The qq̄ relativistic interaction in the Wilson loop approach

The dynamics of a system composed by two heavy quarks is well understood in terms of a potential interaction (static plus relativistic corrections) obtained from the semirelativistic reduction of the QCD dynamics [1–5]. If at least one of the quarks is light the system behaves relativistically (the light quark can no more be considered static) and a pure relativistic treatment becomes necessary (via Dirac or Bethe–Salpeter equations). A lot of phenomenologically justified relativistic equations can be found in the literature but up to now we miss a relativistic treatment which follows directly from QCD. Our work goes in this direction. In order to simplify the problem we focus on the heavylight mesons in the non-recoil limit (i. e. infinitely heavy antiquark). Only at the end we will briefly discuss the two-body case. Our starting point is the quark-antiquark gauge-invariant Green function taken in the infinite mass limit of one particle. The only dynamical assumption is on the behaviour of the Wilson loop (i. e. on the nature of the non-perturbative vacuum). The gauge invariance of the formalism guarantees that the relevant physical information are preserved at any step of our derivation. In this way we obtain a QCD justified fully relativistic interaction kernel for the quark in the infinite mass limit of the antiquark. This kernel reduces in some region of the physical parameters to the heavy quark mass potential, and leads in some other region to the heavy quark sum rules results, providing in this