Linear confinement in momentum space: singularity-free bound-state equations

Abstract

Relativistic equations of Bethe-Salpeter type for hadron structure are most conveniently formulated in momentum space. The presence of confining interactions causes complications because the corresponding kernels are singular. This occurs not only in the relativistic case but also in the nonrelativistic Schrödinger equation where this problem can be studied more easily. For the linear confining interaction the singularity reduces to one of Cauchy principal value form. Although this singularity is integrable, it still makes accurate numerical solutions difficult. We show that this principal value singularity can be eliminated by means of a subtraction method. The resulting equation is much easier to solve and yields accurate and stable solutions. To test the method's numerical efficiency, we performed a three-parameter least-squares fit of a simple linear-plus-Coulomb potential to the bottomonium spectrum.

14 pages, 4 figures. v2: typos corrected, essentially matches version published in Phys. Rev. D

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• Covariant Spectator Theory of heavy-light and heavy mesons and the predictive power of covariant interaction kernels
• $B_c$ meson spectroscopy motivated by general features of pNRQCD
• Quark mass function from a one-gluon-exchange-type interaction in Minkowski space
• The quark spectral functions and the Hadron Vacuum Polarization from application of DSEs in Minkowski space
• Complete analytical solution to the Cornell potential and heavy quarkonium structure
• Heavy and heavy-light mesons in the Covariant Spectator Theory
• Application of the Covariant Spectator Theory to the study of heavy and heavy-light mesons
• Simple high-accuracy method for solving bound-state equations with the Cornell potential in momentum space
• Chiral-symmetry breaking and confinement in Minkowski space
• Removal of singularities from the covariant spectator theory
• Confinement of Fermions in Tachyon Matter at Finite Temperature
• Relativistic phenomenology of meson spectra with a covariant quark model in Minkowski space
• Quarkonia and heavy-light mesons in a covariant quark model
• Spin splitting spectroscopy of heavy quark anti quark systems