dorsal/arxiv
View Schemapi- and K-meson Bethe-Salpeter Amplitudes
| Authors | P. Maris, C. D. Roberts |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9708029 |
| URL | https://arxiv.org/abs/nucl-th/9708029 |
| DOI | 10.1103/PhysRevC.56.3369 |
| Journal | Phys.Rev.C56:3369-3383,1997 |
Abstract
Independent of assumptions about the form of the quark-quark scattering kernel, K, we derive the explicit relation between the flavour-nonsinglet pseudoscalar meson Bethe-Salpeter amplitude, Gamma_H, and the dressed-quark propagator in the chiral limit. In addition to a term proportional to gamma_5, Gamma_H necessarily contains qualitatively and quantitatively important terms proportional to gamma_5 gamma.P and gamma_5 gamma.k k.P, where P is the total momentum of the bound state. The axial-vector vertex contains a bound state pole described by Gamma_H, whose residue is the leptonic decay constant for the bound state. The pseudoscalar vertex also contains such a bound state pole and, in the chiral limit, the residue of this pole is related to the vacuum quark condensate. The axial-vector Ward-Takahashi identity relates these pole residues; with the Gell-Mann--Oakes-Renner relation a corollary of this identity. The dominant ultraviolet asymptotic behaviour of the scalar functions in the meson Bethe-Salpeter amplitude is fully determined by the behaviour of the chiral limit quark mass function, and is characteristic of the QCD renormalisation group. The rainbow-ladder Ansatz for K, with a simple model for the dressed-quark-quark interaction, is used to illustrate and elucidate these general results. The model preserves the one-loop renormalisation group structure of QCD. The numerical studies also provide a means of exploring procedures for solving the Bethe-Salpeter equation without a three-dimensional reduction.
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"abstract": "Independent of assumptions about the form of the quark-quark scattering\nkernel, K, we derive the explicit relation between the flavour-nonsinglet\npseudoscalar meson Bethe-Salpeter amplitude, Gamma_H, and the dressed-quark\npropagator in the chiral limit. In addition to a term proportional to gamma_5,\nGamma_H necessarily contains qualitatively and quantitatively important terms\nproportional to gamma_5 gamma.P and gamma_5 gamma.k k.P, where P is the total\nmomentum of the bound state. The axial-vector vertex contains a bound state\npole described by Gamma_H, whose residue is the leptonic decay constant for the\nbound state. The pseudoscalar vertex also contains such a bound state pole and,\nin the chiral limit, the residue of this pole is related to the vacuum quark\ncondensate. The axial-vector Ward-Takahashi identity relates these pole\nresidues; with the Gell-Mann--Oakes-Renner relation a corollary of this\nidentity. The dominant ultraviolet asymptotic behaviour of the scalar functions\nin the meson Bethe-Salpeter amplitude is fully determined by the behaviour of\nthe chiral limit quark mass function, and is characteristic of the QCD\nrenormalisation group. The rainbow-ladder Ansatz for K, with a simple model for\nthe dressed-quark-quark interaction, is used to illustrate and elucidate these\ngeneral results. The model preserves the one-loop renormalisation group\nstructure of QCD. The numerical studies also provide a means of exploring\nprocedures for solving the Bethe-Salpeter equation without a three-dimensional\nreduction.",
"arxiv_id": "nucl-th/9708029",
"authors": [
"P. Maris",
"C. D. Roberts"
],
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"hep-ph"
],
"doi": "10.1103/PhysRevC.56.3369",
"journal_ref": "Phys.Rev.C56:3369-3383,1997",
"title": "pi- and K-meson Bethe-Salpeter Amplitudes",
"url": "https://arxiv.org/abs/nucl-th/9708029"
},
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