Using new data from 100 GeV c π − interactions, we find the energy dependence of the invariant cross-section in the target fragmentation (central) region to be consistent with an A + Bs − 1 2 (C + Ds − 1 4 ) behavior. The leading particle peak near x = + 1 exhibits a width in x which becomes smaller with increasing energy and an integrated cross section which is approximately energy independent.
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In a sample of 108 563 pictures taken with the Fermilab 30-inch hydrogen bubble chamber, exposed to a 360-GeV/c π− beam, we have observed 19 453 interactions in a selected fiducial region. The observed charged multiplicity distribution has been corrected for the effects of scan efficiency, errors in prong count, missed close-in vees, secondary interactions, and neutron stars and for Dalitz pairs. The two-prong events have been corrected for losses at low −t. The total cross section is measured to be 25.25 ± 0.35 mb, and the elastic cross section is 3.61 ± 0.11 mb with an exponential slope of (8.82 ± 0.30) (GeV/c)−2. The average charged-particle multiplicity for inelastic events is 8.73 ± 0.04, and the second moment f2 is measured to be 9.83 ± 0.23.
SYSTEMATIC CORRECTIONS INCLUDED IN ERRORS.
FROM FIT, FORWARD D(SIG)/DT = 31.84 +- 0.68 MB/GEV**2, AND AGREES WITH OPTICAL POINT FROM MEASURED TOTAL CROSS SECTIONS.
Inclusive cross sections for π 0 , K s 0 , Λ 0 and Λ 0 production in 100, 200 and 360 GeV /c π − p interactions are presented and compared with data at other energies. Invariant cross sections for γ, K s 0 , Λ 0 and Λ 0 production are presented in terms of Feynman x , the rapidity y , and transverse momentum squared, p T 2 . A comparison of the observed γ spectrum is made with the spectra computed assuming that the π 0 momentum distribution is identical to that of the observed π + or π − .
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Inclusive and semi-inclusive cross sections for gp0 production in 100, 200, and 360 GeV/c π−p interactions are presented. Differential cross sections for ρ0 production as functions of c.m. rapidity and transverse momentum are compared with the corresponding differential cross sections for pion production. Effects of various methods of estimating background on the values obtained for ρ0 production cross sections are discussed. About 10% of the final-state charged pions appear to come from ρ0 decay. Thus, while ρ0 production and decay is a significant source of final-state pions, other sources must contribute the majority of the produced pions.
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A coupled channel analysis has been carried out using a new amplitude analysis of the K 0 s K 0 s system produced in the reaction π − p→K 0 s K 0 s n at 22 GeV/ c , which contained about 40 000 new events in the low- t region (| t − t min |<0.1 GeV 2 ). Here only the I G =0 + , J PC =2 ++ amplitude from this analysis is considered, together with available data from other experiments in channels with the same quantum numbers in order to determine which 2 ++ isoscalar mesons have significant pseudoscalar-pseudoscalar couplings. It is found that four poles, f(1270), f'(1525), θ(1690), and f r (1810), are needed, plus a smooth background in order to fit these data; the need for the θ(1690) depends on the J/ψ radiative decay alone, and the f r (1810) is seen only in hadronic production.
Inclusive cross sections and invariant single-particle distributions are presented for positive pions and protons produced in 8.05-GeV/c π−p and 18.5-GeV/c π±p inclusive reactions. Distributions in pT2 and in the longitudinal variables x, y (c.m.) and pl (lab) are shown. Comparisons are made with inclusive distributions for other particles produced in the same reactions.
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Significant two-particle correlations of dynamical origin are observed in 200 GeV/c π−p inclusive interactions. This is demonstrated by comparison with kinematic correlations calculated from an independent-particle-emission model. Two distinct correlation types are observed: (a) unlike-particle correlations with correlation length ∼ 1.3 rapidity units independent of azimuthal separation, and (b) like-particle correlations with correlation length ∼ 0.4 rapidity units which are observed only for small azimuthal separations.
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The KS0KS0π0 system has been studied in the exclusive reaction π−p→KS0KS0π0n at 21.4 GeV/c. Evidence for the production of the f1(1285) and the η(1460) is presented. The η(1460) is produced away from minimum momentum transfer in the presence of nonresonant K*K (S-wave) production and phase-space background. The observed mass, width, and decay properties of the η(1460) are consistent with those attributed to the ι(1460) observed in radiative Jψ decay.
An experiment studying the reaction π+p→Δ++π0π0 using the Argonne National Laboratory 1.5-m streamer chamber combined with a lead-glass hodoscope is described. The data were analyzed in terms of π+π−→π0π0 scattering, and the details of the extrapolation to the pole are discussed. An energy-independent amplitude analysis from threshold to 2.3 GeV is presented. In this analysis the f0(1270), the h0(2040), and a JP=2+ state at 1.8 GeV with a width of 0.280 GeV are observed. The amplitude ambiguity arising from analyses of π+π−→π+π− data in the 1.6-GeV region is resolved. An energy-dependent phase-shift analysis from 1.0 to 1.5 GeV is presented.
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The KS0KS0 system produced in the reaction π−p→nKS0KS0 at 6.0 and 7 0 GeV/c has been studied utilizing the ANL 1.5-m streamer-chamber facility. A 400 000-photograph exposure yielded 5096 unweighted nKS0KS0 events. The cross section for this reaction was determined to be 9.6 ± 1.3 μb at 6.0 GeV/c and 8.7 ± 1.1 μb at 7.0 GeV/c. The decay angular distributions were parametrized in terms of moments of the spherical harmonics. The 〈Y40〉 moment was fitted to interfering Breit-Wigner amplitudes for the f and f′ mesons. Using this fit, the branching ratio R=Γ(f→KK¯)Γ(f→all) was found to be (2.3 ± 0.8)%. An energy-independent production-amplitude analysis revealed an enhancement in the S-wave amplitude near 1300 MeV. The properties of the S-wave enhancement are discussed and compared with those observed in other recent experiments. Extrapolated cross sections for the reaction ππ→KS0KS0 are presented. We find a cross section considerably below the S-wave unitarity limit in the S* region.
FROM FIT TO D-WAVE (M=0) KS KS, CORRECTED FOR <K+ K-> AND <KL KL> DECAY MODES.
The differential cross sections for π + p elastic scattering at0.6, 1.0, 1.5, 2.0, GeV/ c for π - p at 1.0, 1.5, 2.0 GeV/ c , for K - p at 1.2, 1.8, 2.6 GeV/ c and for K - p at 0.9, 1.2, 1.4, 1.6, 1.8, 2.6 GeV/ c have been measured with an overall accuracy ofthe order of 1 to 2% in an electronics experiment over the angular region corresponding to momentum transfer t between 0.0005 and 0.10 GeV 2 . Making use of the interference effects between the Coulomb and the nuclear interaction, we have determined the magnitude and sign of the real part of the scattering amplitude near t = 0. The K ± p real parts have been used in a dispersion relation to derive the value of the KNΛ coupling constant.
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We have measured the differential cross section of the reaction π − p→ π − p in the range 0.92 ⩽ cos θ c.m. ⩽ 0.99 at 15 momenta between 0.875 and 1.580 GeV/ c . The results we report complete the available data; previous measurements of this reaction do not extend beyond cos θ c.m. =0.90. We compare our experimental results with dispersion relation predictions. A comparison of our results for B , the slope of the differential cross section, with earlier results shows many discrepancies.
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We have studied the reactionspp→ppπ+π-,K+p→K+pπ+π−π, π+p→ π+,pπ+π− and π−p →π+π− at 147 GeV/c using the 30-inch Fermilab hybrid system. All four reactions were detected with the same apparatus and analyzed in the same way. The energy dependence of the channel cross section was found to beAp−0.6+B for thepp reaction andAp−1+B for the other three. About 90% of the cross section at 147 GeV/c can be accounted for by either beam or target diffraction. Some of the remaining cross section may come from double Pomeron exchange reactions which we tried to isolate. We have tested the hypothesis of a factorizable Pomeron and our data indicates a violation of this hypothesis. We show that the 3π mass enhancement in the mass region 1.2–1.4 GeV is diffractively produced in the π± beam reactions. Fourprong, four-constraint and six-prong, four-constraint cross sections are reported.
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CROSS SECTIONS FOR DIFFRACTION DISSOCIATION OF BEAM. FEYNMAN X OF OUTGOING PROTON <-0.96.
Final states produced by charged baryon exchange in π − p interactions at 12 GeV/ c laboratory momentum have been studied. Forward neutrons with momenta determined by a calorimeter to be greater than 8.5 ± 1.4 GeV/ c triggered the SLAC 40-inch hydrogen bubble chamber which operated at a 10 Hz expansion rate. We report data on the reactions π − p→n π − π + , π − p→n π − π + π 0 , and π − p→n π − π − π + π + . In π − n π − p→n π + , production of ϱ and f mesons is observed. Differential cross sections are derived and compared with data at lower incident momentum and with theoretical models. In π − p→n π − π + π 0 , ω production is observed with a differential cross section having a deep near u ′= 0.2 (GeV/ c ) 2 . In π − p→n π − π − π + π + , Δ − , ϱ and f production is observed . The observed mass distributions appear to indicate the production of wide resonaces decaying into ϱππ. Some evidence for ϱ-ω interference is also observed.
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CORRECTED FOR BACKGROUND.
The differential cross sections for π − p elastic scattering have been measured near 180°, in the momentum range 875–1580 MeV/c. The results are compared with recent phase shift analysis, showing some notable discrepancies.
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Results on the following π−p reactions involving a hyperon are studied at 4.5 and 6.0 GeV/c from a high-statistics bubble-chamber experiment. (1) π−p→(Λ, Σ0)K0: Differential cross sections and hyperon polarizations are presented. Comparison with the line-reversed reactions K¯N→(Λ, Σ0)π indicates the failure of the predictions of K*(890) and K*(1420) exchange degeneracy. Effective trajectories for these two reactions are compared. Shrinkage is observed in K¯N→Λπ and not in π−p→ΛK0. (2) π−p→(Λ, Σ0)K*(890)0: Differential cross sections, hyperon polarizations, and K*(890)0 density-matrix elements are determined. ΛK*(890)0 decay correlations are found to impose strong constraints on the scattering amplitudes. The data indicate that both natural- and unnatural-parity exchanges contribute large, but opposite, Λ polarizations. This behavior cannot be explained by a simple exchange model utilizing K and the exchange-degenerate K*(890) and K*(1420) only. Additional trajectories or absorption effects are required to obtain the observed Λ-polarization effects. Comparison of ΛK*(890)0 and Σ0K*(890)0 indicates the greater importance of unnatural-parity exchange in the former reaction. We observe no evidence for deviations from isospin predictions in ΛK*(890)0 production where K*(890)0→K+π− and KS0π0. (3) π−p→ΛK*(1420)0 and ΛK*(1300)0: K*(1420)0 density-matrix elements satisfying positivity constraints are determined allowing for s-wave interference effects. Evidence of the existence of a narrow K*(1300)0→Kππ with a dominant K+ρ− decay mode is observed in the 4.5- and 6-GeV/c data. (4) Σ(1385), Λ(1405), Λ(1520) production: Differential cross sections for the quasi-two-body reactions π−p→Y0K0, where Y0 is Λ(1405), Λ(1520), or Σ(1385)0, are presented and found to have a very similar flat slope in the forward direction. Data for forward K+ scattering in the reaction π−p→Σ(1385)−K+ are presented and discussed. It is argued that this forward peak cannot be explained by kinematic reflection or an s-channel effect and therefore must be due to either two-particle exchange or a single exotic exchange in the t channel.
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FIT FOR FORWARD CROSS SECTION AND SLOPE.
We have performed the most comprehensive resonance-model fit of $\pi^-\pi^-\pi^+$ states using the results of our previously published partial-wave analysis (PWA) of a large data set of diffractive-dissociation events from the reaction $\pi^- + p \to \pi^-\pi^-\pi^+ + p_\text{recoil}$ with a 190 GeV/$c$ pion beam. The PWA results, which were obtained in 100 bins of three-pion mass, $0.5 < m_{3\pi} < 2.5$ GeV/$c^2$, and simultaneously in 11 bins of the reduced four-momentum transfer squared, $0.1 < t' < 1.0$ $($GeV$/c)^2$, are subjected to a resonance-model fit using Breit-Wigner amplitudes to simultaneously describe a subset of 14 selected waves using 11 isovector light-meson states with $J^{PC} = 0^{-+}$, $1^{++}$, $2^{++}$, $2^{-+}$, $4^{++}$, and spin-exotic $1^{-+}$ quantum numbers. The model contains the well-known resonances $\pi(1800)$, $a_1(1260)$, $a_2(1320)$, $\pi_2(1670)$, $\pi_2(1880)$, and $a_4(2040)$. In addition, it includes the disputed $\pi_1(1600)$, the excited states $a_1(1640)$, $a_2(1700)$, and $\pi_2(2005)$, as well as the resonancelike $a_1(1420)$. We measure the resonance parameters mass and width of these objects by combining the information from the PWA results obtained in the 11 $t'$ bins. We extract the relative branching fractions of the $\rho(770) \pi$ and $f_2(1270) \pi$ decays of $a_2(1320)$ and $a_4(2040)$, where the former one is measured for the first time. In a novel approach, we extract the $t'$ dependence of the intensity of the resonances and of their phases. The $t'$ dependence of the intensities of most resonances differs distinctly from the $t'$ dependence of the nonresonant components. For the first time, we determine the $t'$ dependence of the phases of the production amplitudes and confirm that the production mechanism of the Pomeron exchange is common to all resonances.
Real and imaginary parts of the normalized transition amplitudes $\mathcal{T}_a$ of the 14 selected partial waves in the 1100 $(m_{3\pi}, t')$ cells (see Eq. (12) in the paper). The wave index $a$ represents the quantum numbers that uniquely define the partial wave. The quantum numbers are given by the shorthand notation $J^{PC} M^\varepsilon [$isobar$] \pi L$. We use this notation to label the transition amplitudes in the column headers. The $m_{3\pi}$ values that are given in the first column correspond to the bin centers. Each of the 100 $m_{3\pi}$ bins is 20 MeV/$c^2$ wide. Since the 11 $t'$ bins are non-equidistant, the lower and upper bounds of each $t'$ bin are given in the column headers. The transition amplitudes define the spin-density matrix elements $\varrho_{ab}$ for waves $a$ and $b$ according to Eq. (18). The spin-density matrix enters the resonance-model fit via Eqs. (33) and (34). The transition amplitudes are normalized via Eqs. (9), (16), and (17) such that the partial-wave intensities $\varrho_{aa} = |\mathcal{T}_a|^2$ are given in units of acceptance-corrected number of events. The relative phase $\Delta\phi_{ab}$ between two waves $a$ and $b$ is given by $\arg(\varrho_{ab}) = \arg(\mathcal{T}_a) - \arg(\mathcal{T}_b)$. Note that only relative phases are well-defined. The phase of the $1^{++}0^+ \rho(770) \pi S$ wave was set to $0^\circ$ so that the corresponding transition amplitudes are real-valued. In the PWA model, some waves are excluded in the region of low $m_{3\pi}$ (see paper and [Phys. Rev. D 95, 032004 (2017)] for a detailed description of the PWA model). For these waves, the transition amplitudes are set to zero. The tables with the covariance matrices of the transition amplitudes for all 1100 $(m_{3\pi}, t')$ cells can be downloaded via the 'Additional Resources' for this table.
Decay phase-space volume $I_{aa}$ for the 14 selected partial waves as a function of $m_{3\pi}$, normalized such that $I_{aa}(m_{3\pi} = 2.5~\text{GeV}/c^2) = 1$. The wave index $a$ represents the quantum numbers that uniquely define the partial wave. The quantum numbers are given by the shorthand notation $J^{PC} M^\varepsilon [$isobar$] \pi L$. We use this notation to label the decay phase-space volume in the column headers. The labels are identical to the ones used in the column headers of the table of the transition amplitudes. $I_{aa}$ is calculated using Monte Carlo integration techniques for fixed $m_{3\pi}$ values, which are given in the first column, in the range from 0.5 to 2.5 GeV/$c^2$ in steps of 10 MeV/$c^2$. The statistical uncertainties given for $I_{aa}$ are due to the finite number of Monte Carlo events. $I_{aa}(m_{3\pi})$ is defined in Eq. (6) in the paper and appears in the resonance model in Eqs. (19) and (20).
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 Fermilab hybrid 30-in. bubble-chamber spectrometer was exposed to a tagged 147-GeV/c positive beam containing π+, K+, and p. A sample of 3003 K+p, 19410 pp, and 20745 π+p interactions is used to derive σn, 〈n〉, f2cc, and 〈nc〉D for each beam particle. These values are compared to values obtained at other, mostly lower, beam momenta. The overall dependence of 〈n〉 on Ea, the available center-of-mass energy, for these three reactions as well as π−p and pp interactions has been determined.
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As part of a program of measurements of the πp system we have measured the backward differential cross section for π+p elastic scattering at 16 momenta from 1.25 to 2.0 GeV/c inclusive. The angular region covered is -0.46 to -0.97 in cosθc.m.. The high resolution in u of 0.03 to 0.04 (GeV/c)2, together with good statistics, enables a detailed examination of the momentum and angular dependence of structure in this channel. The data are compared with distributions from other experiments and with the most recent phaseshift fit.
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We have used an optical spark-chamber spectrometer to perform a systematic study of the reaction π−p→ΛK0 at beam momenta between 930 and 1130 MeV/c. The cross section, angular distribution, and Λ polarization have been measured. We present our complete data from a sample of 11 400 events along with Legendre polynomial coefficients for the angular distributions. No striking cross-section enhancement at ΣK threshold is observed, but there is evidence for a small cusp effect. A simple model which takes account of the ΣK channel provides a good fit to our data.
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The inclusive production of ρ0 mesons was measured in γp andh±p collisions at beam energies of 65 GeV≦Eγ≦175 GeV andEh=80, 140 GeV, respectively, whereh is π orK. Cross sections were determined for all beams and energies as functions ofxF (−0.1≦xF≦1.0),pT (0≦pT≦3.5 GeV/c) and the polar decay angle of the ρ0 by fitting the ρ0 signal in π+π- mass distributions. The ρ0 line shape is found to be distorted from a pure Breit-Wigner distribution throughout most of thexF−pT plane for both photon and hadron beams and a simple explanation is suggested. Throughout the paper emphasis is put on the comparison of photon and hadron beam data. The comparison of cross sections of γp andhp data provides a measure of the Vector Meson Dominance factor throughout thexF−pT range of the ρ0. The ρ0 production at lowpT can be described for both photon and hadron beams by a triple regge model at largexF. Similarly central production is well described by the quark-antiquark fusion model. At largepT there is an excess of ρ0 photoproduction which is consistent with the expected onset of pointlike photon interactions.
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The energy dependence of the average of the charged multiplicity and its dispersion in π + /K + /p interaction on protons at 147 GeV/ c is found to be the same as in e + e − annihilations if an “effective energy” variable is used instead of the total energy. The effective energy S eff is defined as the invariant mass of all secondaries left after the two leading particles have been removed. Fitting the expression aS eff b to the average charge multiplicity 〈 n ch 〉, we find the power b to be in good agreement with the value of 0.25 predicted by Fermi's statistical model and by Landau's hydrodynamical model.
BINS IN WEFF SELECTED SO AS TO YIELD 200 EVENTS IN EACH BIN.
200 EVENTS IN EACH BIN IN WEFF.
50 EVENTS IN EACH BIN IN WEFF.
We have measured the backward differential cross section in π−p elastic scattering at 31 momenta from 1.28 to 3.0 GeV/c. These measurements covered the center-of-mass angular range of 125°-178° corresponding to −0.570≲cosθc.m.≲−0.999. Considerable structure in the angular distribution is found. We compare these data with data from other experimets and to predictions made by the latest phase-shift solution. We find, in general, good agreement with other data in the few regions of overlap. The fits from the phase-shift solution do not accurately reproduce these data at low momenta below 1.9 GeV/c but give excellent agreement above this momentum.
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The differential cross section for π ± p elastic scattering below 2 GeV/ c has been measured at small forward pion angles by an electronics experiment. The interference effects observed between the Coulomb and the nuclear interaction have been used to determine the magnitude and sign of the real parts of the π ± p forward scattering amplitude. The latter are compared to the values predicted by the dispersion relations.
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Inclusive production of ϕ,K*0, and\(\overline {K*^0 } \) mesons has been measured in γp, π±p andK± p collisions at beam energies of 65 GeV<Eγ<175 GeV andEπ/K =80 and 140 GeV. Cross sections have been determined over the range 0<xF<1.0 and 0<PT<1.8 GeV/c. Emphasis is put on the comparison of cross sections for different projectiles as a function ofxF so as to study the effects of common quarks between the beam particle and the detected ϕ,K*0 or\(\overline {K*^0 } \). The data are compared with a parton fusion model. Many features of the data are well explained. In detail the strange quark appears to carry a large fraction of the kaon momentum and the contribution of the valence quarks from the proton is small.
Statistical errors only.
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Statistical errors only.. An entry 0.00 indicates a statistical error of < 0.005.
The spin rotation parameter R has been measured at CERN, for π ± p at 6 GeV c and for π − p at 16 GeV c , with t ranging from −0.19 to −0.51 ( GeV c ) 2 . The parameter A was measured for π − p at 6 GeV c in the interval between t =−0.19 and minus;0.41 ( GeV c ) 2 . The averaged values are the following; R (+6) =−0.08±0.04, R (−6) =−0.23±0.05 and R (−16) =−0.23±0.05. The values obtained for A are close to +1.
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We study the spin-exotic $J^{PC} = 1^{-+}$ amplitude in single-diffractive dissociation of 190 GeV$/c$ pions into $\pi^-\pi^-\pi^+$ using a hydrogen target and confirm the $\pi_1(1600) \to \rho(770) \pi$ amplitude, which interferes with a nonresonant $1^{-+}$ amplitude. We demonstrate that conflicting conclusions from previous studies on these amplitudes can be attributed to different analysis models and different treatment of the dependence of the amplitudes on the squared four-momentum transfer and we thus reconcile their experimental findings. We study the nonresonant contributions to the $\pi^-\pi^-\pi^+$ final state using pseudo-data generated on the basis of a Deck model. Subjecting pseudo-data and real data to the same partial-wave analysis, we find good agreement concerning the spectral shape and its dependence on the squared four-momentum transfer for the $J^{PC} = 1^{-+}$ amplitude and also for amplitudes with other $J^{PC}$ quantum numbers. We investigate for the first time the amplitude of the $\pi^-\pi^+$ subsystem with $J^{PC} = 1^{--}$ in the $3\pi$ amplitude with $J^{PC} = 1^{-+}$ employing the novel freed-isobar analysis scheme. We reveal this $\pi^-\pi^+$ amplitude to be dominated by the $\rho(770)$ for both the $\pi_1(1600)$ and the nonresonant contribution. We determine the $\rho(770)$ resonance parameters within the three-pion final state. These findings largely confirm the underlying assumptions for the isobar model used in all previous partial-wave analyses addressing the $J^{PC} = 1^{-+}$ amplitude.
Results for the spin-exotic $1^{-+}1^+[\pi\pi]_{1^{-\,-}}\pi P$ wave from the free-isobar partial-wave analysis performed in the first $t^\prime$ bin from $0.100$ to $0.141\;(\text{GeV}/c)^2$. The plotted values represent the intensity of the coherent sum of the dynamic isobar amplitudes $\{\mathcal{T}_k^\text{fit}\}$ as a function of $m_{3\pi}$, where the coherent sums run over all $m_{\pi^-\pi^+}$ bins indexed by $k$. These intensity values are given in number of events per $40\;\text{MeV}/c^2$ $m_{3\pi}$ interval and correspond to the orange points in Fig. 8(a). In the "Resources" section of this $t^\prime$ bin, we provide the JSON file named <code>transition_amplitudes_tBin_0.json</code> for download, which contains for each $m_{3\pi}$ bin the values of the transition amplitudes $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, their covariances, and further information. The data in this JSON file are organized in independent bins of $m_{3\pi}$. The information in these bins can be accessed via the key <code>m3pi_bin_<#>_t_prime_bin_0</code>. Each independent $m_{3\pi}$ bin contains <ul> <li>the kinematic ranges of the $(m_{3\pi}, t^\prime)$ cell, which are accessible via the keys <code>m3pi_lower_limit</code>, <code>m3pi_upper_limit</code>, <code>t_prime_lower_limit</code>, and <code>t_prime_upper_limit</code>.</li> <li>the $m_{\pi^-\pi^+}$ bin borders, which are accessible via the keys <code>m2pi_lower_limits</code> and <code>m2pi_upper_limits</code>.</li> <li>the real and imaginary parts of the transition amplitudes $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, which are accessible via the keys <code>transition_amplitudes_real_part</code> and <code>transition_amplitudes_imag_part</code>, respectively.</li> <li>the covariance matrix of the real and imaginary parts of the $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, which is accessible via the key <code>covariance_matrix</code>. Note that this matrix is real-valued and that its rows and columns are indexed such that $(\Re,\Im)$ pairs of the transition amplitudes are arranged with increasing $k$.</li> <li>the normalization factors $\mathcal{N}_a$ in Eq. (13) for all $m_{\pi^-\pi^+}$ bins, which are accessible via the key <code>normalization_factors</code>.</li> <li>the shape of the zero mode, i.e., the values of $\tilde\Delta_k$ for all $m_{\pi^-\pi^+}$ bins, which is accessible via the key <code>zero_mode_shape</code>.</li> <li>the reference wave, which is accessible via the key <code>reference_wave</code>. Note that this is always the $4^{++}1^+\rho(770)\pi G$ wave.</li> </ul>
Results for the spin-exotic $1^{-+}1^+[\pi\pi]_{1^{-\,-}}\pi P$ wave from the free-isobar partial-wave analysis performed in the second $t^\prime$ bin from $0.141$ to $0.194\;(\text{GeV}/c)^2$. The plotted values represent the intensity of the coherent sum of the dynamic isobar amplitudes $\{\mathcal{T}_k^\text{fit}\}$ as a function of $m_{3\pi}$, where the coherent sums run over all $m_{\pi^-\pi^+}$ bins indexed by $k$. These intensity values are given in number of events per $40\;\text{MeV}/c^2$ $m_{3\pi}$ interval and correspond to the orange points in Fig. 15(a) in the supplemental material of the paper. In the "Resources" section of this $t^\prime$ bin, we provide the JSON file named <code>transition_amplitudes_tBin_1.json</code> for download, which contains for each $m_{3\pi}$ bin the values of the transition amplitudes $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, their covariances, and further information. The data in this JSON file are organized in independent bins of $m_{3\pi}$. The information in these bins can be accessed via the key <code>m3pi_bin_<#>_t_prime_bin_1</code>. Each independent $m_{3\pi}$ bin contains <ul> <li>the kinematic ranges of the $(m_{3\pi}, t^\prime)$ cell, which are accessible via the keys <code>m3pi_lower_limit</code>, <code>m3pi_upper_limit</code>, <code>t_prime_lower_limit</code>, and <code>t_prime_upper_limit</code>.</li> <li>the $m_{\pi^-\pi^+}$ bin borders, which are accessible via the keys <code>m2pi_lower_limits</code> and <code>m2pi_upper_limits</code>.</li> <li>the real and imaginary parts of the transition amplitudes $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, which are accessible via the keys <code>transition_amplitudes_real_part</code> and <code>transition_amplitudes_imag_part</code>, respectively.</li> <li>the covariance matrix of the real and imaginary parts of the $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, which is accessible via the key <code>covariance_matrix</code>. Note that this matrix is real-valued and that its rows and columns are indexed such that $(\Re,\Im)$ pairs of the transition amplitudes are arranged with increasing $k$.</li> <li>the normalization factors $\mathcal{N}_a$ in Eq. (13) for all $m_{\pi^-\pi^+}$ bins, which are accessible via the key <code>normalization_factors</code>.</li> <li>the shape of the zero mode, i.e., the values of $\tilde\Delta_k$ for all $m_{\pi^-\pi^+}$ bins, which is accessible via the key <code>zero_mode_shape</code>.</li> <li>the reference wave, which is accessible via the key <code>reference_wave</code>. Note that this is always the $4^{++}1^+\rho(770)\pi G$ wave.</li> </ul>
Results for the spin-exotic $1^{-+}1^+[\pi\pi]_{1^{-\,-}}\pi P$ wave from the free-isobar partial-wave analysis performed in the third $t^\prime$ bin from $0.194$ to $0.326\;(\text{GeV}/c)^2$. The plotted values represent the intensity of the coherent sum of the dynamic isobar amplitudes $\{\mathcal{T}_k^\text{fit}\}$ as a function of $m_{3\pi}$, where the coherent sums run over all $m_{\pi^-\pi^+}$ bins indexed by $k$. These intensity values are given in number of events per $40\;\text{MeV}/c^2$ $m_{3\pi}$ interval and correspond to the orange points in Fig. 15(b) in the supplemental material of the paper. In the "Resources" section of this $t^\prime$ bin, we provide the JSON file named <code>transition_amplitudes_tBin_2.json</code> for download, which contains for each $m_{3\pi}$ bin the values of the transition amplitudes $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, their covariances, and further information. The data in this JSON file are organized in independent bins of $m_{3\pi}$. The information in these bins can be accessed via the key <code>m3pi_bin_<#>_t_prime_bin_2</code>. Each independent $m_{3\pi}$ bin contains <ul> <li>the kinematic ranges of the $(m_{3\pi}, t^\prime)$ cell, which are accessible via the keys <code>m3pi_lower_limit</code>, <code>m3pi_upper_limit</code>, <code>t_prime_lower_limit</code>, and <code>t_prime_upper_limit</code>.</li> <li>the $m_{\pi^-\pi^+}$ bin borders, which are accessible via the keys <code>m2pi_lower_limits</code> and <code>m2pi_upper_limits</code>.</li> <li>the real and imaginary parts of the transition amplitudes $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, which are accessible via the keys <code>transition_amplitudes_real_part</code> and <code>transition_amplitudes_imag_part</code>, respectively.</li> <li>the covariance matrix of the real and imaginary parts of the $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, which is accessible via the key <code>covariance_matrix</code>. Note that this matrix is real-valued and that its rows and columns are indexed such that $(\Re,\Im)$ pairs of the transition amplitudes are arranged with increasing $k$.</li> <li>the normalization factors $\mathcal{N}_a$ in Eq. (13) for all $m_{\pi^-\pi^+}$ bins, which are accessible via the key <code>normalization_factors</code>.</li> <li>the shape of the zero mode, i.e., the values of $\tilde\Delta_k$ for all $m_{\pi^-\pi^+}$ bins, which is accessible via the key <code>zero_mode_shape</code>.</li> <li>the reference wave, which is accessible via the key <code>reference_wave</code>. Note that this is always the $4^{++}1^+\rho(770)\pi G$ wave.</li> </ul>
Measurements are reported of inclusivef2(1270) andf0(975) production in γp, π±p andK±p collisions at photon beam energies of 65 to 175 GeV and hadron beam energies of 80 and 140 GeV. Thef2 andf0 mesons were found at masses of 1.250 GeV and 0.961 GeV respectively. Inclusivef2 production at lowxF was found to have a similarpT dependence for each beam type, whereas an additional pion-exchange contribution was found for production by pions at highxF. Cross sections are compared with those for ρ0 production and give no indication of a non-q\(\bar q\) component in eitherf-meson state.
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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 analysis of exclusive neutral strange particle production in the reactions π − p → K° Λ + K° Σ ° and p p → Λ Λ + Λ Σ° + c.c. at 3.15, 4.95, 7.9 and 12 GeV/ c yielded the differential cross section distributions up to about 90° c.m.s. scattering angle and the Λ-particle polarization at large transverse momentum. Applying a fit to d σ /d t ∞ s − n resulted in n = 8.6 ± 0.9 for the K° Λ + K° Σ° final state which is compatible with the quark counting rule n = 8 for meson-baryon reactions. The average Λ polarization around t = −1.6 (GeV/ c ) 2 was P Λ = 0.79 ± 0.17 at 3.15 GeV/ c beam energy.
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Single charged-particle inclusive cross sections for photon, pion and kaon beams on hydrogen at the CERN-SPS are presented as functions ofpT andxF. Data cover the range 0.0<pT<5.0 GeV/c and 0.0<xF<1.0 at incident momenta from 70 to 170 GeV/c. The comparison between photon- and hadron-induced data indicates a relative excess of particles withpT>1.6 GeV/c for the photon-induced data. Using the hadron-induced data to estimate the hadronic behaviour of the photon, the difference distributions and ratios of cross sections are a measure of the contribution of the point-like photon interactions. The data are compared with QCD calculations and show broadly similar features.
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We have measured the cross section, the angular distribution, and the Λ polarization for the reaction π−p→ΛK0. A spark-chamber spectrometer was used to collect 8400 ΛK0 events at fourteen beam momenta near ΣK threshold. Our data do not show the prominent cross-section enhancement suggested by some previous experiments. However, detailed structure in the cross section and the angular distribution agrees well with a simple model which includes a cusp effect at ΣK threshold.
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BACKWARD-FORWARD PRODUCTION ASYMMETRY.
AVERAGE LAMBDA POLARIZATION.
This Letter reports measurements of the ratios of $\pi$, K, and p production at large values of transverse momentum in $\pi^- −p$ collisions. The charge ratios, such as $\frac {\pi^−} {\pi^+}$, $\frac {K^−} {K^+}$, and $\frac {\overline{p}}{p}$ are seen to be quite different from those measured in p −p collisions. These ratios are sensitive tests of hard-scattering models, and are compared with theoretical predictions. The particle ratios have also been studied as a function of center-of-mass angle ($\theta^*$) at $\theta^*$ = 90°, 77°, and 60°.
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Measurements are reported of inclusive production of π0-mesons in the beam fragmentation region in γp, πp andKp collisions. Results include the ratio of π0 production inKp and πp collisions, showing reduced production from fragmentation of theK-meson, and the ratio of π0 production in photon and hadron collisions which shows agreement with modified Vector Meson Dominance at lowPT, and departures at higherPT signalling the onset of direct photon reactions. The pattern of departure from Feynman scaling at highPT points to a contribution of hard parton-parton collisions in both γp and πp collisions.
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We have measured differential cross sections for both π+p and π−p elastic scattering at incident-pion kinetic energies of 30, 50, 70, and 90 MeV in the center-of-mass angular range between 50° and 150°. The experiment detected pions scattered from a liquid-hydrogen target with multiwire proportional chambers and scintillation-counter range telescopes. The relative accuracy of each angular distribution is better than 5%, while the absolute cross sections have uncertainties of 4% to 25%. Our results for the absolute cross section for π+p scattering at 30 and 90 MeV are inconsistent with previous measurements. Our π−p measurements comprise the first extensive set of precision differential cross sections below 90 MeV.
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A high-statistics search for resonances in the π − p total cross section has been carried out over the incident momentum region from 2 to 14 GeV/ c . The measurements were performed with a transmission technique using multiwire proportional chambers in place of the conventional counter arrays. A microprocessor unit was used for the on-line analysis of the data, allowing a total of ≈ 50 000 events to be examined in a 300 ms burst. The search aimed at detecting the possible formation in π − p collisions of narrow non-strange baryon resonances. The momentum region was uniformly scanned with a total of ≈4500 mmeasurements in fixed fractional momentum steps of d P / P = 5 × 10 −4 . The relative statistical precision of each measurement was d σ / σ = ±0.3%. Within these limits no significant structure was detected.
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Data on 6.2 GeV/ c π − p and K − p elastic scattering cross sections are presented in the range 0.3 < − t < 10.7 (GeV/ c ) 2 .
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From the study of the reaction π − p→p F p p π − using a fast proton (p F ) trigger device in the CERN Omega spectrometer, we find evidence for two narrow p p states produced mainly in association with a Δ° (1232) and a N° (1520). The statistical significance of each peak is greater than 6 standard deviations. Masses and natural widths of these resonances are respectively M = 2020 ± 3 MeV , Λ 1 = 24 ± 12 MeV and M 2 = 2204 ± 5 MeV, Λ 2 = 16 −16 +20 MeV. Our data are consistent with a small production of the narrow ∼ 1935 MeV resonance already reported. Production cross sections for these new p p resonances are given.
ERRORS TAKE INTO ACCOUNT STATISTICAL ERRORS AND BACKGROUND SUBTRACTION UNCERTAINTY BUT NOT ACCEPTANCE CORRECTIONS UNCERTAINTY OF 15 PCT.
We report on a study ofρ0 andf2 inclusive production in π−−p interactions at 360 GeV/c, using the LEBC-EHS set-up at CERN and reconstructing about 165000 events. Theρ0,f2 andρ30 cross sections are determined forxF>0,xF>0.4 andxF>0.6 respectively and theρ0 andf2 Feynman-x distributions and transverse momentum distributions are presented.
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We present a study of A − 2 →K O S K − from the reaction π − p→K O S K − p at 4.5 GeV/ c in the 82-in. hydrogen bubble chamber. From a sample of 542 events from this final state, the mass (and its possible fine structure), width, production distribution and decay correlations of A − 2 are examined.
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We have studied the inclusive production of K*±(890) and Y*±(1385) in pp, π+p, and K+p interactions at 147 GeV/c. The experiment used the Fermilab 30-inch hydrogen bubble chamber with the hybrid spectrometer system. Results are based on a sample of 1916 observed KS and 932 observed A. Inclusive cross sections are given for K*± and Y*± production from the three beams, and comparisons are made with experiments at other energies. Feynman-x and transverse-momentum-squared distributions are also calculated. The results suggest that the K*− is entirely produced in the central region, while the K*+ includes a component from beam fragmentation. Comparisons are made with the additive quark model.
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SIG(C=BACKWARD) = SIG(-UP<1 GEV**2)/(1-EXP(-SLOPE)). UP DISTRIBUTION OF EVENTS HAS A PERFECT EXPONENTIAL SHAPE.
Data on the reactions π − p → p π − , p p → π + π − , K − p → pK and p p → p p at 8 and 12 GeV/ c are presented. Our results agree with line reversal symmetry (between π − p → p π − and p p → π + π − ), Regge pole behaviour for non-exotic reactions ( π − p → p π − , p p → π + π − ), and universal behaviour for exotic reactions ( p p → p p , K − p → pK − ) with d σ /d u | u =0 ∼ s −10 excluding the existence of a “glory” mechanism in p p elastic backward scattering in our energy range.
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We have measured the slope parameter of the π 0 electromagnetic form factor by measuring the partial branching ratio of the Dalitz decay π 0 → γe + e − into high-invariant-mass electron-positron pairs. We obtain a value a =0.026 with a total (statistical and systematic) error of ±0.054, in agreement with vector dominance and quark loop calculations.
The PI0 form factor is parameterized as F(M(ee)**2) = 1 + SLOPE*(M(ee)/M(pi))**2. Two metod are used (see text for detail).
We present the results of a spin determination of the g 1 − (1640) meson from an analysis of its dipion decay mode (π − π 0 ), and find that spin three (or maybe greater) is favored [1,2]. We also report on the observation of an isospin one KK̄ enhancement at 1640 MeV which is consistent with a new decay mode of the g meson. A relative branching ratio of (K K ̄ /ππ) = 8 ± 3 8 % is obtain from our analysis.
The values of the cross sections were presented for reactions with KS finalstates for visible KS decays only.
The cross section value is corrected for invisible KS decay.
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