Confinement in a Bethe-Salpeter model with logarithmic potential

Biswas, S. N. ; Choudhury, S. R. ; Datta, K. ; Goyal, Ashok (1983) Confinement in a Bethe-Salpeter model with logarithmic potential Physical Review D, 27 (10). pp. 2439-2444. ISSN 0556-2821

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We show that the covariant Bethe-Salpeter equation for two scalar quarks confined through a kernel of the form K~[(p-p')2]-3/2 possesses a discrete spectrum: this kernel is a simple covariant generalization of the potential in configuration space proportional to lnr. To investigate the spectrum, we adopt a new approximation scheme to convert the covariant Bethe-Salpeter equation into a three-dimensional one, the consistency of the scheme being checked by applying it to the Wick-Cutkosky equation for the covariant Coulomb problem and obtaining a Balmer-type formula. The spectrum as revealed by investigating the S-wave part of the resulting three-dimensional equation by semiclassical methods is essentially of the type obtained from the Schrodinger equation with a lnr potential; relativistic effects depress the energy levels.

Item Type:Article
Source:Copyright of this article belongs to American Physical Society.
ID Code:26205
Deposited On:06 Dec 2010 12:55
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