Date

Measurement of Differential Cross-Sections in pi+ p Backward Elastic Scattering Between 1.25-GeV/c and 2-GeV/c

Ott, R.J. ; Trischuk, J.M. ; Va'vra, Jaroslav ; et al.
Phys.Rev.D 16 (1977) 2699-2705, 1977.
Inspire Record 126662 DOI 10.17182/hepdata.24495

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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Systematic Study of pi- p Backward Elastic Scattering Between 1.28-GeV/c and 3-GeV/c

Va'vra, Jaroslav ; Ott, R.J. ; Trischuk, J.M. ; et al.
Phys.Rev.D 16 (1977) 2687-2698, 1977.
Inspire Record 126661 DOI 10.17182/hepdata.24505

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.

31 data tables match query

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Measurement of the pi- p elastic scattering cross-section near 180 degrees between 600 and 1280 mev/c

Richards, T.J. ; Crabb, D.G. ; Keller, R. ; et al.
Phys.Rev.D 10 (1974) 45-64, 1974.
Inspire Record 95569 DOI 10.17182/hepdata.4929

Differential cross sections for π−p elastic scattering over the angular range 155° to 177° in the center-of-mass system have been measured at 33 incident pion momenta in the range 600 to 1280 MeV/c. The experiment, which was performed at the Bevatron at the Lawrence Berkeley Laboratory, employed a liquid hydrogen target, a double-arm spectrometer, and standard counter techniques to detect the elastic events. The data from this experiment are compared to all other published data in this momentum region. The over-all agreement is good. The data of this experiment are also compared with the results of the recent phase-shift analysis by Almehed and Lovelace. In the momentum region between 700 and 900 MeV/c, the slope of the backward angular distribution goes rapidly through zero from negative to positive, and the magnitude of the differential cross section falls by more than a factor of 10. Momentum-dependent structure is seen in the extrapolated differential cross sections at 180°. Two prominent dips in the 180° differential cross sections appear at 880 and 1150 MeV/c. This structure is discussed in terms of a direct-channel resonance model that assumes only resonant partial waves are contributing to the cross sections for large scattering angles.

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Pi- p elastic scattering near 180 degrees between 600 and 1280 mev/c

Crabb, D.G. ; Keller, R. ; O' Fallon, J.R. ; et al.
Phys.Rev.Lett. 27 (1971) 216-219, 1971.
Inspire Record 68952 DOI 10.17182/hepdata.21460

The differential cross sections for π−p elastic scattering over the angular range 155° to 177° in the center of mass have been measured at 33 incident-pion momenta in the range 600 to 1280 MeV/c. Angular distributions are presented. The extrapolated differential cross sections at 180° show considerable structure, in particular a dip near 1150 MeV/c. In general the near-180° cross sections do not agree with existing phase shift solutions above 1000 MeV/c

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INTERPOLATED DATA.

INTERPOLATED DATA.

INTERPOLATED DATA.

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Pi- p backward elastic scattering between 1.28 and 3.0 gev/c

Ott, R.J. ; Trischuk, J. ; Va'vra, J. ; et al.
Phys.Lett.B 42 (1972) 133-135, 1972.
Inspire Record 85045 DOI 10.17182/hepdata.76247

The differential cross-section for π - -p elastic scattering over the angular range 125° to 178° center of mass has been measured between 1.28 and 3.0 GeV/ c . Considerable structure is found and is discussed in terms of direct channel resonances.

46 data tables match query

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Measurement of the $\pi^+ p$ and $\pi^- p$ Polarization Parameters at 100 GeV/c

Auer, I.P. ; Hill, D. ; Sandler, B. ; et al.
Phys.Rev.Lett. 39 (1977) 313, 1977.
Inspire Record 121138 DOI 10.17182/hepdata.20982

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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Measurement of the Polarization in the Forward Peak of pi- p --> K0 Lambda at 5-GeV/c

Beusch, W. ; Borghini, M. ; Lauper, S. ; et al.
Nucl.Phys.B 99 (1975) 53-60, 1975.
Inspire Record 89729 DOI 10.17182/hepdata.31783

The π − p→K 0 λ polarization has been measured at 5 GeV/ c in the range 0<− t <1.4 (GeV/ c ) 2 . The polarization is small for − t ⪅0.4 (GeV/ c ) 2 , becoming negative at the higher values of − t .

1 data table match query

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Strange-particle production from pi+ p interactions in the center-of-mass energy range 1820 to 2090 mev

Hanson, P. ; Kalmus, G.E. ; Louie, J. ;
Phys.Rev.D 4 (1971) 1296-1308, 1971.
Inspire Record 74874 DOI 10.17182/hepdata.23180

Data at nine π+ momenta are presented in the following three-body final states: Σ+K+π0, Σ+K0π+, Σ0K+π+, ΛK+π+, pK+K¯0. The data consist of cross sections, Dalitz plots, and angular distributions for the quasi-two-body final state Y*+(1385)K+. In the channel Y*+(1385)K+ the production and Y* decay distributions are compared with the predictions of Stodolsky and Sakurai.

3 data tables match query

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EVENTS ABOVE BACKGROUND - NO FIT.

DATA VALUES TAKEN FROM PDG2 CHEW 73B COMPILATION WHICH READ THEM FROM THE GRAPH AND CONVERTED TO MUB. BACKGROUND NOT SUBTRACTED.


Neutral $D$ Meson Properties in 360-{GeV}/$c \pi^- p$ Interactions

The LEBC-EHS collaboration Aguilar-Benitez, M. ; Allison, W.W. ; Bagnaia, P. ; et al.
Phys.Lett.B 146 (1984) 266-272, 1984.
Inspire Record 202656 DOI 10.17182/hepdata.30495

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)%.

1 data table match query

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Coulomb-Nuclear Interference in pi+- p and K+- p Elastic Scattering Below 3-GeV: Measurements, Real Parts and K+- p Dispersion Relations

Baillon, P. ; Bricman, C. ; Ferro-Luzzi, M. ; et al.
Nucl.Phys.B 105 (1976) 365-430, 1976.
Inspire Record 101037 DOI 10.17182/hepdata.13243

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.

20 data tables match query

'TABLE'. 'BIN'.

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Pi- p forward elastic scattering near 1 gev/c

Abillon, J.M. ; Borg, A. ; Crozon, M. ; et al.
Nucl.Phys.B 46 (1972) 630-636, 1972.
Inspire Record 74955 DOI 10.17182/hepdata.8020

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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Study of the two-charged-particle final states of 3.9-gev/c pi+- p interactions including a longitudinal-momentum analysis of the one-pion- production channels

Bastien, P.L. ; Carmel, Z. ; Dao, F.T. ; et al.
Phys.Rev.D 3 (1971) 2047-2064, 1971.
Inspire Record 68000 DOI 10.17182/hepdata.23677

We have analyzed the two-prong final states in π+p interactions at 3.9 GeVc. Our result for elastic scattering is σ (elastic) = 6.50±0.1 mb (statistical error only). We find the elastic slope to be 6.61±0.14 (GeVc)−2. We find the elastic forward cross section to be 40.0±1.4 mb(GeVc)2. We have applied a longitudinal-momentum analysis to the one-pion-production channel. We find the cross section for the reaction π++p→π++π0+p to be 2.30±0.06 mb and that for π++p→π++π++n to be 1.45±0.05 mb. For resonance-production cross sections in these channels we find Δ(1236)=0.60±0.07 mb, ρ(760)=0.86±0.06 mb, and diffraction dissociation = 1.69±0.11 mb. We find that we can satisfactorily fit all distributions in the one-pion-production channel without assuming any phase-space production. In the missing-mass channel we observe dominant Δ++(1236) production plus evidence for A2+ production.

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X0 ---> 2gamma from pi- p ---> neutral meson + neutron at 3.8 gev/c

Apel, W.D. ; Auslaender, J. ; Mueller, H. ; et al.
Phys.Lett.B 40 (1972) 680-684, 1972.
Inspire Record 75664 DOI 10.17182/hepdata.28261

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)% .

1 data table match query

BY COMPARISON WITH THE KNOWN ETA PRODUCTION CROSS SECTION.


Production of rho0 and f in pi- p Interactions at 16-GeV/c and Separation Into Fragmentation and Central Components

The Aachen-Berlin-Bonn-CERN-Cracow-Heidelberg-Warsaw collaboration Bartke, J. ; Kirk, H. ; Sixel, P. ; et al.
Nucl.Phys.B 107 (1976) 93-117, 1976.
Inspire Record 108513 DOI 10.17182/hepdata.8729

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.

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THE REACTIONS P P ---> P P PI+ PI-, K+ P ---> K+ P PI+ PI-, PI+ P ---> PI+ P PI+ PI- AND PI- P ---> PI- P PI+ PI- AT 147-GeV/c

Brick, D.H. ; Rudnicka, H. ; Shapiro, A.M. ; et al.
Z.Phys.C 19 (1983) 1-9, 1983.
Inspire Record 194363 DOI 10.17182/hepdata.16321

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.

6 data tables match query

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CROSS SECTIONS FOR DIFFRACTION DISSOCIATION OF BEAM. FEYNMAN X OF OUTGOING PROTON <-0.96.

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Polarisation in the reaction pi+ p ---> k+ sigma+ at 1.11 gev/c

Bellamy, E.H. ; Anderson, J. ; Crawford, J.F. ; et al.
Phys.Lett.B 39 (1972) 299-302, 1972.
Inspire Record 75797 DOI 10.17182/hepdata.28308

The polarisation of the recoil sigma in the reaction π + p → K + Σ + has been measured at 12 production angles at a beam momentum of 1.11 GeV /c using counters and spark chambers. The new data are compared with existing phase shift solutions of π p → K Σ channels in the low energy region.

1 data table match query

THE ASYMMETRY PARAMETER, ALPHA, FOR SIGMA+ --> P PI0 IS CLOSE TO -1. THE LAST DATA VALUE IS DEDUCED FROM ALL THE EXPERIMENTAL EVENTS.


Measurement of Polarization in $\pi^- p \to \pi^0n$ and $\pi^-p \to \eta n$

Drobnis, D.D. ; Lales, J. ; Lamb, R.C. ; et al.
Phys.Rev.Lett. 20 (1968) 274-278, 1968.
Inspire Record 942917 DOI 10.17182/hepdata.21731

None

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Search for peripheral k+ production in pi- p interactions from 2.75 to 10 gev/c

Bashian, A. ; Finocchiaro, G. ; Good, M.L. ; et al.
Phys.Rev.D 4 (1971) 2680-2683, 1971.
Inspire Record 74755 DOI 10.17182/hepdata.23181

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+.

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EXTRAPOLATED TO T=0 ASSUMING SLOPE IS 5 GEV**-2.

ISOTROPIC ANGULAR DISTRIBUTION ASSUMED IN GIVEN T-RANGE.


Study of the reactions pi+ p ---> k+ sigma+ and pi+ p ---> k+ y*+(1385) between 3.5 and 14 gev/c

Bashian, A. ; Finocchiaro, G. ; Good, M.L. ; et al.
Phys.Rev.D 4 (1971) 2667-2679, 1971.
Inspire Record 74763 DOI 10.17182/hepdata.23097

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|.

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Backward elastic scattering from 875 to 1580 mev/c

Abillon, J.M. ; Borg, A. ; Crozon, M. ; et al.
Phys.Lett.B 32 (1970) 712-715, 1970.
Inspire Record 63081 DOI 10.17182/hepdata.5883

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.

30 data tables match query

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Study of the k*0 lambda and k*0 sigma0 final states from pi- p interactions at 3.9 gev/c

Abramovich, M. ; Chaloupka, V. ; Chung, S.U. ; et al.
Nucl.Phys.B 39 (1972) 189-200, 1972.
Inspire Record 75244 DOI 10.17182/hepdata.32953

A study of π − p → K ∗ Λ and π − p → K ∗ Σ° at 3.9 GeV /c indicates that the main features of both reactions can be interpreted in terms of simple exchange processes, the first involving both natural and unnatural exchange, the second showing evidence for natural parity exchange only.

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Study of the Reactions $\pi^- p \to K^0 \Lambda$ and $\pi^- p \to K^0 \Sigma^0$ at 3.95-{GeV}/$c$

The CERN-College de France-Madrid-Stockholm collaboration Loverre, P.F. ; Armenteros, R. ; Dionisi, C. ; et al.
Z.Phys.C 6 (1980) 283, 1980.
Inspire Record 153918 DOI 10.17182/hepdata.14374

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.

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Comparison of the Differential Cross-sections for $\pi^- p \to \eta^\prime n$ and $\pi^- p \to \eta n$ at 8.45-{GeV}/$c$

Stanton, N.R. ; Edwards, K.W. ; Legacey, D. ; et al.
Phys.Lett.B 92 (1980) 353-357, 1980.
Inspire Record 8522 DOI 10.17182/hepdata.27193

The ratio R of the differential cross sections for π - p→ η ′n and π - p → η n has been measured with high statistics and small systematic errors at 8.45 GeV/ c . R is generally interpreted as the relative content of nonstrange, ground-state quarks in η' and η. We find that R decreases with increasing ⋎ t ⋎; however, extrapolation to t =0 gives R (0) = 0.672 ± 0.032 (statistical) ± 0.47 (systematic) for the dominant spin flip cross sections, and R (0) = 0.500 ± 0.035 for the spin non-flip, in excellent agreement with results at higher energy. An improved value of the branching fraction ( η '→ γγ )/( η '→all) of 0.0200 ± 0.0018 is obtained.

1 data table match query

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Study of the Reactions $\pi^- p \to K^0 \Sigma^0(1385)$ and $\pi^- p \to K^+ \Sigma^-(1385)$ at 3.95-{GeV}/$c$

The CERN-College de France-Madrid-Stockholm collaboration Aguilar-Benitez, M. ; Albajar, M.C. ; Ferrando, A. ; et al.
Z.Phys.C 6 (1980) 109-123, 1980.
Inspire Record 153921 DOI 10.17182/hepdata.14369

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.

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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.

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Pionic charge exchange on the proton from 40-MeV to 250-MeV.

Breitschopf, J. ; Bauer, M. ; Clement, H. ; et al.
Phys.Lett.B 639 (2006) 424-428, 2006.
Inspire Record 717060 DOI 10.17182/hepdata.31547

The total cross sections for pionic charge exchange on hydrogen were measured using a transmission technique on thin CH2 and C targets. Data were taken for pi- lab energies from 39 to 247 MeV with total errors of typically 2% over the Delta-resonance and up to 10% at the lowest energies. Deviations from the predictions of the SAID phase shift analysis in the 60 to 80 MeV region are interpreted as evidence for isospin-symmetry breaking in the s-wave amplitudes. The charge dependence of the Delta-resonance properties appears to be smaller than previously reported.

1 data table match query

Measured total charge exchange cross sections. The errors are the combined statistical and ststematic errors including normalisation uncertainties.


Confirmation of Exchange Degeneracy Predictions in the Line Reversed Reactions: $\pi^+ p \to K^+ Y^*(1385)$ and $K^- p \to \pi^- Y^*(1385)$ at 11.6-{GeV}/$c$

Ballam, Joseph ; Bouchez, J. ; Carroll, J.T. ; et al.
Phys.Rev.Lett. 41 (1978) 676, 1978.
Inspire Record 130550 DOI 10.17182/hepdata.20815

We have measured in a single experimental setup the differential cross sections and polarizations of the Y*(1385) produced in the two line-reversed reactions π+p→K+Y*(1385) (260 eV/μb) and K−p→π−Y*(1385) (180 eV/μb) at 11.5 GeV/c. We compare these results to Σ+ production in the same experiment. The data have been derived from a triggered bubble-chamber experiment using the SLAC Hybrid Facility. We find that both helicity-flip-dominated (Y*) and helicity-nonflip-dominated (Σ) processes are consistent with weak-exchange-degeneracy predictions.

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Axis error includes +- 10/10 contribution.

Axis error includes +- 10/10 contribution.

Axis error includes +- 10/10 contribution.

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Cross-section Measurement of $\pi^- p \to \pi^- \pi^+ n$ Reaction Near Threshold

The OMICRON collaboration Kernel, G. ; Korbar, D. ; Krizan, P. ; et al.
Phys.Lett.B 216 (1989) 244-248, 1989.
Inspire Record 264989 DOI 10.17182/hepdata.29858

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.

1 data table match query

No description provided.


Experimental J/psi Hadronic Production from 150-GeV/c to 280-GeV/c

The NA3 collaboration Badier, J. ; Boucrot, J. ; Bourotte, J. ; et al.
Z.Phys.C 20 (1983) 101, 1983.
Inspire Record 191240 DOI 10.17182/hepdata.2212

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.

6 data tables match query

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Differential cross-section for backward pi+ p scattering from 3.25 to 10 gev/c

Bashian, A. ; Finocchiaro, G. ; Good, M.L. ; et al.
Phys.Rev.D 9 (1974) 3193-3196, 1974.
Inspire Record 94286 DOI 10.17182/hepdata.21973

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.

2 data tables match query

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Measurement of pi- p ---> eta n from threshold to p (pi-) = 747-MeV/c

Prakhov, S. ; Nefkens, B.M.K. ; Allgower, C.E. ; et al.
Phys.Rev.C 72 (2005) 015203, 2005.
Inspire Record 687736 DOI 10.17182/hepdata.25215

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.

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Total cross sections.

Differential cross section for the 4 lowest beam momenta.

Differential cross section for the 3 highest beam momenta.


Polarization Measurement of the $\Sigma^+$ Produced in the Line Reversed Reactions $\pi^+ p \to K^+ \Sigma^+$ and $K^- p \to \pi^- \Sigma^+$ at 7-{GeV}/$c$ and 11.6-{GeV}/$c$

Baker, P.A. ; Chima, J.S. ; Dornan, P.J. ; et al.
Phys.Rev.Lett. 40 (1978) 678, 1978.
Inspire Record 129108 DOI 10.17182/hepdata.20914

The polarization of the Σ+ has been measured for the line-reversed reactions π+p→K+Σ+ and K−p→π−Σ+ at 7 and 11.6 GeV/c using the SLAC Hybrid Facility. Since the Σ+ decay is observed in the bubble chamber, the trigger of the flash lamps on a fast K+(π−) did not bias the polarization measurements. We find that the Σ+ polarizations from the two reactions have opposite signs but similar magnitudes and are in much better agreement with the predictions of weak exchange degeneracy than previous lower-energy comparisons.

1 data table match query

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Pion-Proton Charge-Exchange Scattering from 500 to 1300 MeV

Chiu, Charles B. ; Eandi, Richard D. ; Helmholz, A.Carl ; et al.
Phys.Rev. 156 (1967) 1415-1426, 1967.
Inspire Record 52278 DOI 10.17182/hepdata.750

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.

19 data tables match query

No description provided.

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Measures of the differential effective sections $\pi ±p$ to 410 MeV and 490 MeV forwards

Banner, M. ; Detoeuf, J.F. ; Fayoux, M.L. ; et al.
Nuovo Cim.A 50 (1967) 431-448, 1967.
Inspire Record 1185325 DOI 10.17182/hepdata.896

Measurements of π±p elastic differential cross-sections have been performed in the forward direction, using a missing-mass spark chamber spectrometer. The films have been seanned by an automatic apparatus. A phase-shift analysis of the experimental data has been done, leading to three solutions. Various experiments are proposed in order to resolve the ambiguities.

4 data tables match query

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Measurement of pi- p --> pi0 pi0 n from threshold to p(pi-) 750-MeV/c.

The Crystal Ball collaboration Prakhov, S. ; Nefkens, B.M.K. ; Allgower, C.E. ; et al.
Phys.Rev.C 69 (2004) 045202, 2004.
Inspire Record 647544 DOI 10.17182/hepdata.25355

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.

5 data tables match query

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.

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A Study of the Reaction $\pi^- p \to \phi \phi n$ at 16-{GeV}/$c$

The Aachen-Bari-Bonn-CERN-Glasgow-Liverpool-Milan collaboration Armstrong, T.A. ; Baccari, B. ; Booth, P.S.L. ; et al.
Nucl.Phys.B 196 (1982) 176-188, 1982.
Inspire Record 165251 DOI 10.17182/hepdata.34217

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.

2 data tables match query

No description provided.

SLOPE OF DIFFERENTIAL TP(P=3,P=2) DISTRIBUTION.


Analysis of the Inclusive Reaction $\pi^- p \to K^*$ (890) X0 at 10-{GeV}/c

The Bari-Bonn-CERN-Daresbury-Glasgow-Liverpool-Milan-Vienna collaboration Di Gennaro, V. ; Evangelista, C. ; Ghidini, B. ; et al.
Nucl.Phys.B 173 (1980) 107-126, 1980.
Inspire Record 153000 DOI 10.17182/hepdata.34495

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.

4 data tables match query

TO TAL (NATURAL+UNATURAL PARITY EXCHANGE) CROSS-SECTIONS.

NATURAL PARITY EXCHANGE CROSS-SECTIONS.

UNATURAL PARITY EXCHANGE CROSS-SECTIONS.

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The Reaction pi- p --> eta n Up to rho* (eta) = 450-MeV/c: Experimental Results and Partial Wave Analysis

Feltesse, J. ; Ayed, R. ; Bareyre, P. ; et al.
Nucl.Phys.B 93 (1975) 242-260, 1975.
Inspire Record 99411 DOI 10.17182/hepdata.32003

An accurate measurement of d σ d Ω (π − p → η n ) at 1531 MeV total energy (expanded) up to l = 4 Legendre polynomials) requires reconsideration of previous angular distribution fits which were expanded only up to l = 2 and of subsequent partial-wave analysis. An energy-dependent partial-wave analysis has been performed here for p η ∗ up to 450 MeV/ c . In addition to the well-known S 11 (1520 MeV) resonance, either the P 11 (1532 MeV) or the P 13 (1530 MeV) resonance is found to be strongly coupled to the η-n channel. In both cases, the P 11 (1729 MeV) resonance is needed as is the weakly coupled D 13 (1525 MeV) resonance. The decay states in the ηn channelare compared to the SU(3) and SU(6) W predictions.

2 data tables match query

No description provided.

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$\pi^+ p$ interactions at 850 MeV/c

Debaisieux, J. ; Dufour, P. ; Grard, F. ; et al.
Nucl.Phys.B 5 (1968) 147-157, 1968.
Inspire Record 1400916 DOI 10.17182/hepdata.32747

Experimental results are presented on $\pi^+ p$ interactions at 850 MeV/c incident momentum. Cross sections for the various reactions are given. The elastic differential cross section has been fitted to a polynomial in, cos$\theta$ and the resulting coefficients are compared to results at neighbouring incident momenta. For the one-pion-production reactions, the (N$\pi$) effective mass distributions and the ratio of $\pi^0$ to $\pi^+$ production have been compared to the predictions of several theoretical models.

1 data table match query

No description provided.


DCS for π − p elastic scattering from 1.2 to 3.0 GeV/ c and phase shift analysis

Aplin, P.S. ; Cowan, I.M. ; Gibson, W.M. ; et al.
Nucl.Phys.B 32 (1971) 253-284, 1971.
Inspire Record 1104030 DOI 10.17182/hepdata.69638

Differential cross sections have been measured for π − p elastic scattering at laboratory momenta in the range 1.2 to 3.0 GeV/ c for the c.m. range 0.97 > cos θ ∗ > −0.98 . The corresponding mass range is 1.78 to 2.56 GeV/ c 2 . The data was obtained from a counter experiment in which the scattered pions and protons were detected in coincidence by arrays of scintillation counters.

31 data tables match query

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DIFFERENTIAL CROSS-SECTION FOR PI- P ---> GAMMA N FROM 427-MEV/C TO 625-MEV/C

Kim, G.J. ; Arends, J. ; Briscoe, W.J. ; et al.
Phys.Rev.D 40 (1989) 244-247, 1989.
Inspire Record 285141 DOI 10.17182/hepdata.23110

Differential cross sections for π−p→γn have been determined from 427 to 625 MeV/c, mainly at 90° and 110° c.m. The data were obtained by combining measurements of the Panofsky ratio in flight with known charge-exchange cross sections. The results are compared with γn→π−p data derived from γd experiments; the difference is typically 30%. The radiative decay amplitudes of neutral πN resonances are therefore uncertain by at least 30%.

3 data tables match query

Charge exchange cross section from PWA.

PI- P --> GAMMA N cross section.

GAMMA N --> PI- P cross section calculated using detailed balance.


A Comparison of the Shapes of pi+ p and p p Diffraction Peaks from 50-GeV/c to 175-GeV/c

The Fermilab Single Arm Spectrometer Group collaboration Ayres, D.S. ; Diebold, Robert E. ; Maclay, G.J. ; et al.
Phys.Rev.Lett. 37 (1976) 548, 1976.
Inspire Record 108238 DOI 10.17182/hepdata.21073

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.

1 data table match query

ACTUALLY THE DATA ARE THE EXPONENTIAL SLOPE OF THE RATIO OF D(SIG)/DT FOR THE TWO REACTIONS.


Charged-Particle Multiplicities in 100-GeV/c anti-p p Interactions

Ansorge, R.E. ; Bust, C.P. ; Carter, J.R. ; et al.
Phys.Lett.B 59 (1975) 299-302, 1975.
Inspire Record 2603 DOI 10.17182/hepdata.27765

Results are presented on the topological cross sections obtained for antiproton-proton interactions from an exposure of the Fermilab 30-inch bubble chamber to a 100 GeV/ c negative beam enriched in p 's. The p p inelastic cross section is found to be σ inel = 34.6 ± 0.4 mb, and the average inelastic charged particle multiplicity to be 〈 n 〉 = 6.74 ± 0.05.

2 data tables match query

ERRORS ARE STATISTICAL ONLY EXCEPT FOR 2-PRONG CROSS-SECTIONS.

EXPONENTIAL FIT TO ELASTIC T DISTRIBUTION TO CORRECT FOR AN APPARENT LOSS OF EVENTS AT SMALL -T.


$\pi^+$-proton interactions at 500 MeV incident energy

Debaisieux, J. ; Grard, F. ; Heughebaert, J. ; et al.
Nucl.Phys. 63 (1965) 273-285, 1965.
Inspire Record 1400917 DOI 10.17182/hepdata.37098

We present results on $\pi^+$-p interactions at 500 MeV from an experiment performed with the Saclay 35 cm hydrogen bubble chamber. A total of 1840 events have been observed. The branching ratio for elastic events is equal to 0.883$\pm$0.008. Eight events are unambiguously attributed to the reaction $\pi^+p\to\pi^+p\gamma$. Cross sections for the various reactions are given. The elastic angular distribution has been determined up to cos$\theta$ = +0.975 and shows evidence for S, P, D waves in good agreement with the results obtained in other experiments. For the one-pion production reactions, the ratio of $\pi^0$ production to $\pi^+$ production is found equal to 4.1$\pm$0.8. This result and the corresponding distributions for momentum and angle of the secondaries are compared with the predictions of the isobaric models.

1 data table match query

No description provided.


Search for Narrow Baryons in $\pi^- p$ Elastic Scattering at Large Angles

The CERN-College de France-Ecole Poly collaboration Baillon, P. ; Barrelet, E. ; Benayoun, Maurice ; et al.
Phys.Lett.B 94 (1980) 533-540, 1980.
Inspire Record 153784 DOI 10.17182/hepdata.27177

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.

1 data table match query

ENERGY SCAN IN BINS OF D(PLAB)/PLAB OF 5*10**-4 AT FOUR FIXED ANGLES (COS(THETA) = -0.4 TO 0.4).


Forward angle pi+- p elastic scattering differential cross-sections at T(pi) = 87-MeV to 139-MeV

Brack, J.T. ; Amaudruz, P.A. ; Ottewell, D.F. ; et al.
Phys.Rev.C 51 (1995) 929-936, 1995.
Inspire Record 400646 DOI 10.17182/hepdata.25894

Absolute π±p elastic scattering differential cross sections have been measured at five incident pion energies between 87 and 139 MeV. An active target of scintillator material (CH1.1) was used to detect recoil protons in coincidence with scattered pions. Pions were detected at forward angles between 27 and 98°c.m. where the low-energy recoil protons stop in the target. The cross sections, typically 5–10% lower than phase shift predictions for π+p and 10–20% lower for the π−p cross sections, are consistent with earlier measurements by this group.

5 data tables match query

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Measurement of $\pi^- p \to \pi^- p \pi^0$ Reaction Near Threshold and Breaking of Chiral Symmetry

The OMICRON collaboration Kernel, G. ; Korbar, D. ; Krizan, P. ; et al.
Phys.Lett.B 225 (1989) 198-202, 1989.
Inspire Record 278272 DOI 10.17182/hepdata.29804

A full-kinematics measurement of the π − p→ π − p π 0 reaction in the incident π − momentum region from 295 to 450 MeV/ c is presented. The measurement was performed with the OMICRON spectrometer at the CERN synchrocyclotron.

1 data table match query

Integrated cross section.


Soft $\pi^- p$ and $p p$ Elastic Scattering in the Energy Range 30-{GeV} to 345-{GeV}

Burq, J.P. ; Chemarin, M. ; Chevallier, M. ; et al.
Nucl.Phys.B 217 (1983) 285-335, 1983.
Inspire Record 182455 DOI 10.17182/hepdata.7556

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.

13 data tables match query

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NEUTRAL PARTICLE PRODUCTION IN PI P INTERACTIONS AT 147-GeV/c AND COMPARISON TO CHARGED PARTICLE PRODUCTION

Brick, D. ; Fong, D. ; Heller, M. ; et al.
Phys.Rev.D 20 (1979) 2123-2134, 1979.
Inspire Record 147455 DOI 10.17182/hepdata.4386

The production of KS, Λ, Λ¯, and γ in π−p collisions at 147 GeV/c is analyzed. Cross sections, rapidity, Feynman-x, and pT2 distributions are presented and compared to charged-particle production. The energy dependence of multiplicities in π−p and pp collisions is shown. A new scaling form for the correlation of neutral- and charged-particle multiplicities is presented for compilations of πp and pp data.

2 data tables match query

Axis error includes +- 0.0/0.0 contribution (?////ERRORS QUOTED ARE MAINLY STATISTICAL BUT INCLUDE CONTRIBUTIONS FROM ESTIMATES OF CONTAMINATION AND OF THE RELIABILITY OF WEIGHTING SCHEMES10 PCT OF ALAMBDA EVENTS COULD BE GAMMA CONTAMINATION, 0.5 PCT OF KS EVENTS COULD HAVE BEEN MISCLASSIFIED AS GAMMA'S).

Axis error includes +- 0.0/0.0 contribution (?////ERRORS QUOTED ARE MAINLY STATISTICAL BUT INCLUDE CONTRIBUTIONS FROM ESTIMATES OF CONTAMINATION AND OF THE RELIABILITY OF WEIGHTING SCHEMES10 PCT OF ALAMBDA EVENTS COULD BE GAMMA CONTAMINATION, 0.5 PCT OF KS EVENTS COULD HAVE BEEN MISCLASSIFIED AS GAMMA'S).


Measurement of the pi- p ---> 3 pi0 n total cross section from threshold to 0.75 GeV/c

Starostin, A. ; Nefkens, B.M.K. ; Manley, D.M. ; et al.
Phys.Rev.C 67 (2003) 068201, 2003.
Inspire Record 620818 DOI 10.17182/hepdata.25279

We report a new measurement of the π−p→3π0n total cross section from threshold to pπ=0.75GeV/c. The cross section near the N(1535)12− resonance is only a few μb after subtracting the large η→3π0 background associated with π−p→ηn. A simple analysis of our data results in the estimated branching fraction B[S11→πN(1440)12+]=(8±2)%. This is the first such estimate obtained with a three-pion production reaction.

1 data table match query

Total cross section from threshold to 750 MeV. Only statistical errors are given in the table.


Light isovector resonances in $\pi^- p \to \pi^-\pi^-\pi^+ p$ at 190 GeV/${\it c}$

The COMPASS collaboration Aghasyan, M. ; Alexeev, M.G. ; Alexeev, G.D. ; et al.
Phys.Rev.D 98 (2018) 092003, 2018.
Inspire Record 1655631 DOI 10.17182/hepdata.82958

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, $0.5 &lt; m_{3\pi} &lt; 2.5$ GeV/$c^2$, and simultaneously in 11 bins of the reduced four-momentum transfer squared, $0.1 &lt; t' &lt; 1.0$ $($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.

2 data tables match query

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).