dorsal/arxiv
View SchemaStability Analysis of the Instantaneous Bethe-Salpeter Equation and the Consequences for Meson Spectroscopy
| Authors | J. Parramore, H. -C. Jean, J. Piekarewicz |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9510024 |
| URL | https://arxiv.org/abs/nucl-th/9510024 |
| DOI | 10.1103/PhysRevC.53.2449 |
| Journal | Phys.Rev.C53:2449-2467,1996 |
Abstract
We investigate the light and heavy meson spectra in the context of the instantaneous approximation to the Bethe-Salpeter equation (Salpeter's equation). We use a static kernel consisting of a one-gluon-exchange component and a confining contribution. Salpeter's equation is known to be formally equivalent to a random-phase-approximation equation; as such, it can develop imaginary eigenvalues. Thus, our study can not be complete without first discussing the stability of Salpeter's equation. The stability analysis limits the form of the kernel and reveals that, contrary to the usual assumption, the confining component can not transform as a Lorentz scalar; it must transform as the timelike component of a vector. Moreover, the stability analysis sets an upper limit on the size of the one-gluon-exchange component; the value for the critical coupling is determined through a solution of the ``semirelativistic'' Coulomb problem. These limits place important constraints on the interaction and suggest that a more sophisticated model is needed to describe the light and heavy quarkonia.
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"abstract": "We investigate the light and heavy meson spectra in the context of the\ninstantaneous approximation to the Bethe-Salpeter equation (Salpeter\u0027s\nequation). We use a static kernel consisting of a one-gluon-exchange component\nand a confining contribution. Salpeter\u0027s equation is known to be formally\nequivalent to a random-phase-approximation equation; as such, it can develop\nimaginary eigenvalues. Thus, our study can not be complete without first\ndiscussing the stability of Salpeter\u0027s equation. The stability analysis limits\nthe form of the kernel and reveals that, contrary to the usual assumption, the\nconfining component can not transform as a Lorentz scalar; it must transform as\nthe timelike component of a vector. Moreover, the stability analysis sets an\nupper limit on the size of the one-gluon-exchange component; the value for the\ncritical coupling is determined through a solution of the ``semirelativistic\u0027\u0027\nCoulomb problem. These limits place important constraints on the interaction\nand suggest that a more sophisticated model is needed to describe the light and\nheavy quarkonia.",
"arxiv_id": "nucl-th/9510024",
"authors": [
"J. Parramore",
"H. -C. Jean",
"J. Piekarewicz"
],
"categories": [
"nucl-th",
"hep-ph"
],
"doi": "10.1103/PhysRevC.53.2449",
"journal_ref": "Phys.Rev.C53:2449-2467,1996",
"title": "Stability Analysis of the Instantaneous Bethe-Salpeter Equation and the Consequences for Meson Spectroscopy",
"url": "https://arxiv.org/abs/nucl-th/9510024"
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