Theory of Meson Production on the Nucleon by Resonance Excitation
Final Report Abstract
Investigations of meson production on the nucleon is one of the few tools at hand to access the dynamics of the formation and decay of baryonic resonances. A major task of meson spectroscopy on the nucleon is to identify nucleonic excitations by separating the resonant parts of scattering amplitudes from background processes. On the theoretical side this demanding task requires methods accounting properly for the various interaction effects among the multitude of possible meson-nucleon or, if also strangeness is included, meson-hyperon exit channels. The Giessen model (GiM ) describes such reactions by a coupled-channels approach. A covariant field-theoretical formulation is used, based on a Lagrangian density obeying the symmetries of QCD. Meson and baryon interactions are described by deriving an equation for the T-matrix, fully accounting for channel coupling within the chosen model space. The resulting system of coupled equation is solved by the well established K-matrix approach. The model parameters are determined phenomenologically by fitting coupling constants and other input quantities to a selected set of data. The large scale numerical calculations provide partial wave amplitudes (PWA) being used to describe total and differential cross sections and polarization variables. The PWA give direct access to the identification of resonance and the extractions of their properties, e.g. through the derivation of multipoles. A distinct and indispensable advantage of the coupled channel treatment is the full control of interference effects. The project has served to improve the approach in various aspects. A major issue for a dynamical description of meson production and resonance formation – like in the GiM – is the inclusion of increasingly higher partial waves demanding the proper treatment of interaction vertices of highspin resonances. In this respect, the nature of spin-3/2 and spin-5/2 fields as fundamental matter fields have been studied. New constraints for a gauge-independent description of the formation, propagation, and decay vertices have been derived, generalizing previous studies of other groups. The results are in general important for any kind of quantum field theory dealing with high-spin Fermion fields. A large part of the research activities was devoted to keep the GiM parameter set up to date. That goal was achieved by large scale calculations for eta-meson and kaon production on the nucleon. The latest experimental results for eta-production on the proton and the population of the KΣ channels were analysed. We could identify a prominent structure in the ηp channels as a coupled-channels interference effect thus ruling out the existence of the formerly advocated state at √s = 1680 MeV. As a by-product, a new value of ηN scattering length was derived. The full set of K^±,0 Σ^∓,0 channels was analysed, thus updating the data base to the latest status. The results could resolve inconsistencies between data sets from different experiments. The work on two-pion channels was performed as planned. First results have been included already into the mentioned publications on eta- and kaon production on the nucleon. A major step forward was made in the last year or so, enabling us to treat consistently 2πN and π∆ propagation as intermediate and final states in the GiM coupled-channels scheme. A major problem was to derive an appropriate description of pion-pion interactions, accounting for the corresponding correlations in the isoscalar and isovector channels, respectively, as reflected by the f0 (600) sigmameson and the ρ(770)-meson.
Publications
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“On a gauge-invariant interaction of spin-3/2 resonances,” Phys. Rev. C 80 (2009) 058201
V. Shklyar and H. Lenske
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“Spin-5/2 fields in hadron physics,” Phys. Rev. C 82 (2010) 015203
V. Shklyar, H. Lenske and U. Mosel
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Eta-meson production in the resonance energy region,” Phys. Rev. C 87 (2013) 015201
V. Shklyar, H. Lenske and U. Mosel
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“Coupled-channel analysis of KΣ production on the nucleon up to 2..0 GeV,” Phys. Rev. C 88 (2013) 5, 055204
X. Cao, V. Shklyar and H. Lenske
