Abstract
We discuss a model for the relativistic bound states of 3-quark baryons based on confining quantum chromoynamics (QCD) with general Yang-Mills symmetry. The model postulates that 3-quark states are formed by consecutive 2-body collisions. For a proton, d and u quarks get together first, and then they capture another u quark so that the d quark is at the core to form a stable proton state with intergral electric charge. The two u quarks form a quantum spheric shell and move in a confining potentialC(r)= Q' rof the core d quark. The confining potentialC(r)is a static solution of new `phase' fields satisfying the fourth-order equation based on general Yang-Mills symmetry. The two u quarks with the confining linear potentialsC(r)in the spherical shell can produce an effective quark Hooke potentialV_(qH)(r)=Qr² + Vₒfor the d quark at the core, where Q andQ'are not independent. The proton mass is assumed to be approximately given by E(d) + 2E(u) , which can be obtained analytically from Dirac Hamiltonians involvingV_(qH)(r)andC(r)for d and two u quarks respectively. The model gives a reasonable understanding of roughly 120 baryon masses based on two different coupling constants and one free parameterVₒfor sub-spectra specfied byJᴾ . These results are roughly within 20% in percent deviation, which appears to be independent of the assumption of color charges. The confining QCD model also gives the neutron-proton mass difference≈ 0.6 MeV . We propose an experimental test of the proton structure.