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).
The reaction K−p→K¯0π−p has been studied at 100 and 175 GeV/c and the reaction π−p→K0K−p at 50, 100, and 175 GeV/c. Both reactions are dominated by production of resonances, K*(890), K*(1430) and A2(1320), A2(2040), respectively. Production cross sections, t distributions, and decay-angular distributions are studied. Isoscalar natural-parity exchange is dominant. The energy dependence of the K* and A2 resonance production between 10 and 175 GeV/c is well described by a Regge-pole model. Our data on A2 corrects that in an earlier paper.
No description provided.
No description provided.
No description provided.
The reaction π−p→K0K−p has been measured from 50 to 175 GeV/c. The production characteristics of the A2 have been analyzed. We find spin and t dependence similar to lower energies, but the cross section falls rapidly with energy. In a Regge description of π−p→A2−p our data imply a rather small Pomeron-exchange component.
No description provided.
RAW CROSS SECTION WITHIN MASS CUTS.
No description provided.
Results from a high-statistics experiment involving an exposure of the SLAC 82-in. hydrogen bubble chamber to a beam of 8-GeV/c π− yielding a final state of π−π+π−p are presented. Copious production of ρ, Δ++, and f is found. Considerable quasi-two-body production in which one particle decays to one of the above resonances is also observed. Some double-resonance production involving baryon and meson resonances is also seen. The production properties of ρ, Δ++, and f mesons are well described by a double-Regge model.
TOPOLOGICAL CROSS SECTIONS. FIRST 2 PRONG VALUE CONTAINS ELASTIC. 0PRONG IS TAKEN FROM A SMALLER AND DIFFERENT PARTIAL SAMPLE.
CROSS SECTION CALCULATED VIA THE OPTICAL THEOREM AS A CROSS CHECK.
SPECIFIC CHANNEL CROSS SECTIONS.
Mesons decaying into π 0 or η and one charged meson were studied using a liquid-argon calorimeter in a non-magnetic double-arm spectrometer. Cross sections and energy dependences are presented. The ϱ ± production mechanisms are discussed in detail: ω and π exchange contribute the largest fractions, but also A 2 exchange is present. ϱ ± production by ω exchange is shown to follow the energy behaviour predicted by the Regge trajectory α ω ( t ) = 0.4 − | t |.
Axis error includes +- 0.0/0.0 contribution (13 TO 25////STATISTICAL ERRORS ARE SMALLER THAN THE SYSTEMATIC ERRORS).
No description provided.
Diffractive production of the 3 π system has been studied at 63 and 94 GeV using a two magnet spectrometer with high, uniform acceptance. The total number of events used in the analysis is ∼600 000. The A 2 meson is shown to be diffractively produced. The existence of a resonant component in both the 1 + and 2 − enhancements is established and resonance parameters for the corresponding A 1 and A 3 mesons are given. There are several indications in the data of states which would correspond to radial excitations in the quark model.
SEE C. DAUM ET AL., PL 89B, 276 (1980) (<a href=http://durpdg.dur.ac.uk/scripts/reacsearch.csh/TESTREAC/red+486> RED = 486 </a>), AND THE RECORD (<a href=http://durpdg.dur.ac.uk/scripts/reacsearch.csh/TESTREAC/red+420> RED = 420 </a>) OF THE GENEVA CONFERENCE PREPRINT, B. ALPER ET AL. (1979).
SEE C. DAUM ET AL., PL 89B, 281 (1980) (<a href=http://durpdg.dur.ac.uk/scripts/reacsearch.csh/TESTREAC/red+487> RED = 487 </a>), AND THE RECORD (<a href=http://durpdg.dur.ac.uk/scripts/reacsearch.csh/TESTREAC/red+419> RED = 419 </a>) OF THE GENEVA CONFERENCE PREPRINT, G. THOMPSON ET AL. (1979).
SEE C. DAUM ET AL., PL 89B, 285 (1980) (<a href=http://durpdg.dur.ac.uk/scripts/reacsearch.csh/TESTREAC/red+488> RED = 488 </a>), AND THE RECORD (<a href=http://durpdg.dur.ac.uk/scripts/reacsearch.csh/TESTREAC/red+421> RED = 421 </a>) OF THE GENEVA CONFERENCE PREPRINT, B. ALPER ET AL. (1979).
The A 2 meson is studied in the decay mode ϱ 0 π − using partial wave analyses of 600 000 events from the reaction π − p→ π − π − π + p at 63 and 94 GeV incident momentum. Common production mechanisms are indicated for this resonance and diffractive 1 + and 2 − components.
No description provided.
A sample of about 230000 events of the reaction pi /sup -/p to pi /sup +/ pi /sup -/n, measured with a magnetic forward spectrometer set up in an unseparated pi /sup -/ beam with a momentum of 63 GeV/c at the SPS has been analysed in terms of one pion exchange. The elastic pi /sup +/ pi /sup -/ cross section has been determined using an extrapolation to the pion pole in the mass range up to m( pi /sup +/ pi /sup -/)=4 GeV. The total pi /sup +/ pi /sup -/ cross section is obtained via the optical theorem. (7 refs).
INTEGRATED 2- S-WAVE INTENSITY FOR 1500 TO 1800 MEV, INCLUDING SIGNIFICANT BACKGROUND.
No description provided.
No description provided.
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.
We perform an amplitude analysis of 10 GeV/ c π − p → K − K S 0 p data as a function of K − K 0 mass from threshold up to 2 GeV. We find that the A 2 and g resonances are produced dominantly by natural and unnatural parity exchange, respectively, and we determine their resonance parameters. We present further evidence for the I = 1, 4 + state A 2 ∗ (1900), in particular by isolating interference effects. The structure of S-wave K − K 0 production suggests an I = 1, 0 + state just below 1300 MeV of width about 250 MeV.
CROSS SECTIONS FROM FITTING MASS SPECTRUM. THE RESONANT AMPLITUDE CONTRIBUTIONS ALSO GIVEN IN PAPER.
In a 48 000-picture exposure of the Fermilab 30-inch hydrogen bubble chamber to a 205 GeV/ c π − beam, we have measured 169 events of the reaction, π − p → π − π + π − p, with a cross section of 635 ± 61 μ b. This reaction proceeds almost entirely via low mass π − → 3 π and p → p ππ dissociation. Factorization is satisfied for p → pππ dissociation in πp and pp interactions.
No description provided.
Cross sections for resonance production in the reactions π ± p → p π ± π + π − at 16 GeV/ c are determined by a maximum likelihood fit, making use of the measurements of all individual events. The reactions are described by a simple parametrization based on an incoherent superposition of amplitudes for quasi two-body and quasi three-body processes and a non-resonant backgroud. In this way the reflections are accounted for in a consistent way. Thus cross sections are obtained for Δ ++ , Δ 0 , ρ 0 and f 0 production which do not suffer from the uncertainties of background subtraction typical of the usual technique of fitting individual mass distributions.
TWO PARTICLE RESONANCE CROSS SECTIONS.
CHANNEL FRACTIONS FROM THE FITS. THE AUTHORS WARN AGAINST DERIVING CROSS SECTIONS FOR THREE-PARTICLE RESONANCES.
The reaction π−p→X−p, X−→ηπ−, η→γγ has been studied in an optical spark-chamber experiment at the Argonne ZGS (Zero Gradient Synchrotron) at a beam momentum of 6.0 GeV/c and with 0.27≤|t|≤0.42 (GeV/c)2. The ηπ mass spectrum contains about 1400 events in the mass range 0.80<M(ηπ)<1.55 GeV/c2, and is dominated by approximately 1000 events of the type A2−→ηπ−. No structure is discernible within the A2 mass spectrum for an experimental resolution of 7.1 MeV/c2 [16.7 MeV/c2 FWHM (full width at half maximum)]. A single D-wave Breit-Wigner distribution fits the data with a high confidence level, yielding for the A2 the parameters M0=1.323±0.003 GeV/c2 and Γ0=0.108±0.009 GeV/c2. The angular distribution of the decay A2−→ηπ− is analyzed and the resultant density matrix elements have the values ρ11=0.45±0.02, ρ1−1=0.45±0.04, and ρ00=0.09±0.04. All other elements are consistent with zero. Finally, the missing-mass spectrum in the region of the A2 is presented. A signal of 230 events above background per 5-MeV/c2 interval is observed at the A2 peak, with a signal to background ratio of greater than 1:1. A single D-wave Breit-Wigner distribution together with a quadratic background fits the data well, with the parameters for the A2 being M0=1.324±0.003 GeV/c2 and Γ0=0.104±0.009 GeV/c2. Both A2 mass spectra are incompatible with the dipole shape.
No description provided.
THIS FIT ASSUMES ALL OTHER DENSITY MATRIX ELEMENTS (RHO(2M) AND RE(RHO(10))) ARE ZERO SINCE THEY ARE QUITE CONSISTENT WITH ZERO IN A FULL FIT. QUOTED ERRORS INCLUDE SYSTEMATIC ERRORS, WHILE STATISTICAL FITTING ERRORS ARE SHOWN SEPARATELY.
The analysis of A2−→ηπ− at 11.2 GeV/c confirms that A2− is essentially produced by natural-parity exchange. In the differential cross-section as a function oft′ there is evidence of the dip at smallt′ values. The branching ratio (A2→ηπ)/(A2→ϱπ) is 0.18±0.05.
No description provided.
NUMERICAL VALUES SUPPLIED BY G. THOMPSON. 100 EVENTS IN A2 REGION DEFINED BY 1.18 < M(ETA PI-) < 1.44 GEV.
ROUGH BACKGROUND SUBTRACTION TO REMOVE NON-TRUE ETA EVENTS. FIRST THREE DENSITY MATRIX COMBINATIONS ARE NATURAL-PARITY EXCHANGE, THE REMAINDER BEING UNNATURAL-PARITY EXCHANGE.
The results of a study of the reaction π-p→π-π-π+p at2 147 GeV/c carried out at the Fermilab Proportional Wire 30″ Bubble Chamber Hybrid Spectrometer are reported. More than 92% of the cross-section ((670±41) μb) for this reaction is contained in those for proton and pion diffraction dissociation. The cross-sections for pion diffraction events with three-pion invariant mass in given regions are in agreement with values obtained by extrapolation of fits to data at lower incidentpion momenta. ρ0π- events make an important contribution in the A1 and A2 mass regions, and the data are consistent with contributions from f0π- in the A3 mass region. The cross-section for proton diffraction events is in agreement with a smooth extrapolation of the data at lower momentum.
No description provided.
A prism plot analysis of the reaction π − p→p π + π − π − at 16 GeV/ c has been made and the results are compared with those obtained in a similar analysis of the reaction π + p→ p π + π + π − at the same energy. The three dominating reaction mechanisms (pion dissociation, reggeon exchange, proton diffraction dissociation) appear to be well separated, while considerable residual overlaps are present inside these classes. The prism plot method is discussed as a means for detecting hidden structures and some evidence is presented for a broad three-pion enhancement around 2 GeV decaying primarily into ϱ 0 π − .
No description provided.
A4(1900) IS CALLED A*(1800) BY AUTHORS. PI+ P CROSS SECTIONS PREVIOUSLY PUBLISHED IN M. DEUTSCHMANN ET AL., NP B99, 397 (1975).
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