Approximating chiral quark models with linear σ-models Original Research Article

We study the approximation of chiral quark models with simpler models, obtained via gradient expansion. The resulting Lagrangian of the type of the linear σ-model contains, at the lowest level of the gradient-expanded meson action, an additional term of the form View the MathML source. We investigate the dynamical consequences of this term and its relevance to the phenomenology of the soliton models of the nucleon. It is found that the inclusion of the new term allows for a more efficient approximation of the underlying quark theory, especially in those cases where dynamics allows for a large deviation of the chiral fields from the chiral circle, such as in quark models with non-local regulators. This is of practical importance, since the σ-models with valence quarks only are technically much easier to treat and simpler to solve than the quark models with the full-fledged Dirac sea.