We report on a study of ρ0, ρ+, ω,\(\bar K^{*0} (892)\) andK*0 (892) inclusive production in π+p interactions at 250 GeV/c, for ρ+,\(\bar K^{*0} (892)\) for the first time in a π+p experiment. The data are compared withK+p data in the same experiment, with results of other experiments and with quark-parton models. Interesting differences are found between ρ+,0 and ω production.
Inclusive cross sections and average multiplicity per inelastic collision.
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Results on the multiplicity structure of diffractively excited meson and proton systems in À+/K+p interactions at 250 GeV/c are presented for diffractive masses up to about 9 GeV. The energy dependence of the average charge multiplicity and the shape of the multiplicity distribution in terms of KNO-scaling and negative binomial distribution are investigated. The diffractive systems are compared toe+e−,lh and non-diffractivehh final states as suggested by modern approaches of the Pomeron-hadron collision. Systematic differences are found between diffractive meson and proton systems but also between diffraction and the reactions compared to.
The inclusive production of neutral kaons is studied inK+p and π+p interactions at 250 GeV/c. Total and semi-inclusive cross sections and average kaon multiplicities are presented and compared with the data at lower energies. The longitudinal and transverse momentum distributions and their energy dependence are analyzed. The results are interpreted in the framework of recent parton models.
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Quasi-elastic scattering with central dipion cluster production is studied in π+p andK+p interactions at 250 GeV/c. The cross section of double pomeron exchange is obtained as σDPE(π+p →π+(π+π−)p)=24 ±5 µb and σDPE(K+p→K+(π+π−)p)=19 ±5 µb. The low energy pomeron-pomeron cross section is estimated for the first time.
Numerical values supplied by W. Kittel.
Numerical values supplied by W. Kittel.
Numerical values supplied by W. Kittel.
We present data on the production of the baryons Λ,\(\bar \Lambda \),p and of the baryon resonances Σ*+ (1385) and Δ++ (1232) inK+p and π+p interactions at 250 GeV/c. Results are given on total and semi-inclusive cross sections, Feynman-x spectra, transverse momentum distributions and Λ polarization. The data are compared with measurements at lower energies, with deep inclastic lepton nucleon data and with predictions of quark-parton models. The models underestimate Λ production in the central c.m. region, a feature also seen in recent heavy-ion data. This failure can be cured in JETSET 6.3 by adjustment of the di-quark break-up probability.
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Data are presented on inclusive π0 production in the forward c.m. hemisphere (xF>0.025) in π+p,K+p andpp interactions at 250 GeV/c. These data are compared to results at other energies and interpreted in terms of quark-parton models.
Using a double arm electromagnetic calorimeter we have searched for narrow states produced in the exclusive reaction π − p→γγn at 13 GeV/c. No enhancements were observed in the mass range 2.0–4.0 GeV/c 2 . For example, the 90% confidence limit on η c production is σ ( π − p→ η c n)× B ( η c → γγ ) < 44 pb.
UPPER LIMIT (90 PCT CL) FOR SIG*BR(ETA/C --> 2 GAMMA).
A determination of branching ratios for D meson decays into all charged particle final states is reported. The values obtained: (D ± → K ∓ π ± π ± /all D ± ) = (14 ± 6)% and ( D 0 /D 0 → K ± π ∓ π + π − /all D 0 /D 0 ) = (10 ± 4)%, are higher than those currently accepted. This result, if confirmed, implies a corresponding reduction in the accepted values for some total cross section measurements. Revised inclusive cross sections for D meson production in the forward hemisphere in π − p and pp interactions at 360 GeV/ c , are presented.
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We have studied the reaction π − p → X − p followed by the decay X − → ωπ − at 11.2 GeV/ c . The partial-wave analysis in the mass range 1.36–2.0 GeV shows a clear structure in the J P = 3 − , m = 0 wave peaking at 1.67 GeV with a width of ∼0.21 GeV. We interpret this result as resulting from the g → ωπ decay. The differential cross section d σ d t is in agreement with the production of the g-meson through one-pion exchange.
FROM BREIT-WIGNER FIT TO <OMEGA PI-> MASS SPECTRUM. CORRECTED FOR OMEGA TAILS AND OTHER DECAY MODES. CROSS SECTION ORIGINALLY GIVEN IN R. GESSAROLI ET AL., NP B126, 382 (1977).
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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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We have searched for exclusive hadronic J/ψ production by looking for narrow resonances in the e+e− mass spectrum of the reaction π−p→e+e−n. No events were observed in the region around 3.1 GeV/c2. The cross section for the reaction π−p→J/ψ n at 13 GeV/c is no more than 103 pb at the 90% confidence level.
Corrected cross section based on 7.4 pct branching ratio.
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PT(P=3,NAME=OUT)**2 - MEAN SQUARE OF THE PROJECTION OF THE ASSOCIATED PARTICLE TRANSVERSE MOMENTUM ONTO THE NORMAL TO THE TRIGGER PARTICLE PRODUCTION PLANE.
PT(P=3,NAME=OUT)**2 - MEAN SQUARE OF THE PROJECTION OF THE ASSOCIATED PARTICLE TRANSVERSE MOMENTUM ONTO THE NORMAL TO THE TRIGGER PARTICLE PRODUCTION PLANE.
PT(P=3,NAME=OUT)**2 - MEAN SQUARE OF THE PROJECTION OF THE ASSOCIATED PARTICLE TRANSVERSE MOMENTUM ONTO THE NORMAL TO THE TRIGGER PARTICLE PRODUCTION PLANE.
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Results on the study of D(1285)→K + K − π 0 -decay are presented. The K + K − effective mass spectrum is measured with statistics which are by an order of magnitude higher than in the previous data. From the analysis of the differential spectrum d N d M KK (in the framework of the δ-dominance model) the δ-meson effective width is Γ δ >180MeV/ c 2 at √ s =1 GeV/ c 2 , which means a strong coupling of the δ-meson with hadrons.
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The ωπ − mass spectrum, in the reaction π −p → ωπ − pat 11.2 GeV/ c , shows the production of the B − meson with a cross section of 27 ± 5 μb as well as a clear enhancement around 1670 MeV. In the differential cross section for B − production, there is a strong forward peak and a change of slope at t ' t 0.2 GeV 2 .
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ABS(D-WAVE/S-WAVE) = 0.4 +- 0.1 FOR B DECAY.
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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FOUR PION RESONANCE CALLED RHO(1.71) BY AUTHORS. DECAY IS CONSISTENT WITH 100 PCT <RHO0 RHO-> MODE.
We present inclusive ϱ ±,0 and ω cross sections in the beam fragmentation region of π + p interactions at 250 GeV/ c . The near equality of the ϱ + and ϱ 0 cross sections implies suppression of valence quark recombination in forward vector meson production.
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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 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.
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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 reaction π-p→pωπ- has been studied at 9.1 GeV/c, its total cross-section is σ=(123±22) μb. The pB− and the quasi-three-body channels contribute with cross-section of σ=(24±7) μb and σ=(94±23) μb, respectively. The main features of the quasi-three-body pωπ- channel, displayed by some techniques of data presentation, are satisfactorily described by a double-Regge-pole model. In this model pomeron-meson and meson-meson exchanges are taken into account. An OPE modelà la Veneziano predicts a total cross-section too high and reproduces very poorly the observed features.
BREIT-WIGNER PLUS BACKGROUND FITS FOR B(1235)- AND OMEGA MESONS.
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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The inclusive production of vector mesons (charged ρ(770), ω(783), ϕ(1020) and neutralK*(892)) in π−p interactions at 360 GeV/c is studied. The data are based on 160 000 reconstructed events recorded in the NA 27 Experiment using the LEBC-EHS facility at CERN. The production cross sections in the forward hemisphere in c.m.s. and the longitudinal momentum distributions are determined. The results are compared with data obtained at lower energies.
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Upper limits of cross sections.
Cross sections extrapolated to x > 0.
Data on the reactions (K+/π+)p→(K+/π+)pπ+π- and (K+/π+)p→(K+/π+)p2π+2π-, obtained with the European Hybrid Spectrometer, are presented and compared with data at lower energies. The contribution of beam and target diffractive dissociation and double Pomeron exchange, and porperties of these reactions are discussed.
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Compensation of transverse momentum is studied in π+p interactions at 250 GeV/c. SignificantpT-transfer is found between c.m.s. hemispheres. With respect to the beam axis transverse momentum is compensated over the whole event, with respect to the sphericity axis mainly within one hemisphere. The highestpT in the event is mainly compensated by increased multiplicity. The QGSM and FRITIOF models qualitatively reproduce these effects, but important differences are observed.
Mean value of total transverse VECTOR defined as sum over all charged particles in the forward or backward hemispheres was measured.
Mean value of total transverse VECTOR defined as sum over all charged particles in the forward or backward hemispheres was measured.
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The production of K s 0 , Λ and Λ is measured in π + p interactions at 32 GeV/ c . The total inclusive cross sections are found to be 2.07±0.14, 1.00±0.10 and 0.14±0.04 mb, respectively. The energy dependence of total inclusive cross sections and inclusive distributions is discussed and a comparison is made with p, p , K + and K − induced reactions. We find that the factorization hypothesis is satisfied for the inclusive reactions π + p→ Λ X and K + p→ Λ X. Multi-strange-particle production is similar in π + p and K + p interactions at 32 GeV/ c . There is evidence for beam fragmentation in Λ production. The hierarchy of Λ inclusive cross sections in p , K + , π + and K − induced reactions at 32 GeV/ c is qualitatively explained by a quark recombination model. The cross sections for inclusive K ∗ + (892) and Σ + (1385) production in 32 GeV/ c π + p interactions are 1.07±0.57 mb and 0.19±0.08 mb, respectively.
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This Letter reports measurements of the ratios of $\pi$, K, and p production at large values of transverse momentum in $\pi^- −p$ collisions. The charge ratios, such as $\frac {\pi^−} {\pi^+}$, $\frac {K^−} {K^+}$, and $\frac {\overline{p}}{p}$ are seen to be quite different from those measured in p −p collisions. These ratios are sensitive tests of hard-scattering models, and are compared with theoretical predictions. The particle ratios have also been studied as a function of center-of-mass angle ($\theta^*$) at $\theta^*$ = 90°, 77°, and 60°.
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Measurements of the polarization parameters and angular distributions are reported for π±p elastic scattering at 100 GeV/c and for pp elastic scattering at 100- and 300-GeV/c incident momentum. The π±p data cover the kinematic range 0.18≤−t≤1.10 GeV2 and are in agreement with current Regge-model predictions. The pp data cover the kinematic range 0.15≤−t≤1.10 GeV2 and 0.15≤−t≤2.00 GeV2 at 100 and 300 GeV/c, respectively, and are found to be consistent with absorption-model predictions.
We present results from a direct photon pair search performed with the NA3 spectrometer, using incident positive and negative beams at 200 GeV/ c interacting with a carbon target. The experiment is sensitive to photons with p T >1.8 GeV / c and −0.4⩽y ∗ ⩽1.0 , one in each arm of the apparatus. A 3 standard deviation signal is seen in τ − and p interactions. The cross section is higher than the second order QCD calculations, but systematic errors are large.
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We report on a study of inclusiveπ0 and η meson production inπ+p andK+p interactions at 250 GeV/c beam momentum. The Feynman-x spectrum ofπ0 is very similar in shape and normalization to that of negatively charged particles produced in the same experiment. The results are compared with data at other energies and with FRITIOF model predictions. This model overestimates the η cross section by a factor of 2.5. It reproduces theπ0 cross section correctly, but predicts a too hardπ0x distribution.
Data from Gamma Detectors only.
Data from Gamma Detectors only.
Data from RCBC only.
Charm D-meson production in 360 GeV π − p interactions has been studied using the high-resolution hydrogen bubble chamber LEBC and the European Hybrid Spectrometer. The data show evidence for leading quark effects both in the number of D-meson types and in the Feynman x distributions. The production cross section is of the form d 2 δ d x d p T 2 ∞(1-x) n exp (-ap T 2 ) with n = 2.8±0.8 and a = 1.1±0.3 (GeV/ c ) −2 . The x distribution is, however, compatible with the presence of both central ( n = 6) and leading (n = 1) D / D production. The fraction of D-messons in the leading component is estimated to be ≈30%. The rapidity gap between members of reconstructed charm pairs is small compared to the available rapidity range. The inclusive cross section for single D-messons in the forward direction is: δ(D/ D )=(40 8 +15 )μ b ( for x>0) .
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Charged multiplicity and π 0 cross sections for π − p inelastic interactions at 70 GeV/ c are presented. The data were obtained from an exposure of the BEBC bubble chamber equipped with a track sensitive target (TST) to an unseparated negative beam at the CERN SPS. About 10 000 events were used for the charged multiplicity study, and about 2000 Dalitz pairs for the π 0 production analysis. A total of 12 e + e − pairs with a mass higher than the π 0 mass were found and analysed in terms of η or ω Dalitz pairs or decay pairs of vector mesons. Comparisons with data at other energies are made in terms of charged prong, π 0 cross sections, and of multiplicity parameters. The moments of longitudinal and transverse momentum distributions of the π 0 are determined and compared to the predictions of quark counting rule models.
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New data have been obtained on a resonance in the ϕπ 0 system, the C meson, which is formed in the π − p → ϕπ 0 n charge-exchange reaction. The experiment has been performed at the Serpukhov 70 GeV accelerator. The mass and the width of the resonance are measured to be M =1480±40 MeV , Γ =130±60 MeV . The production cross section is determined at a π − momentum of 32.5 GeV / c : σ ( π − p → Cn )· BR ( C → ϕπ 0 )=40±15 nb . The C(1480) meson has an isospin I =1 and spin-parity J PC =1 − − . It is strongly coupled to the ϕπ 0 channel and is considered as a possible exotic meson.
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THE ACCEPTANCE CORRECTED DISTRIBUTION.
Cross sections and charged multiplicity distributions for π+p,K+p andpp interactions at 250 GeV/c are presented and compared to each other as well as to earlier (for π+p andK+p lower energy) data. Consistently, the meson-proton (M+p) data have narrower multiplicity distributions and higher average multiplicity thanpp data. Up to our energy, generalized KNO functions describe the energy dependence of the shape of the multiplity distribution with one parameter forM+p and one forpp collisions. If interpreted in terms of negative binomials, the parameter 1/k tends to be slightly lower forM+p than forpp data. For both types of hadron-hadron collision, 1/k is larger than fore+e− andlp collisions.
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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>
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AVERAGE TARGET POLARIZATION WAS 76 +- 3 PCT.
No description provided.
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 differential cross section for elastic scattering of positive pions on protons has been measured at a nominal incident-meson kinetic energy of 250 MeV. The angular range covered in the center of mass by the 13 data was 14.9° to 160°. The fractional rms errors were typically 1.5%. A liquid-hydrogen target was bombarded by a beam of 2.5×106 mesons/sec. The scattered pions were detected by a counter telescope. Recoil protons were eliminated by means of a Čerenkov counter. A phase-shift analysis was performed combining the above-mentioned data with the recoil-proton polarization measurements taken recently with the help of a polarized proton target. Only one acceptable SPD Fermi-type phase-shift set was found. When F waves were included, a total of three possible phase-shift solutions emerged from the analysis. However, arguments based on the data could still be made to eliminate all but one phase-shift set. On the other hand, the remaining phase-shift set, similar in type to the SPD solution, suffers from the disadvantage of large rms errors assigned to its small phase shifts.
No description provided.
We have measured the polarization parameter in π−p elastic scattering at laboratory momenta of 1180, 1250, and 1360 MeV/c in the angular interval 65°<θc.m.<115°. The results were used to show that the polarized target used in these (and other similar) experiments was uniformly polarized. These measurements were also used to resolve pre-existing experimental discrepancies in the determination of the polarization parameter, and to clarify the behavior of scattering amplitudes in this energy range. We show that local measurements of this type are important in resolving discrete ambiguities affecting the energy continuation of the amplitudes. An important by-product of this experiment is the development of a fast method of reconstructing particle trajectories and fitting the elastic events, which could have a significant impact for future high-statistics experiments.
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