Heavy Quarkonium Inclusive Decays: Theoretical Status and Perspectives

In recent years, the study of heavy quarkonia (bb̄, cc̄, ...) has gone through several theoretical and experimental advances. From the theoretical side the introduction of non-relativistic effective field theories (EFTs) of QCD has put our description of these systems on the solid ground of QCD. It has made it possible, in the case of several observables, to factorize the high-energy dynamics into matching coefficients calculable in perturbation theory and the non-perturbative QCD dynamics into few well-defined matrix elements to be fitted on the data or calculated on the lattice. Systematic improvements are possible, either calculating higher-order corrections in the coupling constant or adding higher-order operators. Heavy quarkonium, being a non-relativistic bound state, is characterized by a hierarchy of energy scales m, mv and mv, where m is the heavy-quark mass and v ≪ 1 the relative heavy-quark velocity. A hierarchy of EFTs may be constructed by systematically integrating out modes associated to these energy scales. Integrating out degrees of freedom of energy m, which for heavy quarks can be done perturbatively, leads to non-relativistic QCD (NRQCD). This EFT still contains the lower energy scales as dynamical degrees of freedom. In the last years, the problem of integrating out the remaining dynamical scales of NRQCD has been addressed by several groups and has now reached a solid level of conceptual understanding (an extended list of references can be found in). The ultimate EFT obtained by sub-