Effective Field Theory for Ultrasoft Momenta in NRQCD and NRQED

We study some general aspects of the formalism of potential NRQCD (pNRQCD), an effective field theory that deals with ultrasoft degrees of freedom in Heavy Quarkonium systems. Specific attention is paid to its effective Lagrangian that it is displayed at the present level of accuracy.

We review some recent developments on non-relativistic effective field theories for heavy quark-antiquark systems and how they can bring a well founded connection between QCD and potential models.

In the framework of the QCD effective field theory called potential Non-Relativistic QCD, we explore quark-antiquark bound systems that may be dominated by the perturbative interaction and we discuss the extent of validity of such a picture. Some phenomenological implications are outlined.

We review recent progress in Non-Relativistic QCD and in related Non-Relativistic Effective Field Theories with emphasis on the applications to heavy quarkonia.

We discuss heavy quarkonium in the framework of pNRQCD, a QCD effective theory appropriate for the study of heavy quark bound systems.

A Lagrangean and a set of Feynman rules are presented for Non-Relativistic QCD with manifest power counting in the heavy quark velocity $v$. A r\'egime is identified in which energies and momenta are of order $Mv$. It is neither identical to the ultrasoft r\'egime corresponding to radiative processes with energies and momenta of order $Mv^2$, nor to the potential r\'egime with on shell quarks and gluons providing the Coulomb binding. In this soft r\'egime, gluons are on shell...

I discuss effective field theories for heavy bound systems, particularly bound systems involving two heavy quarks. The emphasis is on the relevant concepts and on interesting physical applications and results.

The next-to-next-to-next-to-leading order (N^3LO) Hamiltonian of potential nonrelativistic QCD is derived. The complete matching of the Hamiltonian and the contribution from the ultrasoft dynamical gluons relevant for perturbative bound-state calculations is performed including one-, two-, and three-loop contributions. The threshold expansion is used to disentangle and match contributions of different scales in the effective-theory calculations. As a physical application, the...

Within an effective field theory framework we study heavy-quark--antiquark systems with a typical distance between the heavy quark and the antiquark smaller than $1/\Lambda_{\rm QCD}$. A suitable definition of the potential is given within this framework, while non-potential (retardation) effects are taken into account in a systematic way. We explore different physical systems. Model-independent results on the short distance behavior of the energies of the gluonic excitations...

Heavy quark bound state systems, mesons and hybrids, are discussed in the framework of the QCD effective field theory called potential Non-Relativistic QCD.