Flavor independence and the dual superconducting model of QCD

Abstract

Baker, Ball, and Zachariasen (BBZ) have developed an elegant formulation of the dual superconducting model of quantum chromodynamics (QCD), which allows one to use the field equations to eliminate the gluon and Higgs degrees of freedom and thus to express the interaction between quarks as an effective potential. Carrying out an expansion in inverse powers of the constituent quark masses, these authors succeeded in identifying the central part, the spin-dependent part, and the leading relativistic corrections to the central potential. The potential offers a good account of the energies and splittings of charmonium and the upsilon system. Since all of the flavor dependence of the interaction is presumed to enter through the constituent masses, it is possible to test the potential in other systems. Logical candidates are the heavy $B$-flavor charmed system and the heavy-light systems, which should be more sensitive to the relativistic corrections. Lattice gauge calculations furnish an additional point of contact for the components of the BBZ potential. Some preliminary calculations of the energies of $B$ and $D$ mesons are presented and the challenge of agreement with experiment is discussed. The spinless Salpeter equation is used to account for the effects of relativistic kinematics.