Bethe-Salpeter equation with a near harmonic interaction: M. K. Sundaresan and P. J. S. Watson. Department of Theoretical Physics, University of Oxford, Oxford, England
- Publisher
- Elsevier Science
- Year
- 1970
- Tongue
- English
- Weight
- 79 KB
- Volume
- 59
- Category
- Article
- ISSN
- 0003-4916
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✦ Synopsis
In this work we study the Bethe-Salpeter equation for the bound states of a quark-antiquark pair interacting by means of a phenomenological interaction which is a relativistic generalization of the three-dimensional harmonic oscillator interaction. For scalar quarks an analytical expression is found for the square of the mass of the bound states which has a linear dependence on the orbital angular momentum between the quarks. Solutions of the equation also exist which can be interpreted as daughter states, with both natural and unnatural parity, although the wave functions for the unnatural parity states vanish identically for particles on the mass shell. For spinor quarks, equations for states with given Jpc are obtained, and, in the case of O-+ and l--states, their spinor structures are shown to have a form required by Llewellyn Smith for explaining the Van Royen-Weisskopf paradox. The mass spectrum obtained in the Spinor case is discussed, and we demonstrate the existence of a new kind of bound state.