Perturbative quark bound states in pNRQCD

If we have a chance to understand the QCD bound-state dynamics without resorting to the lattice or to models [1], this is likely to be in the cases of bound systems whose interaction is dominated by the perturbative dynamics. In such cases non-perturbative corrections exist but are small and can be parameterized in terms of local or non-local condensates. In the following I will call such systems ’Coulombic’ or ‘quasiCoulombic’. These situations are particularly interesting not only because, as I will show, they have phenomenological relevance, but especially because they allow us to understand much more about QCD. Here, I will exclusively address such situations. Typically, systems that may be ’Coulombic or quasi’ are bound states composed only by heavy quarks (and gluons). In such cases, at least for the lowest states, the characteristic radius 〈r〉 (r being the qq̄ distance) of the system is quite small and this intuitively justifies the idea that they are dominated by the perturbative dynamics: the system is too small to probe the confinement effects, which arise at a scale 1/ΛQCD ≫ 〈r〉. Here, I will introduce an effective field theory called potential Non–Relativistic QCD (pNRQCD)[2,3], that clarifies such picture and allows us to include systematically perturbative