dorsal/arxiv
View SchemaOn Size and Shape of the Average Meson Fields in the Semibosonized Nambu & Jona-Lasinio Model
| Authors | R. Wuensch, K. Goeke, Th. Meissner |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9311017 |
| URL | https://arxiv.org/abs/nucl-th/9311017 |
| DOI | 10.1007/BF01289598 |
| Journal | Z.Phys. A348 (1994) 111-116 |
Abstract
We consider a two-flavor Nambu \& Jona-Lasinio model in Hartree approximation involving scalar-isoscalar and pseudoscalar-isovector quark-quark interactions. Average meson fields are defined by minimizing the effective Euklidean action. The fermionic part of the action, which contains the full Dirac sea, is regularized within Schwinger's proper-time scheme. The meson fields are restricted to the chiral circle and to hedgehog configurations. The only parameter of the model is the constituent quark mass $M$ which simultaneously controls the regularization. We evaluate meson and quark fields self-consistently in dependence on the constituent quark mass. It is shown that the self-consistent fields do practically not depend on the constituent quark mass. This allows us to define a properly parameterized reference field which for physically relevant constituent masses can be used as a good approximation to the exactly calculated one. The reference field is chosen to have correct behaviour for small and large radii. To test the agreement between self-consistent and reference fields we calculate several observables like nucleon energy, mean square radius, axial-vector constant and delta-nucleon mass splitting in dependence on the constituent quark mass. The agreement is found to be very well. Figures available on request.
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"abstract": "We consider a two-flavor Nambu \\\u0026 Jona-Lasinio model in Hartree approximation\ninvolving scalar-isoscalar and pseudoscalar-isovector quark-quark interactions.\nAverage meson fields are defined by minimizing the effective Euklidean action.\nThe fermionic part of the action, which contains the full Dirac sea, is\nregularized within Schwinger\u0027s proper-time scheme. The meson fields are\nrestricted to the chiral circle and to hedgehog configurations. The only\nparameter of the model is the constituent quark mass $M$ which simultaneously\ncontrols the regularization. We evaluate meson and quark fields\nself-consistently in dependence on the constituent quark mass. It is shown that\nthe self-consistent fields do practically not depend on the constituent quark\nmass. This allows us to define a properly parameterized reference field which\nfor physically relevant constituent masses can be used as a good approximation\nto the exactly calculated one. The reference field is chosen to have correct\nbehaviour for small and large radii. To test the agreement between\nself-consistent and reference fields we calculate several observables like\nnucleon energy, mean square radius, axial-vector constant and delta-nucleon\nmass splitting in dependence on the constituent quark mass. The agreement is\nfound to be very well. Figures available on request.",
"arxiv_id": "nucl-th/9311017",
"authors": [
"R. Wuensch",
"K. Goeke",
"Th. Meissner"
],
"categories": [
"nucl-th"
],
"doi": "10.1007/BF01289598",
"journal_ref": "Z.Phys. A348 (1994) 111-116",
"title": "On Size and Shape of the Average Meson Fields in the Semibosonized Nambu \u0026 Jona-Lasinio Model",
"url": "https://arxiv.org/abs/nucl-th/9311017"
},
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