Chiral baryon in the coherent pair approximation

Abstract

We revisit the work of K. Goeke, M. Harvey, F. Gr\"ummer, and J. N. Urbano (Phys. Rev. {\bf D37}, 754 (1988)) 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 using the coherent-pair approximation. In this way the quantum pion field can be treated in a non-perturbative 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 with the Hedgehog model and experiment. Using the corrected equations yield slightly different values for nucleon observables but do not correct the large virial deviation in the $\pi$-nucleon coupling. Our results therefore do not significantly alter the conclusions of Goeke, et al..Comment: RevTeX, 24 pages, 5 figure

Coherent pair state of the pion in the constituent quark model

“…13 has indicated that the hedgehog ansatz is better than the CPA as an approximation for the pion field in a ground state nucleon [14,15,16]. Because the hedgehog ansatz breaks the spin-isospin symmetry, the quantum numbers associated with this symmetry must be projected out by semiclassical or adiabatic method.…”

“…We apply the CPA to the study of excited baryons, while this approximation has been used to study the ground state nucleon [14,15]. This application is considered as a good test ground to see the role of mesons in the nucleon structure.…”

Magnetic Catalysis in the Higher-Order Quark Sigma Model

“…For this purpose, we numerically calculate the effective potential in Eq. (6). The parameters of the present model are the coupling constant g and the sigma mass m σ .…”

“…The model was first proposed in the 1960s as a model for pion-nucleon interactions. Today it serves as an effective model for the low-energy phase (zero temperature) of quantum chromodynamics [3,4,5,6] and its modification is suggested as in works [7,8,9,10,11] to provide a good description of the baryon properties. In addition, the quark sigma model is successfully applied to the description of static and dynamic baryon properties at finite temperature and density as in Refs.…”

The baryon mass calculation in the chiral soliton model at finite temperature and density

“…The chiral soliton model could be solved in the mean-field approximation. A semiclassical soliton solution is referred to a baryon, and the baryon properties can be derived easily from the soliton solution [15][16][17][18][19][20].…”