The Light-Cone Hamiltonian Approach And Its Applications At The Meson Systems

Because of some unique features, particularly the apparent simplicity of the light-cone vacuum, the light-cone Hamiltonian approach based on light-cone quantization of quantum field theory is a promising method for the bound-state problem of relativistic composite systems. Starting from the QCD Lagrangian density and disregarding the zero modes in light-cone QCD, Pauli et al. have derived non-perturbatively an effective light-cone Hamiltonian of mesons which act only on the qq sector. The front form meson eigen equations are formulated in momentum-helicity representation which hinders its solution in total angular momentum representation. So we transform it to total angular momentum representation in instant form and explore the physical contents of the meson radial eigen equations. Then the mass spectra of forty flavor off-diagonal mesons consisting of (u, d, s, c, b) quarks and six mesons consisting of heavy quarks cc and bb are calculated relativistically and non-perturbatively. Numerical results show that this light-cone QCD effective Hamiltonian without confining potentials and flavor mixing interactions can well describe the ground states but can not apply for the excited states of mesons and flavor diagonal light mesons. Since the problem of confinement related to zero modes is unsolve in light-cone QCD, we introduce a relativistic confining potential from phenomenological results into the meson Hamiltonian. With this improved method, both the ground state and the excited states of flavor off-diagonal pseudo-scalar mesons are well described. More satisfying results are expected in the near future.