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.     

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.     

An analysis of the scattering π−C around the N resonance

Measurements of the elastic scattering π⁻−¹²C between 120 and 280 MeV permit an investigation of the Kisslinger-Ericson π-nuclear optical potential around the (3, 3) resonance. For this analysis nearly all parameters are assumed to be fixed by other reliable measurements resp. evaluations, apart from two parameters for the strength of the gradient potential (complex c_o). We explore the lines of equal χ² in the complex c_o plane and find two solutions. One of them can be interpreted as the physical solution.     

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.     

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%.     

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.     

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.     

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).     

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.     

ππ Scattering Amplitudes that Satisfy Inelastic Unitarity Constraints

We construct amplitudes which are represented by a Mandelstam representation with a finite number of subtractions and that satisfy ππ crossing symmetry and the unitarity constraints Im f_l^I(s) ≧|f_l^I (s)|², l=0, 1, 2,…, for all energies above threshold s > 4, in the three isospin channels I=0, 1, 2. The following types of solutions are derived.

• 1 The amplitudes have a positive double spectral function ϱ(s, t) ≧ 0. The total cross section decreases like σ_T(s) ∼ (log s)^-δ for arbitrary δ ≧ 1, including the limiting case δ=1.
• 2 The amplitudes are dominated by Regge poles, the total cross section can reach a constant asymptotic value, σ_T(s) → const.
• 3 The amplitudes are dominated by Regge cuts, the total cross section can increase logarithmically σ_T(s) → log s.

     

η,η′→ππγ with coupled channels

The decays η,η′→π⁺π⁻γ are investigated within an approach that combines one-loop chiral perturbation theory with a coupled channel Bethe–Salpeter equation which satisfies unitarity constraints and generates vector mesons dynamically from composite states of two pseudoscalar mesons. It is furthermore shown that the inclusion of the η′ as a dynamical degree of freedom does not renormalize the Wess–Zumino–Witten term.     

Chiral-loop and vector-meson contributions to η → ππγγ decays

The process η → π⁰π⁰γγ is discussed in Chiral Perturbation Theory (ChPT). Special attention is deveted to one-loop corrections, η-η′ mixing effects and vector-meson dominance of ChPT counter-terms. The less interesting η → π⁺π⁻γγ transition is briefly discussed too.     

Double charge exchange and one-pion production in π He collisions at 1.7 GeV/c

We present the results of a study of the exclusive reactions π^{+ 4}He → π⁻ 4p (double charge exchange, DCE) and π^{+ 4}He → π⁺ π⁻ 3pn (one-pion production). The experiment was performed with the Oxford/RHEL helium bubble chamber irradiated with a 1.7 GeV/c π⁺ beam. A general review of DCE models is presented and experimental results at other energies are discussed in the light of these models. None of the existing theoretical models is compatible with out data at 1.7 GeV/c. We propose a new mechanism for DCE, involving three nucleons, which reproduces the integrated as well as the differential cross sections. Some consequences for other models are also discussed.