Chiral Quark-meson Model Research Articles

Strange baryons in a chiral quark-meson model: (I). SU(3)-symmetric model

The chiral quark-meson model based on a linear σ-model is extended to three flavours of quarks. We describe the choice of parameters and the features of the hedgehog solitons both in the SU(3)-symmetric limit and with realistic symmetry breaking. For the case of unbroken symmetry the approximate projection method of Birse and Banerjee is used to calculate properties of the octet baryons. The magnetic moments are found to be in reasonable agreement with experiment, with most of the discrepancy being accounted for by the fact that the kaons and pions are degenerate. Lowest-order cranking is used to calculate the mass splittings between the baryon multiplets. The isospin cranking which governs the octet-decuplet splitting is very similar to that in the SU(2) model. The moment of inertia for “strange” rotations gives the energies of states which must involve mesonic excitations. It is found to be small, indicating that such states, if they exist, lie well above the nucleon.

QUARK CONTRIBUTION TO THE PROTON SPIN IN THE CHIRAL QUARK-MESON MODEL

It has been argued that, to leading order in the 1/Nc expansion, very little of the spin of the proton is carried by the helicities of its constituent quarks, in accordance with the results of a recent EMC experiment. We investigate this question by a direct computation in the chiral quark-meson model, where the proton spin is generated by cranking a mean field hedgehog baryon. For not too small values of the quark-meson coupling constant, our results are consistent with the EMC data.

Strange things in the proton?

We use the RPA to calculate the energy of strange baryons in a three-flavour version of the chiral quark-meson model. For realistic symmetry breaking this energy is found to depend non-linearly on the strength of the SU(3)-breaking term in the hamiltonian. This supports Jaffe's contention that a large πN sigma commutator need not imply a large strange-quark content in the proton.

Cranking an SU(3)-symmetric chiral soliton

The chiral quark—meson model based on a linear σ model is extended to three flavours of quarks. For an SU(3)-symmetric version of the model we use a lowest-order cranking approach to calculate the splittings between the baryon multiplets. The isospin cranking which governs the octet—decuplet splitting is identical to that in the SU(2) model. The moment of inertia for “strange” rotations gives the energies of states which must involve mesonic excitations. It is found to be small, indicating that such states, if they exist, lie well above the nucleon.

Semiclassical projection of hedgehog models with quarks.

A simple semiclassical method is presented for calculating physical observables in states with good angular momentum and isospin for models whose mean-field solutions are hedgehogs. The method is applicable for theories which have both quark and meson degrees of freedom. The basic approach is to find slowly rotating solutions to the time-dependent mean-field equations. A nontrivial set of differential equations must be solved to find the quark configuration for these rotating hedgehogs. The parameters which specify the rotating solutions are treated as the collective degrees of freedom. They are requantized by imposing a set of commutation relations which ensures the correct algebra for the SU(2) x SU(2) group of angular momentum and isospin. Collective wave functions can then be found and with these wave functions all matrix elements can be calculated. The method is applied to a simple version of the chiral quark-meson model. A number of physical quantities such as magnetic moments, charge distributions, g/sub A/, g/sub ..pi..//sub N//sub N/, N-..delta.. mass splitting, properties of the N-..delta.. transition, etc., are calculated.

RPA method for quark-meson solitons

The quark-meson RPA equations, which describe small oscillations of a bound quark-meson system about the stationary configuration, are derived through linearization of the classical time-dependent Euler-Lagrange problem. The method has an immediate application in phenomenological quark-meson models for baryons. It provides a test of the classical stability of these systems. A number of measurable quantities, such as the spectrum of excited states and the meson-soliton phase shifts can be calculated. We demonstrate the QMRPA on a simple, 3 + 1 dimensional model of the nucleon — the chiral quark-meson model.

The nucleon-delta splitting in the chiral quark-meson model

Cranking techniques are employed to calculate the N − Δ splitting in the chiral quark-meson model. A splitting of 322 MeV is obtained. It is determined that about 80% of the angular momentum and isospin in the model are carried by the mesons.