Solution of Two-Body Bound State Problems with Confining Potentials

TL;DR

This paper presents a method to solve two-body bound state problems with confining potentials in momentum space, successfully calculating heavy quarkonium spectra that align well with experimental data.

Contribution

It introduces a regularization technique for singular kernels in the Lippmann-Schwinger equation with confining potentials and applies it to compute heavy quarkonium spectra.

Findings

Mass spectra agree with experimental results

Method effectively handles singularities in confining potentials

Applicable to linear and quadratic potentials

Abstract

The homogeneous Lippmann-Schwinger integral equation is solved in momentum space by using confining potentials. Since the confining potentials are unbounded at large distances, they lead to a singularity at small momentum. In order to remove the singularity of the kernel of the integral equation, a regularized form of the potentials is used. As an application of the method, the mass spectra of heavy quarkonia, mesons consisting from heavy quark and antiquark $(\Upsilon(b\bar{b}), \psi(c\bar{c}))$, are calculated for linear and quadratic confining potentials. The results are in good agreement with configuration space and experimental results.