Hadrons composed of heavy quarks are the simplest ones to study in QCD.
They provide an affordable theoretical laboratory for investigating
the dynamics of gluons, mainly because quarks move slowly with respect
to each other as the sources of gluons and in the analysis of heavy meson
states one can safely take advantage of asymptotic freedom and expand
renormalized interactions in powers of the coupling constant .
The effective quarks and gluons are introduced using the renormalization
group procedure for effective particles (RGPEP), whose details are
addressed in the abstract submitted by Maria Gomez-Rocha to HADRON2017 .
We use the RGPEP to derive the leading-order renormalized light-front QCD
Hamiltonian and to formulate its eigenvalue problem for mesons in terms
of the Fock components with smallest possible number of effective particles,
which resembles the constituent quark model. However, the dynamics of quarks
originates in the gluons in higher Fock sectors. In the second-order
calculation we describe here, only the Fock sector with one gluon in
addition to quarks matters. However, in order to approximately account
for the non-abelian and non-perturbative effects due to higher sectors,
we introduce a mass ansatz for the gluon. As a result, we obtain
the Coulomb force plus a harmonic oscillator force between heavy quarks
in the quark-antiquark Fock sector. In this first approximation,
the harmonic oscillator potential does not depend on the assumed
gluon mass or on the generator of the RGPEP .
 M. Gómez-Rocha, S. D. Głazek, Phys. Rev. D 92, 065005
 María Gómez-Rocha's abstract submitted to HADRON2017.
 S.D. Głazek, M. Gómez-Rocha, J. More, K. Serafin. arXiv:1705.07629