Chiral baryon in the coherent pair approximation

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Abstract
We reexamine the work of Goeke et al., who considered a chiral model for the nucleon based on the linear sigma model with scalar-isoscalar scalar-isovector mesons coupled to quarks, and solved it using the coherent-pair approximation. In this way the quantum pion field can be treated in a nonperturbative fashion. In this work we review this model and the coherent pair approximation, correcting several errors in the earlier work. We minimize the expectation value of the chiral Hamiltonian in the ansatz coherent-pair ground-state configuration, and solve the resulting equations for nucleon quantum numbers. We calculate the canonical set of nucleon observables and compare it with the Hedgehog model and experiment. Using the corrected equations yields slightly different values for nucleon observables, but does not correct the large virial deviation in the π-nucleon coupling. Our results therefore do not significantly alter the conclusions of Goeke et al.
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