The heavy quark potential in pNRQCD

In a recent series of papers [1,2] a detailed study of a suitable Effective Field Theory for heavy quark bound states, called potential NRQCD (pNRQCD) [3], has been started. Since several issues have been treated in that context, we address the reader to the quoted literature for a complete overview of the achieved results. Here we only mention the 1-loop matching [4] and the static energies of the hybrids [5] presented in these proceedings. While in the following, due to its considerable importance, we recollect and summarize our understanding of the heavy quarkonium static potential. Let us define, first, what we mean with heavy quarkonium potential. Being heavy quarkonium a non-relativistic bound system, it is characterized by at least three energy scales: the mass or hard scale, m, the momentum or soft scale, mv, corresponding to the inverse of the bound-state size and the energy or ultrasoft (US) scale, mv (v is the heavy quark velocity). As a consequence, when US degrees of freedom are neglected, heavy quarkonium can be described as a bound state φ governed by a non-relativistic Schrödinger equation of the type