Solving momentum-space integral equations for quarkonium spectra with confining potentials. III. Bethe-Salpeter equation with spin

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Abstract
Singular integral equations for quarkonium (qq¯) spectra are solved in momentum space for relativistic confinement plus Coulomb potentials including spin. The confinement potential in momentum space is defined using an analytical regularization scheme. Further manipulations give rise to integro-differential equations and we obtain analytical approximations for the remaining singular integrals. The procedure is tested with two different reductions of the Bethe-Salpeter equation. Using both scalar and scalar plus pseudoscalar confinement we obtain the spectra of charmonium, b-quarkonium, and the light mesons. We compare the results with experiment and with results obtained by other techniques. Eigenfunctions for selected eigenstates are presented. A good description of both the light and heavy mesons is then obtained with scalar linear confinement in the instantaneous approximation to the Bethe-Salpeter equation. This description is based upon the inclusion of a Breit term to approximate transverse gluon effects.