A lower bound to the π0π0 S-wave scattering length

A new lower bound to the π⁰π⁰ S-wave scattering length is found in terms of the D-wave scattering length. The main ingredients of the method are the Roy exact partial-wave equations and an extensive use of unitarity in the physical region. For a value of a₂ = 7.3 × 10^?4, we get the bound a₀ ? ?0.33.     

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.     

The phase of the forward π+π− → π+π− scattering amplitude

Using methods developed by Pietarinen, we evaluate the phase of the forward scattering amplitude for the process π⁺π^? → π⁺π^? in the energy range 1.0 GeV ? √ s ? 1.8 GeV. Our results are in disagreement with previous work, unless early onset of the asymptotic behaviour of the phase of this amplitude is imposed. They tend to rule out some solutions for the partial-wave amplitudes in this energy range.     

Dispersion-relation analysis of K+p scattering below 2 GeV/c

We have obtained K⁺p scattering amplitudes that fit a large body of data below 2 GeV/c, satisfy phenomenological partial-wave backward dispersion relations, and are consistent with forward dispersion relations for the spin-non-flip amplitude, and forward dispersion-relation sum rules for the K⁺p P-wave scattering lengths. This has been achieved by firstly making an energy-dependent phase-shift analysis of 1 660 pieces of K⁺p data below 2 GeV/c, using parameterised partial-wave dispersion relations, with the additional constraints of forward dispersion relations and P-wave scattering lengths obtained from forward dispersion-relation sum rules, and then checking the resulting solutions for consistency with backward K⁺p dispersion relations.     

Analytic approach to the problem of constructing effective nucleon-nucleon potentials in the region of low and intermediate energies

A new relativistic approach to the problem of constructing effective local hadron-hadron potentials is proposed on the basis of analytic S-matrix theory and Gelfand-Levitan-Marchenko-Martin methods for solving the inverse quantum scattering problem. An effective potential is defined as a local operator in a partial-wave equation of the quasipotential type such that it generates an on-shell relativistic (Feynman) scattering amplitude that has required discontinuities at dynamical cuts. The method is used to construct nucleon-nucleon potentials in the ¹ S ₀-and ³ S ₁-wave states. The dynamical discontinuities of partial-wave amplitudes for nucleon-nucleon scattering are calculated on the basis of the one-bosonexchange model that takes into account the exchanges of π, σ, ρ, ω, η, and α ₀ mesons. It is shown that the nonlinear relation between the discontinuities of partial-wave scattering amplitudes at dynamical cuts and interaction operators generates additional short-range repulsion not associated with omega-meson exchange. The experimental energy dependences of phase shifts in the channels of nucleon-nucleon scattering that are considered here are faithfully reproduced by the results of the calculations up to the projectile-nucleon kinetic energies in the range T = 1.5–2.0 GeV.     

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.     

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.     

The influence of inelastic πω channel on pion form factor at s<(mω + mπ)2

It is shown that F_π(s) can be calculated in a model independent way if one knows the phase δ₁ and the inelasticity η of the p-wave ππ scattering and also F_π and the form factor of the γ¹ → π°ω transition for s> (m_ω + m_π)². The correction on F_π(s) for s< (m_ω + m_π)² due to the πω state with a strong ?′(1250) allows to explain the discrepancy between ?-dominance predictions and the experimental data.     

Spin-rotation measurements in π−p → K0Λ

The first measurements of spin-rotation in meson-baryon scattering in the resonance region are presented. These measurements, for the reaction π^?p → K⁰Λ, confirm the main predictions of a previous partial-wave analysis. Comments are made on resonant couplings in the reaction π^?p → K⁰Λ.     

On the light-by-light contribution to the sixth-order muon anomaly

We have evaluated analytically the coefficient of log m_μ/m_e for the six photon-photon scattering diagrams contributing to the muon g ? 2 in sixth order. The result is remarkably simple, 2π²/3, in complete agreement with the latest numerical evaluation. This completes the analytic calculation of all logarithmic terms in sixth order.     

Off-shell πN scattering near the Δ resonance

A parameter-free form factor for virtual πN scattering near the Δ resonance is derived. It depends only on s and m²_N ?P²_N, not on P²_π.     

Low energy π-π resonances in the Veneziano model

We attempt to impose elastic unitarity on the forward π-π scattering using the Veneziano Amplitude together with a crossing symmetric subtraction term as an input. TheN/D method is used and thep, ? mesons are interpreted as CDD poles. The self consistency requirement led to the evalutation of the low energy parameters and theS andP-wave phase shifts. The values of the scattering lengths obtained area ₀ ⁰ =0.084m _π ^?1 ,a ₂ ⁰ =?0.024m _π ^?1 ,a ₁ ¹ =0.047m _π ^?3 .     

Measurement of diffractive 3π production on a polarized target at 17 GeV/c

The reaction π^?p↑→π^?π⁺π^?p has been measured at 17 GeV/c using a polarized target. The data sample contains about 60 000 interactions on polarized protons. The nucleon polarization as a function of momentum transfer is very similar to elastic π^?p scattering and is nearly independent of the π mass, except for a possible structure around 1.2 GeV.Using the isobar model, we have performed a partial-wave analysis and extracted the 3π amplitudes. The generalized 3π density matrix elements agree with earlier determinations. Relative phases obtained from density matrix elements agree well with the ones obtained from transversity amplitudes. This proves the validity of the coherence assumption made in the interpretation of unpolarized target results. Our results confirm the existence of an A₁ resonance in the region 1.2–1.3 GeV.     

Current algebra calculation of e+e-→4π± and determination of ϱ′(1600) parameters

A current algebra calculation of e⁺e^-→4π^± cross section is carried out using the axial current matrix element obtained from τ→π?ν. Assuming ?′→?+2π(I=0, l=0), the following results are obtained: for the A₁ resonance, 1.05?m_A ?1.15 GeV; for ?′, Γ?′(total)≈0.23 GeV, M_?′≈1.5 GeV, Γ(?′→e⁺e^-)≈0.4 keV×B^?1(?′→?′ →?π⁺π).     

Coupled channel study on the S-wave ππ → KK interaction

We perform a dispersion relation type calculation of the I = 0 S-wave amplitude g₀⁺ (t) for the process $\text{ππ →}\text{K}\text{K}$, in the region from t = 4μ² to t = (1100 MeV)². Crossing is imposed by generalizing the newly developed hyperbolic partial-wave relations to our reaction and by imposing them on our amplitude using experimental Kπ phase-shift information as input. Analyticity and unitarity is imposed by generalizing the formalism of BFP [1] for parametrizing partial-wave amplitudes. This readily allows us to impose the experimental $\text{ππ →}\text{K}\text{K}$ cross section. Finally the low energy behaviour is constrained to lie within certain limits recently deduced from fixed-tKπ dispersion relation studies [2] and including the current algebra prediction as a special case. We are able to resolve a previous controversy regarding the sign of Im g₀⁽⁺⁾ (t).     

Optical potential calculations for the 1s level in pionic atoms

The Ericson-Ericson optical potential for theπ-nucleuss-wave interaction was extended to be applicable also for light nuclei. In particular, terms of order A^?1 were evaluated and the (π2N) dispersion was considered. From comparison with experimental data we found that considerable improvement could be achieved by introducing terms of order A^?1. The (π2N) dispersion was found to be repulsive and of the same magnitude as the absorption. The (πN) scattering lengths were deduced to be α₃?α₁=0.258±0.008m _π ^?1 and α₁+2α₃=?0.018±0.008m _π ^?1 .     

Measurmennt of recoil proton polarization in the process of π− photoproduction from neutrons in the energy range between 700 and 1200 MeV

The recoil proton polarization for γn → π^?p was measured around the third resonance region. Both momentum vectors of the proton and the pion were determined by the magnetic spectrometers. The proton polarization was measured by means of proton-carbon scattering in the polarization analyzer located behind the proton spectrometer. Below 900 MeV incident photon energy, our data are consistent with the other existing experimental data ($\text{θ}{}_{\mathrm{\pi }}{}^1\text{= 90°}$) and the predictions of partial-wave analyses. Above 1000 MeV, however, a large discrepancy was observed between our data and the predictions of the partial-wave analyses. The discrepancy stands out as the pion c.m. angle increases. A new partial-wave analysis was made for γn → π^?p including our polarization data, and the accuracy of the experimentally determined electromagnetic coupling constant of the third resonances were greatly improved. In particular, a finite amount of the helicity $\text{3}\text{2}$ amplitude for the γn → F₁₅(1688) resonance was obtained against the predictions of the quark models, by Copley, Karl and Obryk and by Feynman, Kislinger and Ravendal but in agreement with the relativistic quark models of Sugimoto and Toya, and Kubota and Ohta.     

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.     

Determination of the ππ scattering lengths from data on πN → ππN reactions by the method of Roy equations

Fitted phase-shift curves from the threshold to the dipion mass, which is equal to 1 GeV, are constructed on the basis of all available experimental values of the S-and P-wave phase shifts for five charged channels of pion-pion scattering. The resulting phase-shift curves are introduced in the Roy equations in order to obtain the subtraction constants λ _l ^I (s). By using these subtraction-constant values as functions of the dipion mass, the S ₀-and S ₂-wave pion-pion scattering lengths are found to be a ₀ ⁰ = (0.240 ± 0.023)m _π ^?1 and a ₀ ² = (?0.034 ± 0.013)m _π ^?1 . A strong correlation of the S-wave scattering lengths is demonstrated.     

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.