Effective Field Theories for Heavy Quarkonium

We briefly review how nonrelativistic effective field theories give us a definition of the QCD potentials and a coherent field theory derived quantum mechanical scheme to calculate the properties of bound states made by two or more heavy quarks. In this framework heavy quarkonium properties depend only on the QCD parameters (quark masses and \als) and nonpotential corrections are systematically accounted for. The relation between the form of the nonperturbative potentials and the low energy QCD dynamics is also discussed.Comment: Invited Plenary talk at The 20th European Conference on Few-Body Problems in Physics. September 10-14 2007. Pisa, Italy. To be published on Few-Body System

The 1P quarkonium fine splittings at NLO

We calculate the 1P heavy quarkonium fine splittings at NLO and discuss the impact of the calculation on the chi_b(1P) splittings.Comment: 10 pages, 3 figure

Three-body relativistic flux tube model from QCD Wilson-loop approach

First we review the derivation of the relativistic flux tube model for a quark-antiquark system from Wilson area law as we have given in a preceding paper. Then we extend the method to the three-quark case and obtain a Lagrangian corresponding to a star flux tube configuration. A Hamiltonian can be explicitly constructed as an expansion in $1 / m^2$ or in the string tension $\sigma$. In the first case it reproduces the Wilson loop three-quark semirelativistic potential; in the second one, very complicated in general, but it reproduces known string models for slowly rotating quarks.Comment: 14 pages, latex, uses elsart.sty, 2 figures available upon reques

The qqˉq \bar{q} relativistic interaction in the Wilson loop approach

We study the $q \bar{q}$ relativistic interaction starting from the Feynman-Schwinger representation of the gauge-invariant quark-antiquark Green function. We focus on the one-body limit and discuss the obtained non-perturbative interaction kernel of the Dirac equation.Comment: 5 pages, Latex (espcrc2.sty) To be published in the proceedings of High-Energy Physics International Euroconference on Quantum Chromodynamics:QCD97; 25th Anniversary of QCD, Montpellier, France, 3-9 July 199

Heavy Quarkonium in a weakly-coupled quark-gluon plasma below the melting temperature

We calculate the heavy quarkonium energy levels and decay widths in a quark-gluon plasma, whose temperature T and screening mass m_D satisfy the hierarchy m alpha_s >> T >> m alpha_s^2 >> m_D (m being the heavy-quark mass), at order m alpha_s^5. We first sequentially integrate out the scales m, m alpha_s and T, and, next, we carry out the calculations in the resulting effective theory using techniques of integration by regions. A collinear region is identified, which contributes at this order. We also discuss the implications of our results concerning heavy quarkonium suppression in heavy ion collisions.Comment: 25 pages, 2 figure

Effective field theories for baryons with two- and three-heavy quarks

Baryons made of two or three heavy quarks can be described in the modern language of non-relativistic effective field theories. These, besides allowing a rigorous treatment of the systems, provide new insight in the nature of the three-body interaction in QCD.Comment: 7 pages, 1 figure; published versio

Bethe--Salpeter equation in QCD

We extend to regular QCD the derivation of a confining $q \bar{q}$ Bethe--Salpeter equation previously given for the simplest model of scalar QCD in which quarks are treated as spinless particles. We start from the same assumptions on the Wilson loop integral already adopted in the derivation of a semirelativistic heavy quark potential. We show that, by standard approximations, an effective meson squared mass operator can be obtained from our BS kernel and that, from this, by ${1\over m^2}$ expansion the corresponding Wilson loop potential can be reobtained, spin--dependent and velocity--dependent terms included. We also show that, on the contrary, neglecting spin--dependent terms, relativistic flux tube model is reproduced.Comment: 23 pages, revte