Chiral model of the nucleon: Projecting the hedgehog as a coherent state

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Abstract
The construction of baryon states with good spin and isospin is studied in a chiral model. This is a linear σ model, describing quarks interacting with pions and σ mesons. It has previously been investigated in the mean-field approximation (MFA), using the hedgehog ansatz. The ansatz corresponds to a mixture of spin-isospin eigenstates. A coherent state is used to provide a quantum description for the mesonic part of the wave function. The hedgehog baryon is projected onto states with good spin and isospin. The Peierls-Yoccoz projection is used, in analogy with the treatment of deformed nuclei. As well as N and Δ, a J=T=(5/2) baryon state is obtained. The wave functions are varied after projection. For the N and Δ, the resulting field distributions are fairly similar to those from the MFA. Various nucleon properties are calculated. These include proton and neutron charge radii, for which reasonable agreement with experiment is obtained. Results for other properties are similar to those obtained with an approximate projection method, and indicate the need to extend the present approach to include vector mesons and the effects of vacuum polarization. Comparisons are made with wave functions used in the cloudy bag and Skyrme models.

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