pi- and K-meson Bethe-Salpeter Amplitudes
| dc.creator | Maris, P. | |
| dc.creator | Roberts, C. D. | |
| dc.date | 1997-08-15 | |
| dc.date | 1997-10-27 | |
| dc.date.accessioned | 2026-07-07T11:11:19Z | |
| dc.date.available | 2026-07-07T11:11:19Z | |
| dc.description | 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. | |
| dc.description | 35 pages, REVTEX, to appear in PRC, minor typ.-errors corrected | |
| dc.identifier | https://arxiv.org/abs/nucl-th/9708029 | |
| dc.identifier | http://arxiv.org/abs/nucl-th/9708029 | |
| dc.identifier | Phys.Rev.C56:3369-3383,1997 | |
| dc.identifier | doi:10.1103/PhysRevC.56.3369 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/191057 | |
| dc.subject | Nuclear Theory | |
| dc.subject | High Energy Physics - Phenomenology | |
| dc.title | pi- and K-meson Bethe-Salpeter Amplitudes | |
| dc.type | text |