Quark Confinement in Light-Front QCD and A Weak-Coupling Treatment to Heavy hadrons

In this paper, we develop a weak-coupling treatment of nonperturbative QCD to heavy hadrons on the light-front. First, we present a derivation of quark confining interaction in light-front QCD for heavy quark systems, based on the recently developed light-front similarity renormalization group approach and the light-front heavy quark effective theory. The resulting effective light-front QCD Hamiltonian $H_\lambda$ at a low-energy cutoff $\lambda$ manifests the coexistence of a confining potential and a Coulomb potential. A clear light-front picture of quark confinement emerges. Using this low energy QCD Hamiltonian $H_\lambda$, we study heavy hadron bound state equations in the framework of a recently proposed possible weak-coupling treatment of non-perturbative QCD. Light-front heavy hadron bound states with definite spin and parity are constructed and the general structure of the corresponding wavefunctions is explored. A Gaussian-type wavefunction ansatz is used to solve the light-front quarkonium bound state equation. We find that the effective coupling constant determined from the quarkonium bound state equation can be arbitrarily small so that the weak-coupling treatment to heavy hadron bound states in light-front QCD is explicitly achieved. Finally, the scale dependence of the effective coupling constant is analytically calculated and the similarity renormalization group $\beta$ function is determined, from which the running coupling constant in small momentum transfer is given qualitatively by $\overline{\alpha}(Q^2) \sim {\Lambda_{QCD}^2 \over Q^2}$. Such a running coupling constant is the basic assumption in the successful Richardson $Q\overline{Q}$ potential that ensures the existence of a linear confining potential at large distance, but now can be obtained from light-front QCD.