Ground-stateqq¯mass spectrum in quantum chromodynamics

Abstract

We use a relativistic equation of the Bethe-Salpeter type for quark-antiquark bound states in QCD. Its kernel, determined by the gluon propagator, is split into a constant part and a correction. This allows us to write the bound-state equation as an eigenvalue equation for an operator which can be identified as a nonrelativistic Hamiltonian for the $q\overline{q}$ system in the center-of-mass frame. The constant part of the kernel leads to a quark propagator indicative of confinement. With this propagator we obtain from the bound-state equation a good fit to both the pseudoscalar and vector ground-state masses for all flavor combinations. Our only inputs are the quark masses and one constant of dimensions of mass.