Backward pion-nucleon scattering

A global analysis of the world data on differential cross-sections and polarization asymmetries of backward pion-nucleon scattering for invariant collision energies above 3GeV is performed in a Regge model. Including the N_a\ensuremath N_{\alpha} , N_g\ensuremath N_{\gamma} , D_d\ensuremath \Delta_{\delta} and D_b\ensuremath \Delta_{\beta} trajectories, we reproduce both angular distributions and polarization data for small values of the Mandelstam variable u , in contrast to previous analyses. The model amplitude is used to obtain evidence for baryon resonances with mass below 3GeV. Our analysis suggests a G₃₉\ensuremath G_{39} -resonance with a mass of 2.83GeV as member of the D_b\ensuremath \Delta_{\beta} -trajectory from the corresponding Chew-Frautschi plot.     

Low-energy pion-nucleon scattering

Several topics in pion-nucleon scattering at low energies are addressed. First, we review the predictions of chiral symmetry for the near-threshold region. The pion-nucleon scattering lengths and the Cheng-Dashen theorem with the related issue of the strangeness content of the nucleon are discussed in some detail. Finally, the status of the scalar mesons and the relevance of the pomeron and the concept of duality for pion-nucleon dynamics is pointed out.Lecture given at the 8th Summer School on Intermediate Energy Physics: Hadron Dynamics at Low and Intermediate Energies, Prague, July 10–14, 1995.I would like to thank the organizers of the Praha Indian-summer school for inviting me to this beautiful city. I am indebted to Th. Rijken and J. J. de Swart for discussions about the pomeron, the scalar mesons, and partial-wave analysis, and to U. van Kolck and J. Friar for discussions about chiral symmetry. This work was included in the research program of the Stichting voor Fundamenteel Onderzoek der Materie (FOM) with financial support from the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO).     

Measurement of the polarization parameterP inπ + p elastic scattering in the region of low-lying pion-nucleon resonances

This paper presents the results of an experiment in which the polarization parameterP in π⁺ p elastic scattering has been measured in the energy range from 335 to 580 MeV. The experiment was performed on a pion channel of the LNPI synchrocyclotron using a polarized proton target and wire spark chambers with magnetostrictive read-out. The results have substantially higher precision in comparison with the most of other experiments in this energy range and allow to determine unambiguously the shape of angular dependenceP(θ ^*) in the whole investigated region. New phase-shift analysis of π⁺ p scattering data has been performed. The results of this experiment were used also to check isospin invariance.     

Constant-cutoff approach to pion-nucleon scattering

Pion-nucleon scattering amplitudes as well as Born amplitudes are calculated in a constant-cutoff approach to the canonical quantization of skyrmions, with the subsidiary conditions imposed on the quantum fields and their conjugate momenta such that all infrared singularities from the zero-frequency modes are eliminated. It is shown that the Born terms with recoil corrections are reproduced by the pion-nucleon linear and quadratic interactions.     

The pion-nucleon forward scattering amplitude

The pion-nucleon forward scattering amplitude has been calculated from new data of the total cross sections, using several assumptions on the energy dependence above 20 GeV. The results are presented as complex diagrams of the forward amplitude, which are of interest for the discussion of the nucleonic resonances and the non-resonant background scattering. In addition the predictions for the elastic forward cross sections are given as well as the contributions of the real parts to this quantity. A comparison with the new Saclay data of the charge exchange forward cross section leads to the estimate αρ≈0.6, if a Regge behaviour is assumed above 20 GeV. There are indications in favour of a new\(T = \tfrac{1}{2}\) resonance at the total c.m. energyW≈2.8 GeV.     

The isospin bounds and phase-contours in pion-nucleon scattering

In this paper we investigate the isospin constraints on differential and integrated (unpolarized and polarized) cross sections in pion-nucleon scattering. Defining$\text{Σ}{}^{\mathrm{(n)}}\text{-}\text{integrated}$ cross sections and using the classical Minkowski and Hölder inequalities we obtain a large class of isospin bounds. The saturation of the isospin bounds is investigated using dispersion relation predictions and a CERN theoretical solution for the phase shifts.     

Pion scattering and nuclear dynamics

A phenomenological optical-model analysis of pion elastic scattering and single- and doublecharge-exchange scattering to isobaric-analog states is reviewed. Interpretation of the opticalmodel parameters is briefly discussed, and several applications and extensions are considered. The applications include the study of various nuclear properties, including neutron deformation and surface-fluctuation contributions to the density. One promising extension for the near future would be to develop a microscopic approach based on powerful momentum-space methods brought to existence over the last decade. In this, the lowest-order optical potential as well as specific higher-order pieces would be worked out in terms of microscopic pion-nucleon and delta-nucleon interactions that can be determined within modern meson-theoretical frameworks. A second extension, of a more phenomenological nature, would use coupled-channel methods and shell-model wave functions to study dynamical nuclear correlations in pion double charge exchange.Invited talk to the symposium 'Mesons and Light Nuclei IV, Bechyn, Czechoslovakia, September 5–10, 1988.The author would like to express his appreciation to Dr. Mach and the organizers for their the hospitality at the Conference.     

The pion-nucleon scattering lengths from pionic deuterium

We use the framework of effective field theories to discuss the determination of the S-wave scattering lengths from the recent high-precision measurements of pionic deuterium observables. The theoretical analysis proceeds in several steps. Initially, the precise value of the pion-deuteron scattering length is extracted from the data. Next, is related to the S-wave scattering lengths a ₊ and a _-. We discuss the use of this information for constraining the values of these scattering lengths in the full analysis, which also includes the input from the pionic hydrogen energy shift and width measurements, and thoroughly investigate the accuracy limits for this procedure. In this paper, we also give a detailed comparison to other effective field theory approaches, as well as to the earlier work on the subject, carried out within the potential model and multiple scattering framework. Received: 28 January 2005, Published online: 8 April 2005 PACS: 36.10.Gv, 12.39.Fe, 13.75.Cs, 13.75.Gx A. Rusetsky: On leave of absence from High Energy Physics Institute, Tbilisi State University, University St. 9, 380086 Tbilisi, Georgia. This research is part of the EU Integrated Infrastructure Initiative Hadron Physics Project under contract number RII3-CT-2004-506078. Work supported in part by DFG (SFB/TR 16, “Subnuclear Structure of Matter”). An erratum to this article is available at .     

Pion Compton scattering in perturbative QCD

Pion Campton scattering is studied in perturbative QCD for real and space-like initial photons. Different methods for the convolution of the hard amplitude with the pion wave-functions, which have in the past led to conflicting results, are compared.     

Pion fluctuation in deep inelastic scattering

The forward neutron production in the ep collisions at 300GeV measured by H1 and ZEUS Collaborations at DESY has been used to estimate the total probability for proton fluctuation into nπ⁺ and pπ⁰. The probability found is on the order of 30%. This number is compared with the numbers obtained for the probability of quark fluctuation into π⁺ from several alternative DIS processes (Gottfried sum rule, polarized structure function) and the axial-vector coupling constant, where the pion fluctuation is believed to play an important role.     

Sum rules for forward elastic pion-nucleon scattering

A number of energy weighted sum rules relating amplitudes and differential cross sections for forward elastic and charge exchange scattering to the total pion-nucleon cross section are derived from dispersion relations.     

Reggeized symmetry models and pion-nucleon scattering in forward and backward directions

A Reggeization procedure is developed for higher symmetry schemes and its relationship with the SU(6) × SU(6) Reggeization is exhibited. The kinematic singularities arising from SU(6)_W-invariant vertex functions are removed with the help of fixed cuts and the resulting scattering amplitudes are extrapolated to hadron poles. The essentially parameter free theory thus obtained is shown to lead to reasonable forward and backward differential cross sections in pion-nucleon scattering at high energies.     

Fermion Regge poles and relations between phase shifts in the pion-nucleon scattering

A Regge pole model is proposed. It is shown that simple relations between the smallπN phase shifts can be obtained without using any Regge pole parameters.