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

Dimensionality of the spatio-temporal entanglement of PDC photon pairs

In this work the Schmidt number of the two-photon state generated by parametric-down conversion (PDC) is evaluated in the framework of a fully spatio-temporal model for PDC. A comparison with the results obtained in either purely spatial or purely temporal models shows that the degree of entanglement of the PDC state cannot be trivially reduced to the product of the Schmidt numbers obtained in models with lower dimensionality, unless the detected bandwidth is very narrow. This result is a consequence of the non-factorability of the state in the spatial and temporal degrees of freedoms of twin photons. In the limit of a broad pump beam, we provide a geometrical interpretation of the Schmidt number, as the ratio between the volume of the phase matching region and of a correlation volume.Comment: 17 pages, 10 figures. Submitted to Phys. Rev.

Experimental observation of the X-shaped near field spatio-temporal correlation of ultra-broadband twin beams

In this work we present the experimental observation of the non factorable near field spatio-temporal correlation of ultra-broadband twin beams generated by parametric down conversion (PDC), in an interferometric-type experiment using sum frequency generation, where both the temporal and spatial degrees of freedom of PDC light are controlled with very high resolution. The revealed X-structure of the correlation is in accordance with the predictions of the theory.Comment: 5 pages, 3 figure

The QCD Potential at O(1/m)O(1/m)

Within an effective field theory framework, we obtain an expression for the next-to-leading term in the $1/m$ expansion of the singlet $Q{\bar Q}$ QCD potential in terms of Wilson loops, which holds beyond perturbation theory. The ambiguities in the definition of the QCD potential beyond leading order in $1/m$ are discussed and a specific expression for the $1/m$ potential is given. We explicitly evaluate this expression at one loop and compare the outcome with the existing perturbative results. On general grounds we show that for quenched QED and fully Abelian-like models this expression exactly vanishes.Comment: 19 pages, LaTeX, 1 figure. Journal version. Discussion refined, misprints corrected, few references added; results unchange

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

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