  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.
