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.
No description provided.
LEGENDRE POLYNOMIAL FIT USED TO CORRECT FOR ELASTIC EVENTS LOST FROM THE FORWARD BIN.
No description provided.
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.
No description provided.
No description provided.
The reactionsπ−p→K0∑0(1385) andπ−p→K+∑−(1385) are studied at an incident momentum of 3.95 GeV/c using data from a high statistics bubble chamber experiment corresponding to approximately 90 events/μb. The total and differential cross sections and the density matrix elements of the Σ(1385) are presented. The results are compared with those obtained for the related processesπpp→K+∑+(1385) and\(K^ -p \to \pi ^ \mp\sum ^ \pm(1385)\) in this energy range. Evidence is presented for the existence of production mechanisms with exotic exchanges in thet channel.
FROM THE CHANNEL PI- P --> LAMBDA K0 PI0 WHICH HAS A CROSS SECTION OF 72 +- 4 MUB.
FROM THE CHANNEL PI- P --> LAMBDA K+ PI- WHICH HAS A CROSS SECTION OF 79 +- 3 MUB.
FORWARD CROSS SECTION.
The reactionsπ−p→K0(890) Λ,K0(890)Σ0 andK0(890)Σ0 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, density matrix elements of the vector meson and hyperon polarizations are presented. A transversity amplitude analysis is performed for each of the reactions. The results are compared with those obtained for the SU(3) related processesK−p→ϕΔ, ϕΣ0, ϕΣ0(1385) andϱ−Σ+(1385) and with predictions of the additive quark model and SU(6) sum rules.
BREIT-WIGNER FIT WITH BACKGROUND POLYNOMIAL.
BACKWARD CROSS SECTION.
TOTAL CROSS SECTION USING SLICING TECHNIQUE. FORWARD (-TP < 1.2 GEV**2) CROSS SECTION IS 25 +- 2 MUB: DOUBLE MASS CUT GIVES 20 +- 7 PCT BACKGROUND CONTAMINATION.
Inclusive φ production is studied in π − p collisions at 16 GeV/ c . The φ cross section for Feynman variable x φ > 0.2 is found to be (15.5 ± 3.6) μb. This leads to an extrapolated cross section of (29.9 ± 7.0) μb for x φ > 0.0. Fitting the momentum transfer squared distribution of the φ to the form e −bp 2 T gives an average slope of b = (2.4 ± 0.3) (GeV/ c −2 for x φ > 0.5.
No description provided.
No description provided.
DATA OBTAINED FROM FIGURE BY A.A. LEBEDEV.
None
No description provided.
No description provided.
No description provided.
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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Theπ0 andη0 production is studied inπ−p interactions at 360 GeV/c. The cross section forπ0 production in the forward hemisphere (X>0) isσ(π0)=(49.7 ± 1.0 ± 1.1) mb and for η withX>0.1,Nch>2,σ(η0)=(3.1 ± 0.5) mb. The ratio of theπ0 toη0 cross section forX>0.1,Nch>2 isσ(π0)/σ(η0). Results on FeynmanX andpT distributions are presented. The data were obtained using the European Hybrid Spectrometer EHS and the bubble chamber LEBC at CERN.
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