Speaker
Description
The well-known Cornell quark-antiquark potential in momentum space has singularities in both its one-gluon-exchange (OGE) and linear confining parts. These singularities prevent the direct application of the convenient Nyström method to solve the corresponding bound-state integral equation for meson masses. While the Coulomb-type singularity in the OGE potential can be treated with a subtraction technique, only very complicated methods have been developed to deal with the stronger singularity in the linear potential.
We present a simple subtraction method to remove this singularity from the kernel, making the Nyström method applicable. The derivatives of the wave function resulting from the subtraction are represented using interpolating functions, and we found Lagrange polynomials to be highly efficient. Test calculations demonstrate excellent agreement with precisely known energy eigenvalues. By increasing the number of integration points and the order of the Lagrange interpolation polynomials, extremely high accuracy can be achieved. We have also extended this method to spin-dependent first-order relativistic corrections of the Cornell potential, which generate spin-spin, spin-orbit, and tensor forces. This method is also applicable to relativistic Bethe-Salpeter type equations with singular kernels.
| Theoretical or experimental | Theoretical |
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