiment is such that signals would have been seen corresponding to the formation of non-strange baryon resonances having width larger than ≈ 0.1 MeV and elasticity larger than a few per cent. Within these limits no resonances were sighted.
ENERGY SCAN IN BINS OF D(PLAB)/PLAB OF 5*10**-4 AT FOUR FIXED ANGLES (COS(THETA) = -0.4 TO 0.4).
The contradiction of the σ term of pion-nucleon scattering as deduced from the Karlsruhe-Helsinki phase shifts with the smaller value calculated by the chiral perturbation theory of QCD is well known. In an effort to clarify the discrepancy we have determined the real part of the isospin-even forward-scattering amplitude of pion-nucleon scattering at a pion energy Tπ=54.3 MeV by measurement of the elastic scattering of positive and negative pions on protons in the Coulomb-nuclear interference region. The deduced value is in agreement with the prediction of the Karlsruhe-Helsinki phase-shift analysis for that energy. The resulting large value of the σ term may be interpreted as being due to the influence of s¯s sea pairs even at large distances (small Q2) as previously suggested by the European Muon Collaboration measurement of deep-inelastic scattering of polarized muons on polarized protons.
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IM(AMP) VIA OPTICAL THEOREM FROM TOTAL CROSS SECTIONS OF L. M. VASILYEV ET AL., PL 36B, 528 (1971).
The real part of the isospin-even forward-scattering amplitude of pion-nucleon scattering has been determined at a pion energy of Tπ=55 MeV by measurement of the elastic scattering of positive and negative pions on protons within the Coulomb-nuclear interference region. The value confirms the prediction of the Karlsruhe-Helsinki phase-shift analysis for that energy. These phases have been used to determine the σ term of pion-nucleon scattering by means of dispersion relations, resulting in a value for σ which is in contradiction with chiral perturbation theory of QCD.
PI- P cross sections normalised to the Coulomb cross section taken from the Karlesruhe-Helsinki phase shift analysis (R. Koch, E. Pietarinen (NP A336(80)331).
A simple, large-solid-angle apparatus, specially suited for the measurement of backward elastic scattering of medium-energy pions on protons and deuterons, is described. The method of analysis which reduces background and determines elastic events from a data sample of 185 MeV negative pions incident on a D 2 O target is discussed. Results for 141 MeV π + p and 185 MeV π − p backward cross-sections are also presented and compared with cross-sections calculated from known phase shifts.
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Differential cross sections for pi- p and pi+ p elastic scattering were measured at five energies between 19.9 and 43.3 MeV. The use of the CHAOS magnetic spectrometer at TRIUMF, supplemented by a range telescope for muon background suppression, provided simultaneous coverage of a large part of the full angular range, thus allowing very precise relative cross section measurements. The absolute normalisation was determined with a typical accuracy of 5 %. This was verified in a simultaneous measurement of muon proton elastic scattering. The measured cross sections show some deviations from phase shift analysis predictions, in particular at large angles and low energies. From the new data we determine the real part of the isospin forward scattering amplitude.
Elastic PI- P cross section for incident kinetic energy 43.3 MeV for the rotated target data. Errors shown are statistical only.
Elastic PI- P cross section for incident kinetic energy 43.3 MeV. Errors shown are statistical only.
Elastic PI- P cross section for incident kinetic energy 37.1 MeV. Errors shown are statistical only.
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