A comparative study of the NNπ system: (I). The πd → πd, πd → NN channels

Numerical results are presented for πd → πd, πd NN observables for 290 ? T_π (MeV) ? 50. We discuss sensitivity of predictions for various input elements like the deuteron form factor, the range of the NNπ vertex and the parametrization of the background part of the P₁₁πN scattering matrix and remark on possible parallels for A(π, π) and A(π, 2N) amplitudes. A comparison is made with previously obtained results of similar scope.     

Comparison between γN→π and πN→ϱN in the resonance region up to s=1.75 GeV via the vector-dominance-model

We display the helicity amplitudes for the N_? system for each J^P state of the N_π system in the reaction Nπ→N?. These amplitudes are obtained from a K-matrix fit to amplitudes of the reaction Nπ→Nπ and Nπ→Nππ (via the isobar model). We then take either these amplitudes or the resonance couplings estimated from these amplitudes and compare them to the photoproduction amplitudes via the V.D.M. Two possible kinematics are considered for the N_? system below its threshold. These four methods give a range in which the V.D.M. can be accomodated even at this low energy.     

Analysis of decay of πN resonances into Nππ channels

Couplings of πN resonances with masses between 1.65 and 1.97 GeV/c² to Δπ and ?N channels are determined using the scattering matrix elements resulting from inelastic partial-wave analyses of πN → Nππ. The inelastic amplitudes were derived using an isobar model with a π-exchange based high partial-wave input. These couplings are compared to those derived from an analysis of πN → Nππ without a high partial-wave input. Some (weak) evidence for coupling of the ?N channel to the P31(1910) resonance seen in elastic phase-shift analyses is found.     

Exact solution of a model for πd induced reactions and its application to pion-nucleus reactions

Reduction techniques are applied to πd elastic scattering and π-absorption in a theory without anti-nucleons. In a one-pion approximation we derive two sets of exact coupled-channel equations for respectively the amplitudes T_πd,NN, T_{Nδ, NN} and T_{πd, πd}, T_{d, NΔ}- Alternatively we express in terms of the absorption amplitude T_{πd, NN} available solutions for a three-body problem restricted to the πd and NΔ channels. We explicitly demonstrate that our model (which comes close to the one of Thomas, Mizutani and Koltun) strictly respects the Pauli principle and avoids double-counting. Using the same technique we determine amplitudes for the (π, 2N) reaction and for π (in)elastic scattering on general nuclei in terms of amplitudes amongst the NN, NNπ channels. Both the elastic amplitude and the πA optical potential are shown to decompose into a multiple scattering part based on an input πN amplitude without the P₁₁ partial wave and calculable absorption corrections.     

Investigation of the low-lying nucleon resonances in reactions of π<Superscript>+</Superscript>π<Superscript>−</Superscript> pair electroproduction on protons

The cross sections of the reaction ep → e′p′π⁺π^? for small photon virtualities were measured on a CEBAF large acceptance spectrometer (CLAS detector) at the Thomas Jefferson National Accelerator Facility for the first time. A complete set of one-dimensional cross sections of the reaction was obtained for photon virtualities in the range 0.2 GeV² < Q ² < 0.6 GeV² and invariant masses of the final hadronic system in the range 1.3 GeV < W < 1.6 GeV. A preliminary analysis of the obtained data in the framework of the phenomenological model demonstrated that the Q ² dependence of the electromagnetic form factors for the P ₁₁ (1440) and D ₁₃ (1520) resonances can be determined in the kinematic region (which is the most sensitive to the contribution from the meson cloud) and that the axial transition form factor p → Δ can be derived.     

Resonant and nonresonant contributions from unphysical regions in dispersion relations

Unphysical regions on the right hand cut in partial wave dispersion relations for a two-particle processA+B→A′+B′ are expressed by measurable quantities, under the assumption that there is only one important 2-particle channel in the unphysical region. The solution is unique, if the phase shiftδ _l for the elastic scattering in the channel responsible for the appearance of the unphysical region takes a value between 0 andπ at the physical threshold forA+B→A′+B′. The difference between non resonant (δ_l≠π/2 in the unphysical region) and resonant contributions is shortly discussed.     

Phases of resonant amplitudes: πN → ϱN

Using SU(6)_W symmetry in its l-broken form we find that the newly reported relative signs of πN → ?N resonant amplitudes seem to indicate a universal “SU (6)_W-like” preference for all observed multiplets. Since the corresponding πN → πΔ phases favour an “anti-SU(6)_W” solution for the 70, L^P = 1^? multiplet the l-broken SU (6)_W model now faces a serious contradiction.     

Two and three pion-cut contributions to nucleon-nucleon scattering

Examining information from NN forward scattering in terms of discrepancy functions, we show that the 2π cut contributions as calculated via dispersion methods from πN scattering are in perfect agreement with NN scattering. Furthermore, we demonstrate the need for 3π cut contributions which are quantitatively well described by a nucleon exchange model. Finally, in addition to the 2π and 3π cut contributions, we determine the coupling constants of the ω and A₁ to be: g_Vω²/4π = 8.1 ± 1.5, g_Tω/g_Vω = 0.14 ± 0.20 and g_A1²/4π = 7.3 ± 3.0. The coupling of the η turns out to be zero.     

Dispersion theory of parity non-conservation in pion-nucleon scattering at low energies

We examine the possibility for testing the weak parity non-conserving (pnc) interaction in pion-nucleon scattering at low energies. We start out analysis by assuming the existence of a pnc πNN coupling which conserves time reversal invariance and has the isospin selection rule ΔI = 1, and the existence of fixed-t dispersion relations obeyed by the pnc invariant amplitudes. By using the nonrelativistic expansion, we then derive dispersion relations for the partial-wave amplitudes.We calculate parity-odd observables in π^?p → π^?p and in π^?p → π⁰n, e.g., the up-down asymmetry α in the total cross section for a polarized target and the longitudinal polarization P of the recoil nucleon. In the conventional Cabibbo model for the weak interaction P and α are found to be of order 10^?7 to 10^?8.We have also examined the t-channel pnc ?-exchange process which has the isospin selection rule ΔI = 0, 2 and found it to contribute dominantly to P in the charge-exchange channel π^?p → π⁰n.     

π−A1 interference in πN → ϱN

An estimate of the A₁NN coupling is made using axial vector meson dominance of weak form factors, PCAC and current algebra. We use this to predict a vanishingly small polarisation due to unnatural parity exchanges in πN → ?N near the forward direction. In contrast, the contribution to πN → ωN of the Z (the J^PC = 2^?? exchange degenerate partner of the A₁) is found to be significant as indeed indicated by experiment.     

The three-component dual deck model,factorization and double diffractive dissociation

We propose the generalization to double diffractive dissociation (DDD) of the three-component dual Deck model which was designed to describe single diffractive dissociation and successfully applied to N → Nπ dissociation. With no free parameter we get a very satisfactory agreement with the existing data in nn → (pπ^?)(pπ^?) including the observed pronounced structure in the momentum transfer distributions. We also predict unexpected correlations between the cos θ_J of the two decays, which, through factorization are typical of our three-component dual Deck model. A general discussion of factorization properties is given.     

The I = 0, s-wave ππ scattering length

Interior dispersion relations are applied to πN scattering amplitudes to extract the I = 0, s-wave ππ scattering length, a₀⁰. Two methods are used, the second of which also incorporates known ππ scattering phase shifts. We have used the πN amplitude analysis of Pietarinen and obtained values of a₀⁰: (0.28 ± 0.09)μ^? and (0.25 ± 0.08)μ^? for the two methods respectively, consistent with other recent determinations from K_e4 and πN → ππN data. The 1971 πN phase-shift analysis of Ahmehed and Lovelace was also used successfully in the first method to obtain the value a₀⁰: (0.15 ± 0.14)μ^?, consistent with the above. The second method was found to be ineffective in the face of relatively unsmooth discrepancy functions obtained from the Ahmehed-Lovelace phase shifts.     

A quark model of mesons based on chiral symmetry

We construct a model of mesons as q$\text{q}$ pairs in the infinite momentum frame. The basic symmetry is spontaneously broken chiral SU₂ × SU₂. We compute the rates for the decays ? → 2π, σ → 2π, A₁ → ?π, A₁ → σπ, A₂ → ηπ, π_N → ηπ, D → ηπ, f → 2π and the coupling constant, g²_?ωπ. We find qualitative agreement with the experimental values. The theory is similar to that of Gilman and Harari.     

Duality diagrams and the decays of the ψ and ψ′

We apply duality diagrams to the ψ and ψ′ decays. We propose that the ψ → 3π decay is described by a Virasoro formula, and show that the low mass ππ suppression in ψ′ → ψ2π is a consequence of the threshold factor contained in the Pomeron-2π coupling. We stress the importance of the ψ and ψ′ decays for the study of heavy mesonic resonances.     

η → 3π decay and πη scattering in chiral SU(2) × SU(2) symmetry

The problem of η → 3π decay in chiral SU(2) × SU(2) symmetry is investigated. We argue that the well-known difficulties of the conventional pole model originate from underestimating the role of the η-meson pole graph. This model is shown to be suitable for describing η → 3π decay if the strong ηηππ vertex in the η-pole graph is determined by an SU(2) × SU(2)-invariant interaction. The π^o ? η transition constant g_πη is evaluated from U-spin invariance with the help of a current-mixing model: | g_πη | ≈ 0.05. It turns out that the experimental data on both the decay widths and the energy spectrum can be satisfied by fitting the value of the ηηππ coupling constant as a parameter. As a result, predictions for the s- and p-wave πη scattering lengths are obtained: |a_πη⁰| ≈ 0.2m_π^?1, |a_πη¹| ≈ 0.1m_π^?3.     

Two-nucleon production of hyperons and the search for strange dibaryons

The double charge exchange reaction³He(K^?,π ⁺)Xn was studied at 870 MeV/c. In the X missing mass range below the sigma-nucleon production threshold (2130 MeV/c²), events were detected which can be attributed to the two-nucleon process pp(K^?,π ⁺)λn. This reaction and mass range also offers good prospects for finding theI=1/2,l=1 (¹ P₁) spin-singlet dibaryon D_s suggested as the lowest massS=?1 dibaryon in the MIT Bag Model. Although the existence of the D_s is not ruled out by the present data, there is no need to invoke such an object to account for the observed events below σ production threshold. We show that the cross section level for these events is compatible with a dominant two-nucleon mechanism K^?p→π ⁰λ,π ⁰p →π ⁺n. We also offer an interpretation of the recent (K^?,K⁺) data on nuclear targets from Iijimaet al., which display a broad peak centered around a K⁺ momentum of 600 MeV/c. We find that the two-nucleon mechanism K^?N →πY,πN→K⁺Y produces cross sections which are at least an order of magnitude smaller than those observed, and we suggest that the one nucleon process K^?p →Φλ, followed by the decayΦ → K⁺K^?, accounts for the data.     

Asymptotic restrictions and ππ scattering lengths in non-linear chiral SU(2) × SU(2) dynamics

The most general effective lagrangian for ππ scattering, that takes into account the exchange of scalar (0⁺), tensor (2⁺) and ? mesons, is constructed within the framework of non-linear chiral SU(2) × SU(2) dynamics. Asymptotic restrictions proposed by Weinberg are imposed on the amplitude of ππ scattering. These restrictions allow one to obtain four independent sum rules containing particle masses, coupling constants and the coefficient A₂ in an expansion of the symmetry-breaking term in a power series of π². The use of only the f⁰ meson in the obtained sum rules leads to the following values of the ππ scattering lengths, the width of ?(700) → 2π decay, and the parameter A₂: α₀⁰ = 0.92m_π^?1, α₀² = 0.27 m_π^?1, α₁¹ = 0.033 m_π^?3, Γ[ε(700) → 2π] = 390 MeV, A₂ = + 1.6. It is shown that the inclusion of heavier mesons results in some increase of the ππ scattering lengths and the parameter A₂, but a decrease of the value of Γ(? → 2π). The field-algebra requirements lead to negligible changes in the results. Analysis of the sum rules shows the incompatability of the asymptotic restrictions with a symmetry breaking which has the transformation properties of the fourth component of a chiral vector.     

Scattering lengths of pionic 3He and 4He

Scattering lengths of pionic ³He and ⁴He and the charge exchange contribution to the 1s width of pionic ³He are calculated within the fixed scatterer approximation of the multiple scattering formalism. Particular attention is focussed on the nuclear physics part and on πN p-wave contributions. For the first time triple scattering and double-spin-flip contributions have been included. We find significant deviations from previous estimates and calculations. Good agreement is achieved with the experimental π^?3He scattering length, whereas in the case of ⁴He a repulsive dispersion contribution is clearly needed. We propose to use the measured 1s level shift of pionic ³He as a constraint to deduce a precise value of the isoscalar πN scattering length. Furthermore, we find that multiple scattering reduces the impulse approximation value for Γ_1s(π^?3He → π^{0 3}H) by more thsn 20 %. This result casts some doubt on impulse approximation calculations of radiative pion capture as well.     

Diffraction dissociation of neutrons in the reaction dp → pppπ− at 25 GeV/c

We observe the reaction dp → p_spec (pπ^?)p in a bubble chamber exposure at 25 GeV/c incident deuteron momentum. The (pπ^?) system with invariant mass below 2.0 GeV is interpreted as neutron diffraction dissociation. The (pπ^?) mass spectra show little if any direct evidence of N¹ production. The decay angular distributions and the momentum transfer distributions of the (pπ^?) system suggest a smooth increase in contributions from higher partial waves $\text{(J ?}\text{3}\text{2}\text{)}$ with increased mass or momentum transfer. A simple partial-wave analysis shows a P₁₁ contribution below 1.3 GeV for small ?t′ and a dominant D₁₃ contribution elsewhere. Both the P₁₁ and D₁₃ amplitudes peak far below the N¹(1470) and N¹(1520) resonances. We also find evidence for the charge-exchange reaction np → p(pπ^?). In this process the (pπ^?) system shows evidence for Δ^o(1236) and N¹(1520) production.