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The ITEP-PNPI collaboration presents the first results of the spin rotation parameter A + measurements in the second resonance region. The experiment was performed at the ITEP accelerator at a positive pion beam momentum 1.43 GeV/c for scattering angles θ cm = 127° and 133°. The setup was based on a polarized proton target and a carbon-plate polarimeter. The obtained data is compared with the predictions of the existing partial-wave analyses.
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We report measurements of the polarization parameters in π+p and π−p elastic scattering at an incident momentum of 100 GeV/c. The results cover the range 0.18<~−t<~1.4 GeV2 and are in agreement with current Regge-model predictions.
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Based on a sample of 22 four-prong D 0 / D 0 decays produced in hydrogen by 360 GeV/ c π − , we present the following new results: mean lifetime τ = (3.5 −0.9 +1.4 ) x 10 −13 s ; production cross section for x F > 0.0, σ = (10.3 ± 3.5) ωb ; the D → K ± π ± π + π − branching ratio = (7.1 ± 2.5)%.
No description provided.
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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Measured values of the differential cross section for pion-nucleon charge exchange are presented at momenta 148, 174, 188, 212, 238, 271, 298, and 323 MeV/c, a region dominated by the Delta resonance. Complete angular distributions were obtained using the Crystal Ball detector at the Alternating Gradient Synchrotron (AGS) at Brookhaven National Laboratory (BNL). Statistical uncertainties of the differential cross sections are typically 2-6%, exceptions being the results at the lowest momentum and at the most forward measurements of the five lowest momenta. We estimate the systematic uncertainties to be 3-6%.
The errors shown are statistical only.
The errors shown are statistical only.
The total charge-exchange reaction cross section as a function of pion momentum obtained by integrating the differential cross sections. The errors shown are the total and statistical errors.
Results of a high-statistics study of π++p→ρ++p at 1.55-1.84 GeVc are consistent with dominance of π and ω exchange close to threshold. A pronounced dip in ρ00sdσdt at −t≃0.4 GeV2 may be attributed to pion exchange with strong absorption.
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We report on a measurement for the branching-ratio X 0 → 2γ X 0 ar all. Our result is X 0 → 2γ X 0 → all = (2.9 ± 0.9)% .
BY COMPARISON WITH THE KNOWN ETA PRODUCTION CROSS SECTION.
The reaction π − p → ηφ has been studied at 1.8 GeV/ c incident pion momentum using the Bologna-CERN NBC set-up, in order to investigate the electromagnetic decay mode φ → ηγ . We observed (27 ± 6) events, yielding a branching ratio Γ(φ → ηγ) Γ(φ → total ) = (7.3 ± 1.9)% . The theoretical implications of this result are discussed.
ASSUMING THE TOTAL PHI CROSS SECTION IS 35 +- 5 MUB, THIS YIELDS THE BRANCHING RATIO OF (7.3 +- 1.9) PCT FOR PHI --> ETA GAMMA.
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No description provided.
We report a new measurement of the differential cross section for π−p→π0n from pπ=649 to 752 MeV/c, which is around the opening of the η channel (685 MeV/c). Our data support the main features of the π−p charge-exchange differential cross sections generated by the SAID πN partial-wave analysis. The opening of the η channel has a clear effect on the shape of the excitation function for dσ(π−p→π0n), which is most noticeable in the backward direction.
Differential cross section for incident pion momentum 649, 654 and 657 MeV.
Differential cross section for incident pion momentum 661, 666 and 669 MeV.
Differential cross section for incident pion momentum 673, 678 and 681 MeV.
The production of ρ 0 (770) and f(1270) is studied in π − p interactions at 16 GeV/ c . By comparison with inclusive K ∗0 production in the reaction K − p → K ∗0 + anything, and with inclusive ρ 0 production in the reaction pp → ρ 0 + anything, it is found that the data can be interpreted in terms of two production processes: the central production of resonances and the fragmentation of the beam particle. For the π − p reaction, the inclusive ρ 0 beam fragmentation cross section is 3.1 ± 0.3 mb while that for central production is 1.6 ± 0.5 mb. The ρ 0 central production cross section is consistent with increasing with energy as ln s behaviour. The ratio of ρ 0 to π − inclusive cross sections (excluding the leading π − ) is ∼0.2, independent of energy. The ρ 0 to π − ratio increases as a function of p T to a constant value of ∼ 1 2 above 1 GeV/ c . The ρ (charged and neutral) and f decays account for (25 ± 4)% and (1.4 ± 0.3)%, respectively, of all pions produced.
No description provided.
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Measurements were made of the cross section of the reactions π − p → ν ′(958)n, η ′ → 2 γ at momenta at 15, 20, 25, 30 and 40 GeV/c. The experiment was carried out on the IHEP 70 GeV accelerator using the 648 channel hodoscope spectrometer NICE for γ-ray detection. A total of 6000 η′ mesons were recorded. A sharp drop is seen in the differential cross section for t → 0. The dependences of the differential cross sections for the π − p → η ′n and π − p → η n on t are identical. On the basis of the ratio of the cross sections for these reactions at t = 0, i.e. R( η′ n ) t=0 = 0.55 ± 0.06 , the singlet-octet mixing angle for pseudoscalar mesons was determined to be β = −(18.2 ± 1.4)°.
DATA AT 20, 25 AND 30 GEV/C SUMMED AND NORMALIZED TO THE CROSS SECTION AT 25 GEV/C.
DATA AT 20, 25 AND 30 GEV/C SUMMED AND NORMALIZED TO THE CROSS SECTION AT 25 GEV/C.
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.
No description provided.
No description provided.
CROSS SECTIONS FOR DIFFRACTION DISSOCIATION OF BEAM. FEYNMAN X OF OUTGOING PROTON <-0.96.
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In this paper we present the π + p differential elastic scattering cross sections at five momenta between 0.6 and 0.8 GeV/ c . The data were collected in a bubble chamber exposure and consequently are susceptible to different systematic errors from counter experiments. Our results are generally in good agreement with those of counter experiments in the same momentum range and with the predictions of the various elastic partial wave analyses. The majority of partial wave analyses do not however yield parameters which fit our data in detail without modification.
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Upper limits are presented for the differential cross section in the reactions π−p→K+Σ− and π−p→K+Y*−(1385) with small momentum transfer from π− to K+.
EXTRAPOLATED TO T=0 ASSUMING SLOPE IS 5 GEV**-2.
ISOTROPIC ANGULAR DISTRIBUTION ASSUMED IN GIVEN T-RANGE.
A high-statistics measurement of the reaction π − p→ η n; η →2 γ has been performed at the 70 GeV Serpukhov accelerator for 15, 20, 25, 30 and 40 GeV/ c incident pion momentum using the NICE set-up with its associated 648-channel hodoscope spectrometer for γ-ray detection. It is found that the spin-flip and non-spin-flip amplitudes can be parametrized, for small | t |, as exponentials with the same slopes to within a few percent. For | t | ≳ 1 (GeV/ c ) 2 there is a break in the differential cross section. In addition, the A 2 effective trajectory deviates markedly for | t | ≳ 1 GeV/ c ) 2 from the linear behaviour valid for smaller | t |.
No description provided.
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Measurements of the differential cross section for the reactions π+p→K+Σ+ and π+p→K+Y*+(1385) are reported at 3.5, 3.75, 4.0, 4.25, 4.5, 4.75, 5.0, 6.0, 10.0, and 14.0 GeV/c. Polarization in π+p→K+Σ+ is also reported at 6.0, 10.0, and 14.0 GeV/c. At small |t|, the cross section for π+p→K+Σ+ is well described by an exponential Aebt with slopes in the range b≈8−10 (GeV/c)−2; for |t|>0.5 (GeV/c)2 this slope decreases considerably. The cross section for π+p→K+Y*+(1385) is well described for |t|>0.2 (GeV/c)2 by a single exponential of slope about half that for π+p→K+Σ+; there is no break near |t|>0.5 (GeV/c)2. We observe a dip in this cross section near t=0. The polarization in π+p→K+Σ+ is consistent with zero for |t|<0.4 (GeV/c)2 and becomes large and positive for larger |t|.
No description provided.
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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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K−−p interactions in the Columbia-BNL 30-in. hydrogen bubble chamber were studied at nine momenta from 594 to 820 MeVc. The results for elastic-scattering and zero-prong-plus-V0 events are presented here. Differential cross sections are given for the K−p, K¯0n, and Λπ0 final states. A fit to the K¯N channels was obtained which shows the effects of a 32− resonance at 1701 MeV. This energy is appreciably displaced from the peak in the inelastic cross section.
No description provided.
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The reactions π−p→K0Λ,K0Σ0 are studied at an incident momentum of 3.95 GeV/c using data from a high statistics bubble chamber experiment corresponding to ∼90 events/μb. The differential cross sections and hyperon polarizations are presented and compared with existing data from earlier electronic experiments. The data in the forward hemisphere are used to perform an amplitude analysis of the 0−1/2+→0−1/2+ hypercharge exchange processes.
No description provided.
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The reactionsπ−p→K0∑0(1385) andπ−p→K+∑−(1385) are studied at an incident momentum of 3.95 GeV/c using data from a high statistics bubble chamber experiment corresponding to approximately 90 events/μb. The total and differential cross sections and the density matrix elements of the Σ(1385) are presented. The results are compared with those obtained for the related processesπpp→K+∑+(1385) and\(K^ -p \to \pi ^ \mp\sum ^ \pm(1385)\) in this energy range. Evidence is presented for the existence of production mechanisms with exotic exchanges in thet channel.
FROM THE CHANNEL PI- P --> LAMBDA K0 PI0 WHICH HAS A CROSS SECTION OF 72 +- 4 MUB.
FROM THE CHANNEL PI- P --> LAMBDA K+ PI- WHICH HAS A CROSS SECTION OF 79 +- 3 MUB.
FORWARD CROSS SECTION.
A description is given of an experimental study of exchange degeneracy (EXD) in hypercharge-exchange reactions using the line-reversed partners π + p→K + Σ + (K − p→ π − Σ + ) and π + p→ K + Σ + (1385) (K − p→ π − Σ + (1385)) at incident momenta of 7.0 and 10.1 GeV/ c . Both pairs of reaction were measured in the same apparatus, with particular care being taken to minimize relative normalization errors. For the Σ production reactions we present high statistics measurements of the differential cross sections and polarizations from t ′=0 to large t . The general trends of the data agree with naive expectations from weak EXD. The cross-section difference in the extreme forward direction at the higher momentum is consistent with zero and there is a general reduction in the cross-section differences going from the lower to the higher momentum. The polarizations are approximately equal in magnitude and of opposite sign between the two reactions. On the other hand, the data do not agree with the detailed predictions of EXD. The slope for the positive reaction is systematically steeper in the forward region than for the negative reaction and there is a complex s and t dependence for the cross-section differences including a cross-over at t ⋍ −0.8( GeV /c) 2 . For the Σ(1385) production reactions, we present differential cross-section measurements in the forward region (| t |<0.3(GeV/ c ) 2 ). The cross-section differences are substantial and essentially constant over the s and t ranges studied.
THE RESULTS AT 10.1 GEV WERE FIRST PUBLISHED IN A. BERGLUND ET AL., PL 60B, 117 (1975), THE RECORD OF WHICH INCLUDES THE TABULATED DATA.
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.
Integral cross sections for the scattering of pions by protons into angles greater than 30° (lab) have been measured at a wide range of energies spanning the delta resonance using liquid hydrogen targets. Cross sections were measured for π+p scattering at 40 energies from 39.8 to 283.9 MeV and for π−p at 15 energies from 80.0 to 283.9 MeV. Comparisons with phase shift predictions from the Karlsruhe group show good agreement on resonance but significant deviations below 100 MeV.
The uncertainties shown include statistical and systematic contributions.
The uncertainties shown include statistical and systematic contributions.
Result of cross section measurements for the reaction π − p → π − π + n are presented. They cover a range of incident pion momenta between 295 and 450 MeV/ c . It is the first time that the cross section has been measured so close to threshold. The experiment was performed with Omicron, a large-solid-angle spectrometer, which enables a measurement of the full set of kinematic variables. In the region of overlap there is a good agreement with other experiments. The extracted value for the chiral-symmetry-breaking parameter ξ is seen to be largely extrapolition dependent but the measured value of -0.5±0.8 leaves Weinberg's prediction of ξ =0 the only remaining choice.
No description provided.
A detailed study ofJ/ψ hadronic production has been performed in a high statistics experiment (more than 1.5 106J/ψ observed in their dimuon decay mode). Data have been taken with incident π±,K±,p±, on hydrogen and platinum targets, at 150, 200 and 280 GeV/c. We find from the observed nuclear dependance of the cross sections, that about 18% of theJ/ψ are produced diffractively. Using known structure functions of the quarks in the nucleon and in the pion, we derive estimations for the gluon structure functions.
No description provided.
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We present differential cross-section data for the reaction π+p→π+p near 180° in the center-of-mass system at beam momenta between 3.25 GeVc and 10 GeVc.
No description provided.
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Total and differential cross sections for π−p elastic scattering are presented at 35 energies between 1400 and 2000 MeV.
No description provided.
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The π−p charge-exchange analyzing power has been measured from 547 to 687 MeV/c in the center-of-mass angular range -0.9≤cosθ̃π≤0.9 using a transversely polarized target. The recoil neutron was detected in coincidence with a photon from π0 decay. The results are compared with the three recent partial-wave analyses (PWA’s); the VPI analysis is most consistent with our measured distributions except at 687 MeV/c where no PWA agrees with our data. The charge-exchange transversity cross sections are evaluated using the differential cross sections of Borcherding et al. These transversity cross sections are used in conjunction with earlier π±p data by our group to test the triangle inequalities which are a model-independent test of isospin invariance. Our data satisfy these inequalities everywhere; in contrast, Abaev et al. have reported a violation of more than 5 standard deviations at 685 MeV/c.
No description provided.
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The differential cross section for η production in reaction π−p→ηn has been measured over the full angular range at seven incident π− beam momenta from threshold to pπ−=747 MeV/c using the Crystal Ball multiphoton spectrometer. The angular distributions are S wave dominated. At 10 MeV/c above threshold, a small D-wave contribution appears that interferes with the main S wave. The total η production cross section σtot is obtained by integration of dσ/dΩ. Starting at threshold, σtot rises rapidly, as expected for S-wave-dominated production. The features of the π−p→ηn cross section are strikingly similar to those of the SU(3) flavor-related process K−p→ηΛ. Comparison of the π−p→ηn reaction is made with η photoproduction.
Total cross sections.
Differential cross section for the 4 lowest beam momenta.
Differential cross section for the 3 highest beam momenta.
η′η pair production in the charge exchange reaction π−p→η′ηn has been observed and studied in a search for glueballs with the 38 GeV/c pion beam of the 70 GeV IHEP accelerator. The γ-rays from the decay η′η→4γ were detected with the hodoscope spectrometer GAMS-2000. The η′η events in the mass range from threshold up to 1.8 GeV are decays of the scalar G(1590)-meson which has been already observed in its ηη decay mode. The measured ratio of the partial widths of the G→η′η and the G → ηη decay channels is 2.7±0.8 in agreement with the value expected for glueballs.
No description provided.
New results on a high statistics measurement of pion-nucleon charge exchange scattering at 40 GeV/ c , extending in momentum transfer up to − t = 1.8 (GeV/ c ) 2 , are reported and compared with an optical impact parameter model, together with previous data for the reaction π − p → ηn at the same energy. The imaginary part of the pole trajectory b 0 ( s ) is determined from the slope of the tangent to the maxima of (−t) 1 2 d σ d t . The linear increase of Im b 0 ( s ) with log s , which has been observed at low energies, continues up to 40 GeV/ c .
AT SMALL -T, THE BINNING TENDS TO SMEAR OUT THE FORWARD DIP.
Differential cross sections for the reaction π−p→π0n were measured at nine incident-pion kinetic energies in the interval from 500 to 1300 MeV. The negative pion beam from the bevatron was focused on a liquidhydrogen target completely surrounded by a cubic array of six steel-plate spark chambers. The spark chambers were triggered on events with neutral final states. Charge-exchange events were identified from the one-shower and two-shower events in the spark-chamber pictures. By the Monte Carlo technique, the π0 distributions were calculated from the bisector distributions of the two-shower π0 events together with the observed γ-ray distributions of the one-shower π0 events. These π0 distributions were fitted with both Legendre-polynomial expansions and power-series expansions by the method of least squares. The extrapolated forward differential cross sections are in good agreement with the dispersion calculations. The Legendre coefficients for the differential cross sections in isospin state T=12 were obtained by combining our results with available data on π±p elastic scattering. In the light of existing phase-shift solutions, the behavior of these coefficients is discussed. The D5F5 interference term that peaks near 900 MeV is verified to be in isospin state T=12 only. We report here also the total neutral cross sections and the cross sections for the production of neutral multipion final states 2π0n and 3π0n. The 4π solid angle and the calibrated energy response of the spark chambers contribute to the accuracy of the results.
No description provided.
No description provided.
No description provided.
Reaction π−p→π0π0n has been measured with high statistics in the beam momentum range 270–750MeV∕c. The data were obtained using the Crystal Ball multiphoton spectrometer, which has 93% of 4π solid angle coverage. The dynamics of the π−p→π0π0n reaction and the dependence on the beam energy are displayed in total cross sections, Dalitz plots, invariant-mass spectra, and production angular distributions. Special attention is paid to the evaluation of the acceptance that is needed for the precision determination of the total cross section σt(π−p→π0π0n). The energy dependence of σt(π−p→π0π0n) shows a shoulder at the Roper resonance [i.e., the N(1440)12+], and there is also a maximum near the N(1520)32−. It illustrates the importance of these two resonances to the π0π0 production process. The Dalitz plots are highly nonuniform; they indicate that the π0π0n final state is dominantly produced via the π0Δ0(1232) intermediate state. The invariant-mass spectra differ much from the phase-space distributions. The production angular distributions are also different from the isotropic distribution, and their structure depends on the beam energy. For beam momenta above 550MeV∕c, the density distribution in the Dalitz plots strongly depends on the angle of the outgoing dipion system (or equivalently on the neutron angle). The role of the f0(600) meson (also known as the σ) in π0π0n production remains controversial.
Measured total cross section. Statistical errors only.
Differential angular distributions of the 2PI0 system for the LH2 data at beam momenta 355 to 472 MeV/c. Statistical errors only.
Differential angular distributions of the 2PI0 system for the LH2 data at beam momenta 550 to 678 MeV/c. Statistical errors only.
The reaction π − p → φφ n has been isolated at 16 GeV/ c and its cross section determined to be 40 ± 10 nb. The φφ mass spectrum shows a threshold enhancement between 2.1 and 2.5 GeV. A successful description of the angular content of the φφ system requires two interferingss J P = 2 + states.
No description provided.
SLOPE OF DIFFERENTIAL TP(P=3,P=2) DISTRIBUTION.
Experimental results on the reaction π − p → K ∗0 (890) X 0 at 10 GeV /c are presented. By using the K ∗0 polarization measurements, a detailed study of the production has been carried out as a function of the missing mass squared and of the four-momentum trasnfer squared to the K ∗0 . We found that: (a) K ∗0 production is dominated by natural parity exchange; (b) K ∗0 helicity-zero production dominates the unnatural parity exchange contribution and (c) the main features of the reaction are in agreement with the predictions of the finite mass sum rules.
TO TAL (NATURAL+UNATURAL PARITY EXCHANGE) CROSS-SECTIONS.
NATURAL PARITY EXCHANGE CROSS-SECTIONS.
UNATURAL PARITY EXCHANGE CROSS-SECTIONS.
Two (Δ(1238)ππ) enhancements at 1.93 and 2.12 GeV have been observed in an analysis of the invariant-mass spectra of Δ++(1238)π-π0 and Δ++(1238)π-π- from π-p→π-pπ+π-π0 events in 4.5 GeV/c π-p interactions. An enhancement at 2.2 GeV is also seen with a dominant branching to the Δ(1238)ρ system. The 1.93 and 2.12 enhancements seem to be produced mainly through a ρ-meson exchange process. The 2.2 GeV enhancement seems to be produced diffractively and is considered to correspond to theG17(2190) state.
No description provided.
EXPONENTIAL FITS TO T-DISTRIBUTIONS.
The reaction π − p→ π + π − n has been measured in a high-statistics experiment on a transversely polarized proton target at 17.2 GeV, and unexpectedly large nucleon polarization effects have been observed. Combining the results of this experiment with a measurement on a hydrogen target allows a model-independent partial-wave analysis in terms of the “nucleon transversity” amplitudes. Unique or at most twofold ambiguous solutions are obtained. In particular we find a high lower limit ( ⪆30% ) of the spin non-flip unnatural exchange amplitudes at low | t |. These amplitudes, interpreted as being due to the exchange of an object with the quantum numbers of the A 1 , have been assumed to be absent in previous analyses. In checking the consequences of this finding on the old results, we test the validity of the rank-two assumotions for the density matrix. We find a small but significant deviation, which shows the need for a new phase-shift analysis including the A 1 exchange contribution.
MASS DEPENDENCE OF NORMALIZED T-CHANNEL MOMENTS SCALED TO 100 PCT POLARIZED PROTONS.
T DEPENDENCE OF NORMALIZED T-CHANNEL MOMENTS IN THE RHO REGION SCALED TO 100 PCT POLARIZED PROTONS.
We present the results and the analysis of a high-statistics experiment to study A 2 and g production in the reaction π − p→K − K S 0 p at 10 GeV/ c . In each resonance region we perform a moment analysis of the data, and from the moments we determine the production amplitudes as a function of t . We find A 2 production proceeds dominantly by natural-parity (pomeron and f) exchange. We compare A 2 and diffractive K ∗ (1420) production. We find g production proceeds by π and ω exchanges; we determine the g → K K branching ratio.
No description provided.
No description provided.
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FIRST VARIANT OF INSTALLATION.
SECOND VARIANT OF INSTALLATION.
We present data on 3652 analyzed events of the reaction π - p → φφn at 22 GeV/ c . A partial wave analysis has been performed on the φφ system. The results are well represented by three resonances all with quantum numbers I G J PC = 0 + 2 ++ . The absence of the Okubo-Zweig-Iizuka suppression observed in this reaction, the selection of only three J PC =2 ++ states ( g T , g T′ , and g T ″ ) which comprise virtually all of the cross section, and the large φφn signal over a very different φK + K - n background are all well explained if these states are produced by 1–3 glueballs (i.e. multigluon resonances).
Slope indicates pion exchange process.
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).
A quasi-two-body model based on one-particle exchange and diffraction dissociation has been fitted to data from π−p interactions at 3.9 and 11.9 GeV/c in which a nucleon and 3-6 pions are present in the final state. It is used to estimate partial cross sections for the contributing interaction mechanisms and the dominant resonances which are produced at these energies. The energy dependence of the cross sections is examined and found to be consistent with expected behavior, and reactions are compared and found to agree with simple factorization.
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