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Bound q-bar q systems in the framework of two-body Dirac equations obtained from different versions of 3D-reductions of the Bethe-Salpeter Equations
High Energy Physics - Phenomenology · Submitted 6 Aug 2003
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim For the systems (u bar s), (c bar u), (c bar s) the dependence of the stable solutions of the Dirac equations obtained in the different version on the mixture parameter x is investigated and results is compared with such dependence of 3D-equations derived from Bethe-Salpeter equations without the additional approximation and some new conclusions are obtained.
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The two-body Dirac equations for the bound q bar q systems are obtained from the different (five) versions of the 3D-equations derived from Bethe-Salpeter equation with the instantaneous kernel in the momentum space using the additional approximations. There are formulated the normalization conditions for the wave functions satisfying the obtained two-body Dirac equations. The spin structure of the confining qq interaction potential is taken in the form x gamma0 X gamma0 + (1-x) I X I, with 0 < x < 1. It is shown that the two-body Dirac equations obtained from the Salpeter equation does not depend on x. As to other four versions such a dependence is left. For the systems (u bar s), (c bar u), (c bar s) the dependence of the stable solutions of the Dirac equations obtained in the different version on the mixture parameter x is investigated and results is compared with such dependence of 3D-equations derived from Bethe-Salpeter equations without the additional approximation and some new conclusions are obtained.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The two-body Dirac equations for the bound q bar q systems are obtained from the different (five) versions of the 3D-equations derived from Bethe-Salpeter equation with the instantaneous kernel in the momentum space using the additional approximations. | method 0.57 | 0.89 | 0.07 | asserted 1.00 |
| s1 | There are formulated the normalization conditions for the wave functions satisfying the obtained two-body Dirac equations. | contribution 0.60 | 0.88 | 0.05 | asserted 1.00 |
| s2 | The spin structure of the confining qq interaction potential is taken in the form x gamma0 X gamma0 + (1-x) I X I, with 0 < x < 1. | method 0.98 | 0.71 | 0.05 | asserted 1.00 |
| s3 | It is shown that the two-body Dirac equations obtained from the Salpeter equation does not depend on x. | result 1.00 | 0.86 | 0.20 | asserted 1.00 |
| s4 | As to other four versions such a dependence is left. | result 1.00 | 0.79 | 0.11 | asserted 0.99 |
| s5 | For the systems (u bar s), (c bar u), (c bar s) the dependence of the stable solutions of the Dirac equations obtained in the different version on the mixture parameter x is investigated and results is compared with such dependence of 3D-equations derived from Bethe-Salpeter equations without the additional approximation and some new conclusions are obtained. | contribution 0.92 | 0.92 | 0.44 | asserted 0.98 |
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The two-body Dirac equations for the bound q bar q systems are obtained from the different (five) versions of the 3D-equations derived from Bethe-Salpeter equation with the instantaneous kernel in the momentum space using the additional approximations. There are formulated the normalization conditions for the wave functions satisfying the obtained two-body Dirac equations. The spin structure of the confining qq interaction potential is taken in the form x gamma0 X gamma0 + (1-x) I X I, with 0 < x < 1. It is shown that the two-body Dirac equations obtained from the Salpeter equation does not depend on x. As to other four versions such a dependence is left. For the systems (u bar s), (c bar u), (c bar s) the dependence of the stable solutions of the Dirac equations obtained in the different version on the mixture parameter x is investigated and results is compared with such dependence of 3D-equations derived from Bethe-Salpeter equations without the additional approximation and some new conclusions are obtained.
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In the following, we intend to exemplify our technique of constructing exact solutions to the reduced Salpeter equation by considering only a few of those Lorentz structures $Γ⊗Γ$ of the interaction kernel $K(p,q)$ that are commonly used in phenomenological descriptions of hadrons, notably, of mesons, as bound states of quarks confined by the strong interactions.[Since the first encounter [ref] of unstable solutions of Salpeter equations with confining interactions, the stability of solutions of different relativistic bound-state equations has been an issue of concern [ref] .
Exact Solutions of Bethe-Salpeter Equations with Instantaneous Interactions · Radial Eigenvalue Equations · 0.93
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