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).
Experimental results are presented for the available channels in the 1.2 GeV/ c π + p interaction. An isobaric model with incoherent addition of the amplitudes is used to determine the π, Δ and N ∗ abundance rates in the π + π o p final state. The multipole parameters in the density matrix of the Δ ++ are determined as functions of its production angle.
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LEGENDRE POLYNOMIAL FIT USED TO CORRECT FOR ELASTIC EVENTS LOST FROM THE FORWARD BIN.
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Cross sections or upper limits are reported for 12 meson-baryon and two baryon-baryon reactions for an incident momentum of 9.9 GeV/c, near 90° c.m.: π±p→pπ±,pp±,π+°±,K+Σ±, (Λ0/Σ0)K0; K±p→pK±; p±p→pp. By studying the flavor dependence of the different reactions, we have been able to isolate the quark-interchange mechanism as dominant over gluon exchange and quark-antiquark annihilation.
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We present the final results of a measurement of the polarization parameter P 0 in high-energy n~-p and p-p elastic scattering, performed using a target which contained polarized protons. Data were taken at beam momenta of 6.0, 8.0, 10.0 and 12.0 GeV/c for n-, and of 6.0, 10.0 and 12.0 GeV/c for n+ and p, in the interval of invariant four-momentum transfer squared-t from 0.1 to 0.75 (GeV/c)2.
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K−−p interactions in the Columbia-BNL 30-in. hydrogen bubble chamber were studied at nine momenta from 594 to 820 MeVc. The results for elastic-scattering and zero-prong-plus-V0 events are presented here. Differential cross sections are given for the K−p, K¯0n, and Λπ0 final states. A fit to the K¯N channels was obtained which shows the effects of a 32− resonance at 1701 MeV. This energy is appreciably displaced from the peak in the inelastic cross section.
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The differential elastic scattering cross sections for negative pions on ; protons were measured at incident momenta of 1.51, 2.01, and 2.53 Bev/c with ; emphasis on the angular region outside the diffraction peak. The purpose of the ; experiment was to examine the behavior of the largeangle differential elastic ; cross section as a function of energy from the energy of the highest known ; resonance in the pion-nucleon system into the region where the total. cross ; sections appear to be approaching an asymptotic value. The experiment was ; performed at the Bevatron, using a luminescent chamber system to photograph the ; tracks of the scattered pion and the recoil proton from a liquid hydrogen target. ; A total of 2412 elastic scatterings were analyzed at 1.51 Bev/c, 1300 events at ; 2.01 Bev/c, and 1080 events at 2.53 Bev/c. From the existing data it may be ; noted that the backward bump, which has a maximum height of 2.1 mb/sr at 900 Mev ; and 1.1 mb/sr at 1020 Mev, is down to 0.4 mb/sr at 1.51 Bev/c (1.37 Bev), and is ; not present at 2.01 or 2.53 Bev/c. The angular distributions behind the ; diffraction peak at 2.01 and 2.53 Bev/c are rougly constant, decreasing from 0.18 ; mb/sr at 2.01 Bev/c to 0.125 mb/sr at 2.53 Bev/c. Although the data can be taken ; to suggest some oscillatory structure in this region, they are not inconsistent ; with an isotropic distribution that might be interpreted as evidence for an S-; wave scattering behind the diffraction peak. Large-Angle Elastic Scattering of Negative Pions by Protons at 1.51, 2.01, and 2.53 Bev/c.
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The results of a measurement of recoil proton polarization for π−p → π−p at 300 MeV are given, and a phase shift analysis is made with the help of other data.
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Measurements have been made of the asymmetry in the scattering of π− mesons by a polarized proton target. Scattered π mesons and recoil protons were detected in arrays of scintillation counters; data were obtained at 16 scattering angles at each of 8 beam momenta between 875 and 1578 MeV/c. Analysis of these data together with earlier differential-cross-section measurements shows that there must exist at least three resonances in this energy region: (i) mass 1920 MeV/c2, Γ=170 MeV/c2, I=32, F72; (ii) mass 1682 MeV/c2, Γ=100 MeV/c2, I=12, F52; and (iii) mass 1674 MeV/c2, Γ=100 MeV/c2, I=12, D52.
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Results of measurements of differential cross sections for the elastic scattering of 11'- mesons of energies 240, 270, 307 and 333 Mev by hydrogen are given.
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The elastic scattering of 300-Mev negative pions from hydrogen was studied with the aid of a hodoscopic system with pulse-fed counters. Equation (1) gives the angular distribution for the elastic scattering under the hypothesis that the fundamental contribution to the scattering comes from the S and P waves.
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THE study of elastic scattering at high energies in the region of the diffraction maximum has gained in interest recently in connection with the verifica- tion of the asymptotic expressions obtained by cal- culating the Regge-pole trajectories. We have in- vestigated the elastic scattering of 3. 5- Be VIc 7r- mesons by protons. The measurements were made with the aid of a liquid-hydrogen bubble chamber 25 em in diameter, placed in a 14 kOe magnetic field.
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DATA READ FROM GRAPH BY SRS.
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Results are presented of an investigation of the polarization of recoil protons appearing in elastic 1r+ -p scattering through an angle of 140 ± 8° in the c.m.s. at an energy of 307 ± 5 Mev. A polarization value P 1 = -0.19 ± 0.17 has been deriver from the data on the magnitude of the left-right asymmetry in elastic scattering of recoil protons on photographic emulsion nuclei. Phase shifts satisfying the indicated polarization value and consistent with the differential cross section for elastic scattering of 71"+ -mesons by protons are given by Eq. (1). Problems connected with the use of various phase shift sets for analysis of the experimental data are discussed.
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The differential cross section for π ± p elastic scattering below 2 GeV/ c has been measured at small forward pion angles by an electronics experiment. The interference effects observed between the Coulomb and the nuclear interaction have been used to determine the magnitude and sign of the real parts of the π ± p forward scattering amplitude. The latter are compared to the values predicted by the dispersion relations.
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Interactions of 781-MeV π+ mesons with protons were investigated using the Brookhaven National Laboratory 14-in. hydrogen bubble chamber. A total of 2305 events was observed. The data were normalized to a total cross section of 22.2 mb, giving partial cross sections σ(π+p→π+p)=9.5±0.5 mb, σ(π+p→π+pπ0)=9.3±0.5 mb, σ(π+p→π+π+n)=2.15±0.17 mb, and a multiple-pion-production cross section of 1.15±0.17 mb. The elastic angular distribution was obtained and is dσdω=(0.25±0.03)+(0.90±0.11)cosθc.m.+(2.57±0.24)cos2θc.m.+(0.19±0.22)cos3θc.m.−(1.73±0.34)cos4c.m.. The kinetic-energy and angular distributions of the outgoing particles in single-pion production are given. The data are compared with other experiments in this energy region and their relevance to the shoulder in the π+p total cross section near 830 MeV is discussed.
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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.
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The polarization of the recoil proton at this energy depends on the interference of the P 33 phase shift with the P 11 and S 11 phase shifts. The measured values indicate the existence of a large P 11 phase shift. The polarization was measured by scattering from carbon blocks in spark chambers using a Vidicon scanner to record the data.
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Invariant single-particle cross sections for pion and proton production in π ± p interactions at 8 and 16 GeV/ c are presented in terms of integrated distributions as functions of x , reduced rapidity ζ and p ⊥ 2 , and also in terms of double differential cross sections E d 2 σ /(d x d p ⊥ 2 ) and d ζ d p ⊥ 2 ). A comparison of π ± and π − induced reactions is made and the energy dependence is discussed. It is shown that the single-particle structure function cannot be factorized in its dependece on transverse and longitudinal momentum. For the beam-unlike pion, there is an indication for factorizability in terms of rapidity and transverse momentum in a small central region.
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We have made measurements of polarization in π−p elastic scattering, with emphasis over the backward region, at 1.60 to 2.28 GeVc. The results indicate the absence of u-channel dominance in the backward region, as was observed in the case of π+p scattering. Comparisons have been made with predictions of various phase-shift analyses which show that the agreement is generally very poor in the backward region.
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The asymmetry in the scattering of π− mesons by polarized protons has been measured at 50 different momenta from 0.643 to 2.14 GeV/c. Results were obtained at values of cosθ ranging from approximately +0.9 to -0.95 in the c.m. system at each incident pion momentum. The pion beam was incident on a 7.6-cm-long crystal assembly of lanthanum magnesium nitrate, in which the hydrogen in the water of crystallization was polarized by the "solid effect." The total momentum spread of the beam was 10% (full width at half-height) and data were collected simultaneously in 4 momentum channels, each with 2½% full width at half-height. A gas Čherenkov counter was used to reject incoming electrons. Scattered particles were detected in scintillation counter arrays placed within the 10-cm gap of the polarized target magnet. Encoded information from each array was stored in the memory of a PDP-5 computer connected on-line to a fast electronic logic network. The computer was programmed to classify the events according to momentum and scattering angle and subdivide them into coplanar and noncoplanar categories. The latter provided a measure of the background. The results have been expressed in the form of an expansion in terms of first associated Legendre polynomial series and compared with the predictions of recent phase-shift solutions. It is concluded that although these analyses give satisfactory predictions of the general features of the results, no one solution gives complete agreement with the data above about 1.0 GeV/c.
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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.
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The energy dependence of the differential cross section for $\pi^+ p$ elastic scattering at a c.m. angle near 174 ° has been measured. The momentum range of incident $\pi^+$ was 2.06-4.70 GeV/c. On this energy dependence one can see a structure, i.e. maxima corresponding to the baryon resonances $\Delta(2420)$ and $\Delta(2840)$. The structure is used for determination of the parities of these resonances.
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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.
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The elastic scattering of 3.55 GeV/ c π + and π − mesons by protons was measured at centre-of-mass angles between 165° and 177°. The angular distributions for 864 events show a steeply rising backward peak for π + p, while the shape is less clear for π − p.
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Extrapolations.
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Backward elastic scattering has been measured for π + p at 2.85 and 3.30 GeV/ c and for π − p at 3.30 GeV/ c . The π + p angular distributions show steep backward peaks, whereas the π − p distribution is flatter. At 2.85 GeV/ c the π + p differential cross section close to 180° is more than twice that at 3.30 GeV/ c , supporting the assignment J P = 11 2 + for Δ δ (2420) resonance. The π + p data at 2.85 GeV/ c indicate the onset of a dip at cos θ c.m. ≈ −0.97.
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The data for cos(theta) = 1 and U = 0 are the extrapolations.
The data for cos(theta) = 1 and U = 0 are the extrapolations.
Photographic plates were used to study the angular distribotion of 360 plus or minus 10 Mev pi /sup +/ mesons elastically scattered by protons. The differential cross sections derived from 218 scattering events for SP analysis and for SPD analysis are given. The phase shifts which correspond to these distributions are also given.
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NAME=THEORY DENOTES THE MONTE-CARLO GENERATED CROSS SECTIONS.
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POLARIZED PROTON TARGET.
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