Abstract
We consider a relativistic hydrogen-like model for meson mass spectra. The model is based on a Lagrangian with a new general Yang-Mills symmetry. The strong interactions involve a fourth-order field equation that generates a linear confining potential. Notably, this model for meson masses requires quarks to carry only a single `confining charge'f_(c)rather than three color charges. We classify meson mass spectra into sub-spectra defined by isospin, G-parity, total angular momentum and parity. By applying a numerical solver to the Dirac Hamiltonians–incorporating two short-range confining potentials, we obtain energy eigenvalues in natural units. The model has three coupling constants and one parameter. It provides a robust fit of 31 pions and kaons masses (from≈ 140 MeVto≈ 2,300 MeV ) to within≈ 18%of relative percentage error. The model suggests that the confining chargef_(c) =0.045/MeV = 8.87 fm plays the role of the basic length in the quark interactions.