The asymmetry in π−He scattering

We show that the π⁺−³He asymmetry data obtained in a recent TRIUMF experiment at T_π = 100 MeV can be understood in terms of the elementary πN amplitudes. Through a comparison to a full optical-potential calculation that employs realistic Faddeev wave functions for the trinucleon we show that all nuclear-structure dependence cancels for at lower energies. At higher pion energies around the Δ-resonance region the sign flip of offers the possibility of extracting information about the smaller partial waves.     

Study of the δ− → π +π−π− Decay Mode

No enhancement in δ^? → π ⁺π^?π^? decay mode appeared at mass 962 MeV or at 996 MeV produced in π^?p → δ^?p interaction near its production threshold in a missing mass counter experiment. This finding fully supports the fact that the δ^? → π ⁺π^?π^? decay mode is not allowed by the conservations of the angular momentum and the parity.     

Coupled-channels calculations of intermediate energy π−C inelastic scattering and charge exchange

Coupled-channels calculations have been carried out for pion inelastic scattering and charge exchange on 1p-shell nuclei at pion energies between 120 and 226 MeV. A momentum space technique is used, with the 1p-shell shell-model wavefunctions of Cohen and Kurath. Results are presented here for A=13. Channel-coupling effects are negligible in the strong 3/2^- and 5/2^- inelastic excitations of ¹³C, but enhance the analog charge-exchange cross sections by 7 to 20%.     

ππ scattering amplitudes within the sub-threshold triangle

The on-shell ππ scattering amplitudes within and on the boundary of the subthreshold triangle (0 ≤ s ≤ Σ, 0 ≤ t ≤ Σ, 0 ≤ u ≤ Σ ≡ 4μ²) are investigated. Interior Dispersion Relations, when combined with experimental ππ phase shifts, inelasticities, and scattering lengths, provide an almost perfect tool for this study. The general results obtained are in striking agreement with the chiral model of Weinberg.     

Pion-pion amplitude from the πN→ππN reaction

The possibilities of extracting parameters of ππ interaction from the experimental data on the πN→ππN reaction are analyzed in detail. The interval 300<P_lab<500 MeV/c is shown to be the smoothness domain of the πN→ππN amplitude. The expression for the background part of the amplitude is developed model-independently. The ππ scattering is described by four parameters to be extracted from experimental data (along with 11 background parameters).     

A Partial Wave Analysis of the Reaction π+p→ (π+π−π0) Δ++ at 16 GeV/c

A partial wave analysis of the 3π-system has been performed for the reaction π⁺p→ (π⁺π^?π⁰) Δ⁺⁺ (1232) at 16 GeV/c. Beside the well-established A₂⁰ (1300), the resonant state ω* with isospin I = 0 and spin-parity J^P = 3^? decaying mainly into (?π) has been found. Its mass and width have been determined to be M = (1.71 ± 0.03) GeV and Γ = (0.22 ± 0.10) GeV. The cross section for the reaction π⁺p→ ω* (1700) Δ⁺⁺ (1232) is σ = (12 ± 6) μb.     

Model amplitude analysis of πp→ππn

We present an amplitude analysis of the process π⁻p→π⁺π⁻n at 15 GeV/c assuming spin and phase coherence of the production amplitude. The bearing of the results on aspects of dipion production phenomenology is discussed.     

Rigorous pion-pion scattering lengths from threshold πN → ππN data

A new evaluation of the universal ππ scattering length relation is used to extract the ππ s-wave scattering lengths from threshold pion production data. Previous work has shown that the chiral perturbation series relating threshold pion production to ππ scattering lengths appears to converge well only for the isospin-2 case, giving a₂ = −0.031 ± 0.007m_π⁻¹. A model-independent and data-insensitive universal curve then implies a₀ = 0.235 ± 0.03m_π⁻¹ for the isospin-0 scattering length.     

A Multidimensional Study of Clustering in the Reactions π±p→pπ+π±π− at 16 GeV/c using the Yang Variables

The clustering of events in 7-dimensional phase space is studied in the reactions π^±p→pπ⁺π^±π^? at 16GeV/c. The Yang variables are used for locating events in the phase space. Clusters are defined and events are allocated by a novel iterative technique. This is based on a measure of the distance of each event from the cluster center, weighted by the covariance matrix of the event density. The clusters found are then related to reaction mechanisms such as diffraction dissociation of pion and proton, resonance production, etc. High mass enhancements in the (3π) system and in the (pπ⁺π^?) system are identified and separated from other mechanisms. Cross sections are given for individual sub-channels and compared to results obtained by other techniques.     

Experimental study of the time-dependent rate of K → πππ

The time-dependence of the decay rate of initially pure K⁰ into the final state (π⁺π⁻π⁰) has been studied in search for the decay k_S⁰→π⁺π⁻π⁰. No evidence is found in a sample of 384 observed events. The ratio of the CP -violating K_S⁰ amplitude and the K_L⁰ amplitude is η₊₋₀ = (0.13_−0.20^+0.17) + i(0.17_−0.26^+0.27); the ratio of the CP-conserving K_S⁰ amplitude and the K_L⁰ amplitude is < 0.4. The energy dependence of the K⁰→π⁺π⁻π⁰ matrix element is found to be a₊₋₀ = −0.31 ± 0.03.     

Measurement of the differential cross section for πp → πn around the Δ(1232) resonance and test of the charge independence principle

Differential cross sections for the charge-exchange reaction of π⁻ on protons in the region of the Δ(1232) resonance (128 MeV T_π⁻ 246 MeV) are reported. Measurements were performed by detecting the neutron with a time-of-flight technique. The neutron counter efficiency was measured over the entire energy range. Particular care was devoted to eliminating possible sources of systematic error. Statistical errors are of the order of 4%, total errors of the order of 7%. The experimental results are in fair agreement with the most recent phase-shift analysis. Our data satisfy the triangle inequality. An analysis based on recent phase-shift values does not favour violation of charge independence.     

An Approximation Scheme for Constructing π°π° Amplitudes from ACU Requirements

The requirements of analyticity, crossing symmetry and unitarity (ACU) are used as input to construct amplitudes for the scattering of neutral π mesons. They are obtained explicitly as polynomials in certain conformally transformed variables which ensure the correct analyticity structure. Crossing symmetry is expressed as a set of linear relations between the expansion coefficients. The same is true for the threshold behaviour of the partial waves and the behaviour for large energies of either the partial waves and the amplitudes itself. To enforce the positivity of the partial waves (up to a certain l) a new set of variables is introduced. It is obtained by solving the system of linear inequalities expressing the positivity condition. In this way one gets explicit expressions for all amplitudes satisfying the ACU requirements to some approximation. The rigorous constraints obtained from these ACU requirements are used to test the accuracy of this construction. The properties of all amplitudes are investigated in detail. It is indicated how this approximation scheme may be improved to any degree of accuracy and how it may be generalized to the full isospin case.     

Note on the angular analysis of the decay J/ψ→f(→ππ)+γ

We derive the general (4-parameter) angular decay distribution for the cascade decay J/ψ→f(→ππ)+γ and determine its angular coefficients from the absorptive and dispersive contributions of the lowest order QCD diagram.