We study the spin-exotic $J^{PC} = 1^{-+}$ amplitude in single-diffractive dissociation of 190 GeV$/c$ pions into $\pi^-\pi^-\pi^+$ using a hydrogen target and confirm the $\pi_1(1600) \to \rho(770) \pi$ amplitude, which interferes with a nonresonant $1^{-+}$ amplitude. We demonstrate that conflicting conclusions from previous studies on these amplitudes can be attributed to different analysis models and different treatment of the dependence of the amplitudes on the squared four-momentum transfer and we thus reconcile their experimental findings. We study the nonresonant contributions to the $\pi^-\pi^-\pi^+$ final state using pseudo-data generated on the basis of a Deck model. Subjecting pseudo-data and real data to the same partial-wave analysis, we find good agreement concerning the spectral shape and its dependence on the squared four-momentum transfer for the $J^{PC} = 1^{-+}$ amplitude and also for amplitudes with other $J^{PC}$ quantum numbers. We investigate for the first time the amplitude of the $\pi^-\pi^+$ subsystem with $J^{PC} = 1^{--}$ in the $3\pi$ amplitude with $J^{PC} = 1^{-+}$ employing the novel freed-isobar analysis scheme. We reveal this $\pi^-\pi^+$ amplitude to be dominated by the $\rho(770)$ for both the $\pi_1(1600)$ and the nonresonant contribution. We determine the $\rho(770)$ resonance parameters within the three-pion final state. These findings largely confirm the underlying assumptions for the isobar model used in all previous partial-wave analyses addressing the $J^{PC} = 1^{-+}$ amplitude.
Results for the spin-exotic $1^{-+}1^+[\pi\pi]_{1^{-\,-}}\pi P$ wave from the free-isobar partial-wave analysis performed in the first $t^\prime$ bin from $0.100$ to $0.141\;(\text{GeV}/c)^2$. The plotted values represent the intensity of the coherent sum of the dynamic isobar amplitudes $\{\mathcal{T}_k^\text{fit}\}$ as a function of $m_{3\pi}$, where the coherent sums run over all $m_{\pi^-\pi^+}$ bins indexed by $k$. These intensity values are given in number of events per $40\;\text{MeV}/c^2$ $m_{3\pi}$ interval and correspond to the orange points in Fig. 8(a). In the "Resources" section of this $t^\prime$ bin, we provide the JSON file named <code>transition_amplitudes_tBin_0.json</code> for download, which contains for each $m_{3\pi}$ bin the values of the transition amplitudes $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, their covariances, and further information. The data in this JSON file are organized in independent bins of $m_{3\pi}$. The information in these bins can be accessed via the key <code>m3pi_bin_<#>_t_prime_bin_0</code>. Each independent $m_{3\pi}$ bin contains <ul> <li>the kinematic ranges of the $(m_{3\pi}, t^\prime)$ cell, which are accessible via the keys <code>m3pi_lower_limit</code>, <code>m3pi_upper_limit</code>, <code>t_prime_lower_limit</code>, and <code>t_prime_upper_limit</code>.</li> <li>the $m_{\pi^-\pi^+}$ bin borders, which are accessible via the keys <code>m2pi_lower_limits</code> and <code>m2pi_upper_limits</code>.</li> <li>the real and imaginary parts of the transition amplitudes $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, which are accessible via the keys <code>transition_amplitudes_real_part</code> and <code>transition_amplitudes_imag_part</code>, respectively.</li> <li>the covariance matrix of the real and imaginary parts of the $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, which is accessible via the key <code>covariance_matrix</code>. Note that this matrix is real-valued and that its rows and columns are indexed such that $(\Re,\Im)$ pairs of the transition amplitudes are arranged with increasing $k$.</li> <li>the normalization factors $\mathcal{N}_a$ in Eq. (13) for all $m_{\pi^-\pi^+}$ bins, which are accessible via the key <code>normalization_factors</code>.</li> <li>the shape of the zero mode, i.e., the values of $\tilde\Delta_k$ for all $m_{\pi^-\pi^+}$ bins, which is accessible via the key <code>zero_mode_shape</code>.</li> <li>the reference wave, which is accessible via the key <code>reference_wave</code>. Note that this is always the $4^{++}1^+\rho(770)\pi G$ wave.</li> </ul>
Results for the spin-exotic $1^{-+}1^+[\pi\pi]_{1^{-\,-}}\pi P$ wave from the free-isobar partial-wave analysis performed in the second $t^\prime$ bin from $0.141$ to $0.194\;(\text{GeV}/c)^2$. The plotted values represent the intensity of the coherent sum of the dynamic isobar amplitudes $\{\mathcal{T}_k^\text{fit}\}$ as a function of $m_{3\pi}$, where the coherent sums run over all $m_{\pi^-\pi^+}$ bins indexed by $k$. These intensity values are given in number of events per $40\;\text{MeV}/c^2$ $m_{3\pi}$ interval and correspond to the orange points in Fig. 15(a) in the supplemental material of the paper. In the "Resources" section of this $t^\prime$ bin, we provide the JSON file named <code>transition_amplitudes_tBin_1.json</code> for download, which contains for each $m_{3\pi}$ bin the values of the transition amplitudes $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, their covariances, and further information. The data in this JSON file are organized in independent bins of $m_{3\pi}$. The information in these bins can be accessed via the key <code>m3pi_bin_<#>_t_prime_bin_1</code>. Each independent $m_{3\pi}$ bin contains <ul> <li>the kinematic ranges of the $(m_{3\pi}, t^\prime)$ cell, which are accessible via the keys <code>m3pi_lower_limit</code>, <code>m3pi_upper_limit</code>, <code>t_prime_lower_limit</code>, and <code>t_prime_upper_limit</code>.</li> <li>the $m_{\pi^-\pi^+}$ bin borders, which are accessible via the keys <code>m2pi_lower_limits</code> and <code>m2pi_upper_limits</code>.</li> <li>the real and imaginary parts of the transition amplitudes $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, which are accessible via the keys <code>transition_amplitudes_real_part</code> and <code>transition_amplitudes_imag_part</code>, respectively.</li> <li>the covariance matrix of the real and imaginary parts of the $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, which is accessible via the key <code>covariance_matrix</code>. Note that this matrix is real-valued and that its rows and columns are indexed such that $(\Re,\Im)$ pairs of the transition amplitudes are arranged with increasing $k$.</li> <li>the normalization factors $\mathcal{N}_a$ in Eq. (13) for all $m_{\pi^-\pi^+}$ bins, which are accessible via the key <code>normalization_factors</code>.</li> <li>the shape of the zero mode, i.e., the values of $\tilde\Delta_k$ for all $m_{\pi^-\pi^+}$ bins, which is accessible via the key <code>zero_mode_shape</code>.</li> <li>the reference wave, which is accessible via the key <code>reference_wave</code>. Note that this is always the $4^{++}1^+\rho(770)\pi G$ wave.</li> </ul>
Results for the spin-exotic $1^{-+}1^+[\pi\pi]_{1^{-\,-}}\pi P$ wave from the free-isobar partial-wave analysis performed in the third $t^\prime$ bin from $0.194$ to $0.326\;(\text{GeV}/c)^2$. The plotted values represent the intensity of the coherent sum of the dynamic isobar amplitudes $\{\mathcal{T}_k^\text{fit}\}$ as a function of $m_{3\pi}$, where the coherent sums run over all $m_{\pi^-\pi^+}$ bins indexed by $k$. These intensity values are given in number of events per $40\;\text{MeV}/c^2$ $m_{3\pi}$ interval and correspond to the orange points in Fig. 15(b) in the supplemental material of the paper. In the "Resources" section of this $t^\prime$ bin, we provide the JSON file named <code>transition_amplitudes_tBin_2.json</code> for download, which contains for each $m_{3\pi}$ bin the values of the transition amplitudes $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, their covariances, and further information. The data in this JSON file are organized in independent bins of $m_{3\pi}$. The information in these bins can be accessed via the key <code>m3pi_bin_<#>_t_prime_bin_2</code>. Each independent $m_{3\pi}$ bin contains <ul> <li>the kinematic ranges of the $(m_{3\pi}, t^\prime)$ cell, which are accessible via the keys <code>m3pi_lower_limit</code>, <code>m3pi_upper_limit</code>, <code>t_prime_lower_limit</code>, and <code>t_prime_upper_limit</code>.</li> <li>the $m_{\pi^-\pi^+}$ bin borders, which are accessible via the keys <code>m2pi_lower_limits</code> and <code>m2pi_upper_limits</code>.</li> <li>the real and imaginary parts of the transition amplitudes $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, which are accessible via the keys <code>transition_amplitudes_real_part</code> and <code>transition_amplitudes_imag_part</code>, respectively.</li> <li>the covariance matrix of the real and imaginary parts of the $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, which is accessible via the key <code>covariance_matrix</code>. Note that this matrix is real-valued and that its rows and columns are indexed such that $(\Re,\Im)$ pairs of the transition amplitudes are arranged with increasing $k$.</li> <li>the normalization factors $\mathcal{N}_a$ in Eq. (13) for all $m_{\pi^-\pi^+}$ bins, which are accessible via the key <code>normalization_factors</code>.</li> <li>the shape of the zero mode, i.e., the values of $\tilde\Delta_k$ for all $m_{\pi^-\pi^+}$ bins, which is accessible via the key <code>zero_mode_shape</code>.</li> <li>the reference wave, which is accessible via the key <code>reference_wave</code>. Note that this is always the $4^{++}1^+\rho(770)\pi G$ wave.</li> </ul>
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).
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The reaction π−p→η′η′n has been studied atpπ=37 GeV/c. Total of 14 events of this reaction have been selected. It has been shown that in the effective mass spectrum of the η′η′ system the events are concentrated mainly near the reaction threshold, which might be caused by the decayX(1910)→η′η′. The reaction cross-section has been evaluated: σ(π−p→η′η′n)=110±40 nb.
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FROM EXPONENTIAL FIT OF D(SIG)/D(T) IN RANGE 0. < ABS(T) < 1. GEV.
The experimental results are presented for ratios of ν-meson inclusive differential cross sections in 10.5 GeV/ c π + p, π + D and π + A collisions, R D/p =(d σ /d x F )( π + D → η X)/ (d σ /d x F ) π + p→ η X), R A =(d σ /d x F )( π + D→ η X) in the beam fragmentation region. The results are based on the statistics of ≈ 5 × 10 4 detected η → 2 γ decays. It is shown that the power α in the parametrisation R A ≈ A α ( xf ) does not change significantly with x F and its mean value is 0.50±0.02. The lower limit is obtained for the effective coefficient with string tension in the colour string model, κ ⩾ 3 GeV/fm. The observed growth of R A with x F can be explained by an assumption of a neutron halo with the factor H ≈ 4 in the nuclei.
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The polarization parameter in the reactions π−p→ηn and π−p→η′n at 40 GeV/c with −t ranging from 0 to 2.6 (GeV/c)2 and 1.0 (GeV/c)2, respectively, was measured in experiments using a propanediol polarized target. Only gamma particles from the neutral meson decay were detected. The polarization parameter of the first reaction turns out to be negative in a widet interval (0.05<−t<1.6 (GeV/c)2) and probably changes its sign at larger values oft. The average value of the polarization parameter of the second reaction is equal to −17±8)% in the region 0.05<−t<0.5 (GeV/c)2.
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Axis error includes +- 0.0/0.0 contribution (?////NOT GIVEN).
Axis error includes +- 0.0/0.0 contribution (?////NOT GIVEN).
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The results of the study of the π + p→K + ∑ + (1) and π + p→K + ∑ + (1385) (2) reactions at 12 GeV/ c are presented. The differential cross sections d σ /d t in| t min |<| t |<0.8 (GeV/ c ) 2 momentum transfer range are measured. The ∑ + polarisation for | t |<0.5 (GeV/ c ) 2 for reaction (1) is defined. Binary reactions (1) and (2) were selected by analyzing the missing mass spectra for the forward emitted fast K + meson. The total cross sections in the studied momentum transfer range are 20.2±2.4 μ b and 7.3±1.1 μ b for the reactions (1) and (2) respectively. The experimental results are compared with the predictions of the Regge models which take into account rescattering and secondary singularities.
SYSTEMATIC ERRORS INCLUDED.
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The paper presents results on measuring the polarization in the reaction π − p→ π 0 n at 40 GeV/ c in the 4-momentum transfer range 0<| t |⩽2 (GeV/ c ) 2 . The results based on the statistics of about 2.2 million recorded events made it possible to observe a noticeable value and complex structure in the polarization behaviour up to | t |⩽2 (GeV/ c ) 2 .
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We have studied the reactionspp→ppπ+π-,K+p→K+pπ+π−π, π+p→ π+,pπ+π− and π−p →π+π− at 147 GeV/c using the 30-inch Fermilab hybrid system. All four reactions were detected with the same apparatus and analyzed in the same way. The energy dependence of the channel cross section was found to beAp−0.6+B for thepp reaction andAp−1+B for the other three. About 90% of the cross section at 147 GeV/c can be accounted for by either beam or target diffraction. Some of the remaining cross section may come from double Pomeron exchange reactions which we tried to isolate. We have tested the hypothesis of a factorizable Pomeron and our data indicates a violation of this hypothesis. We show that the 3π mass enhancement in the mass region 1.2–1.4 GeV is diffractively produced in the π± beam reactions. Fourprong, four-constraint and six-prong, four-constraint cross sections are reported.
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CROSS SECTIONS FOR DIFFRACTION DISSOCIATION OF BEAM. FEYNMAN X OF OUTGOING PROTON <-0.96.
Energy, charge and strangeness flow inK+p interactions at 32 and 70 GeV/c, and π+p interactions at 32 GeV/c are studied in terms of the angular variable λ=|x|/pT. The data ondQ/dλ anddE/dλ show only a weak indication of scale breaking between 32 and 70 GeV/c. For inclusive “non-diffractive”, inclusive “diffractive” and exclusive “non-diffractive” jets, the fraction of charge in any angular region ΔΩ away from the central region is found to be proportional to the energy fraction in the same interval. The data ondQ/dE versus λ are compatible with some versions of dual-sheet models and agree also with the LUND Monte-Carlo model. The data are also compared with\(v(\bar v)p\) interactions in BEBC. In exclusive channels the average ratiodQ/dS=0.78±0.04 is consistent, in the framework of fragmentation models, with a larger probability for the fragmentation of the\(\bar s\)-valence quark than theu-valence quark in theK+-meson.
CHARGE FLOW IN NONDIFFRACTIVE PROTON-LIKE AND KAON-LIKE JETS.
CHARGE FLOW IN NONDIFFRACTIVE PROTON-LIKE AND KAON-LIKE JETS.
CHARGE FLOW IN NONDIFFRACTIVE PROTON-LIKE AND KAON-LIKE JETS.
The Fermilab hybrid 30-in. bubble-chamber spectrometer was exposed to a tagged 147-GeV/c positive beam containing π+, K+, and p. A sample of 3003 K+p, 19410 pp, and 20745 π+p interactions is used to derive σn, 〈n〉, f2cc, and 〈nc〉D for each beam particle. These values are compared to values obtained at other, mostly lower, beam momenta. The overall dependence of 〈n〉 on Ea, the available center-of-mass energy, for these three reactions as well as π−p and pp interactions has been determined.
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We have studied the inclusive production of K*±(890) and Y*±(1385) in pp, π+p, and K+p interactions at 147 GeV/c. The experiment used the Fermilab 30-inch hydrogen bubble chamber with the hybrid spectrometer system. Results are based on a sample of 1916 observed KS and 932 observed A. Inclusive cross sections are given for K*± and Y*± production from the three beams, and comparisons are made with experiments at other energies. Feynman-x and transverse-momentum-squared distributions are also calculated. The results suggest that the K*− is entirely produced in the central region, while the K*+ includes a component from beam fragmentation. Comparisons are made with the additive quark model.
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Results of a high-statistics study of elastic scattering and meson resonances produced by π−p interactions at 8 GeV/c are presented. Large statistics and small systematic errors permit examination of the complete kinematic region. Total differential cross sections are given for ρ0,−, f0, g0,−, Δ±, Δ0, and N* resonances. Spin-density matrix elements and Legendre-polynomial moments are given for ρ, f, and Δ resonances. The results for ρ0 and f0 resonances are compared with the predictions of a Regge-pole-exchange model. Properties of the above resonances are compared and discussed. In particular, we present evidence that the ρ0 and f0 production mechanisms are similar. The similarity of the g0 t distribution to that of the ρ0 and f0 suggests a common production mechanism for all three resonances.
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SLOPE REFERS TO EXPONENTIAL FIT IN U.
From a study of 8-GeV/c π−p interactions, the various two-pion and four-pion decay channels available to the g− meson have been investigated. Our results indicate that the dominant 4π decay modes involve intermediate ρ and ω production without significant A2 formation.
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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.
The results on measuring polarization in charge exchange reaction π−+p→π0+n at 40 GeV/c are presented for the 4-momentum transfer range from 0 up to 2 (GeV/c)2. At |t|≦0.4 (GeV/c)2 the polarization has a positive sign. In the “crossover” region of π± elastic scattering a possible minimum in the polarization behaviour has been seen for the first time. the polarization is zero within the statistical accuracy near this point. In the “deep” region of the charge-exchange differential cross-section the polarization has a negative sign. The presented data are not in agreement with the modern theoretical models.
In an experiment with the 30-inch Hybrid Spectrometer at Fermilab we have obtained the inclusive and semi-inclusive production cross sections of the ϱ0 meson using a conventional background subtraction technique. Production cross sections for the ϱ0 are derived as a function of the Feynman scaling variablex, and the transverse variablespt2 andEt=(pt2+M2)1/2. The longitudinal distributions are compared with the (1−x) dependence of the proton and meson valence quark structure functions, using various forms of recombination and fragmentation models. The transverse distributions are compared with thermodynamic models. We give density matrix elements for the ϱ0 production from pions in the extreme forward region.
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The energy dependence of the average of the charged multiplicity and its dispersion in π + /K + /p interaction on protons at 147 GeV/ c is found to be the same as in e + e − annihilations if an “effective energy” variable is used instead of the total energy. The effective energy S eff is defined as the invariant mass of all secondaries left after the two leading particles have been removed. Fitting the expression aS eff b to the average charge multiplicity 〈 n ch 〉, we find the power b to be in good agreement with the value of 0.25 predicted by Fermi's statistical model and by Landau's hydrodynamical model.
BINS IN WEFF SELECTED SO AS TO YIELD 200 EVENTS IN EACH BIN.
200 EVENTS IN EACH BIN IN WEFF.
50 EVENTS IN EACH BIN IN WEFF.
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AVERAGE TARGET POLARIZATION WAS 76 +- 3 PCT.
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This paper presents the results of a study of the dominant neutral final states from π−p interactions. The data were obtained in an experiment performed at the Brookhaven National Laboratory Alternating Gradient Synchrotron, using a set of steel-plate optical spark chambers surrounding a liquid-hydrogen target. We present differential and total cross sections for the reactions (1) π−p→n+π0 and (2) π−p→n+η0(η0→2γ) and total cross sections for the reactions (3) π−p→n+kπ0 (k=2, 3, 4, and 5) and (4) π−p→all neutrals for eighteen values of beam momentum in the interval 1.3 to 4.0 GeV/c. The angular distributions for (1) and (2) have been analyzed in terms of expansions in Legendre polynomials, the coefficients for which are also given.
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SIG = 4*PI*LEG(L=0).
FORWARD DIFFERENTIAL CROSS SECTION CALCULATED FROM LEGENDRE POLYNOMIAL COEFFICIENTS AND ERROR MATRICES.
Results are presented from a study of inclusive neutral strange particle production by a 147 GeV/ c tagged π + /K + /p beam in the Fermilab 30-inch hydrogen bubble chamber. The experiment made use of the proportional hybrid spectrometer system. Results are based on 995 K S 0 , 485 Λ, and 83 Λ found in a sample of 132 000 pictures. Cross sections are given for inclusive production of these particles by each of the three beam particles, and comparisons are made with measurements at other energies. Topological cross sections are also calculated, and KNO multiplicity scaling is investigated. Distributions are presented of invariant cross sections as functions of the Feynman scaling variable x and c.m. rapidity y . The transverse momentum-squared distributions with their fitted slopes are also given. Comparisons are made of the production characteristics for the three beam types.
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The experimentally determined average charged-particle multiplicities, 〈nX〉, of the systems, X, produced in the following reactions for 147 GeV/c incident pion momentum are presented as functions of the square of the invariant mass of X, MX2, and of |t|:π−p→πfast−X, π−p→pX, π−p→Δ++X, π−p→(π−π+)ρ0X, and π−p→Λ0X. Details of the analysis are discussed. These data can be fit by the expression 〈nX〉=A+B ln MX2+C|t| and the coefficients obtained for B are equal within their uncertainties. C is significantly different from zero only for π−p→πfast−X. These results and 〈nX〉 data from other inclusive and total-inelastic-reaction studies are discussed in terms of a simple model which assumes contributions to 〈nX〉 from the target-fragmentation, the central, and the beam-fragmentation regions in the case of total-inelastic reactions. For inclusive reactions, either the beam or target fragmentation is replaced by an exchange-particle-fragmentation contribution. The s, t, and MX2 dependence of the parameters of the model are deduced from triple-Regge considerations. The data are found to be consistent with the model and values are presented for the parameters.
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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.
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).
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The results presented in this paper were obtained from a 105 000 frame exposure of the FNAL Hybrid Proportional Wire Chamber-30 inch Bubble Chamber System, in a tagged beam of 147 GeV/ c negative particles. Elastic, total and topological cross sections were obtained for both π − p and K − p interactions. Comparisons with other data, taken with various beam particles over large momentum intervals, show good agreement with KNO scaling, and similarity in the scaling behavior of σ n for the different beam particles.
THESE CROSS SECTIONS ARE NOT NORMALIZED TO ANY OTHER ABSOLUTE MEASUREMENT. THE ERRORS INCLUDE SOME SYSTEMATIC ERRORS.
THE FORWARD CROSS SECTION AGREES WELL WITH THE OPTICAL POINT FROM TOTAL CROSS SECTION MEASUREMENTS.
THESE CROSS SECTIONS ARE NOT NORMALIZED TO ANY OTHER ABSOLUTE MEASUREMENT.
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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.
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The pπ+π0 and pπ+π+π− final states from π+p interactions at 3.9 GeV/c have been analyzed by the prism-plot technique and the following three quasi-two-body channels have been studied in detail: π+p→ρ+p, π+p→π0Δ++, and π+p→ρ0Δ++. Results are presented on cross sections, differential cross sections, and single and joint spin density matrix elements. These are compared with the Dar-Watts-Weisskopf absorption model and Reggeized pion-exchange model predictions. Relations among joint spin density matrix elements for ρ0Δ++ are compared with quark-model predictions.
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We present data on inclusive and semi-inclusive ϱ 0 production in 147 GeV/ c π − p interactions. We find a total cross section of 7.3 ± 1.3 mb. Most of this cross section is found in the lower topology events (⩽ 10 prongs), and in the central and forward rapidity regions. The P T 2 dependence of ϱ 0 production, 〈: n > ϱ 0 per event, and the ϱ 0 / π + ratios are also discussed.
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We have done an inclusive study of ϱ 0 production in π − p interactions at 15 GeV/ c . Evidence for two different production mechanisms, in addition to the known quasi two-body processes, is presented: production of ϱ 0 's in the central region of rapidity similar to the “pionization” region seen in the inclusive studies of pions; and forward production in the beam dissociation region of rapidity. Cross sections and rapidity distributions for the ϱ 0 are given inclusively and by topology, and the results are compared with similar studies at other energies and with other incident particles. Results are also presented for the semi-inclusive reaction π − p → p ϱ 0 + X − and the exclusive final state p π − ϱ 0 .
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We have investigated the ρ-meson production mechanism in the three reactions π±p→ρ±p and π−p→ρ0n at 3.9 GeV/c (s=8.2 GeV2) using the prism-plot technique. Differential cross sections at all momentum transfers are presented. A significant backward peak has been found in all three reactions. The differential cross sections for these backward peaks are given and are compared with the equivalent pion elastic and charge-exchange cross sections in the backward direction. Using a linear combination of the three differential cross sections we have isolated the I=0 exchange contribution in the forward direction. This differential cross section has a zero at −t=0.45 (GeV/c)2 and is fitted by the dual absorptive model of Harari with an interaction radius of ∼ 1.2 F. The total I=0 cross section is calculated and compared with similarly determined cross sections at higher momenta. An analysis of the properties of the other possible spin-parity exchanges is also presented.
SLOPE FITTED OVER 0.05 < -T < 0.3 GEV**2.
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The π−+p→π0+n differential cross section at 180° has been measured for 52 values of π− momentum from 1.8 to 6.0 GeV/c using a constant-geometry detection system. The average statistical uncertainty is ∼5% and the systematic uncertainty is ∼10%. The details of the experiment and the data analysis are discussed. The data are compared with those of other experiments with which they are generally in agreement. One set of data disagrees with those presented here and a possible reason for this is discussed. A five-parameter fit of the predictions of a dual-resonance model to our data gave excellent agreement. The differential cross sections at 180° for π±p elastic scattering have been compiled and the moduli and relative phase of the T=12 and T=32 pion-nucleon s- and u-channel amplitudes (|A12|, |A32|, and cosδ) have a minimum at u=0.4 GeV/c and, in the s channel, a corresponding minimum at s=2.2 GeV/c.
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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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BREIT-WIGNER RESONANCE FITS WITH BACKGROUND.
We present a new technique for analyzing multibody states. This analysis makes possible the selection of samples of events that contain only resonances, particle correlations, or phase space. A unique feature of this analysis is that every event in the data is assigned to a particular sample. The three-body final state π++p→p+π++π0 is analyzed as an example.
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An experiment designed to study the π−p total neutral cross section and its breakdown into several channels has been performed at eleven incident pion momenta ranging from 654 to 1247 MeV/c. Angular distributions for the charge exchange π0 and for η0 production are given in terms of Legendre-polynomial expansion coefficients. Forward and backward differential cross sections are presented for the charge-exchange channel and comparisons with recent dispersion-relation predictions for the forward cross section are made.
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