Comparing the QCD potential in Perturbative QCD and Lattice QCD at large distances

We compare the perturbatively calculated QCD potential to that obtained from lattice calculations in the theory without light quark flavours. We examine E_tot(r) = 2 m_pole + V_QCD(r) by re-expressing it in the MSbar mass m = m^MSbar(m^MSbar) and by choosing specific prescriptions for fixing the scale mu (dependent on r and m). By adjusting m so as to maximise the range of convergence, we show that perturbative and lattice calculations agree up to 3*r_0 ~ 7.5 GeV^-1 (r_0 is the Sommer scale) within the uncertainty of order Lambda^3 r^2.Comment: Version to appear in Eur.J.Phys; 16 pages, 7 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

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

Poincare' invariance and the heavy-quark potential

We derive and discuss the constraints induced by Poincare' invariance on the form of the heavy-quark potential up to order 1/m^2. We present two derivations: one uses general arguments directly based on the Poincare' algebra and the other follows from an explicit calculation on the expression of the potential in terms of Wilson loops. We confirm relations from the literature, but also clarify the origin of a long-standing false statement pointed out recently.Comment: 20 pages, 4 figure

A first estimate of triply heavy baryon masses from the pNRQCD perturbative static potential

Within pNRQCD we compute the masses of spin-averaged triply heavy baryons using the now-available NNLO pNRQCD potentials and three-body variational approach. We focus in particular on the role of the purely three-body interaction in perturbation theory. This we find to be reasonably small and of the order 25 MeV Our prediction for the Omega_ccc baryon mass is 4900(250) in keeping with other approaches. We propose to search for this hitherto unobserved state at B factories by examining the end point of the recoil spectrum against triple charm.Comment: 18 figures, 21 page

Quarkonium spectroscopy and perturbative QCD: massive quark-loop effects

We study the spectra of the bottomonium and B_c states within perturbative QCD up to order alpha_s^4. The O(Lambda_QCD) renormalon cancellation between the static potential and the pole mass is performed in the epsilon-expansion scheme. We extend our previous analysis by including the (dominant) effects of non-zero charm-quark mass in loops up to the next-to-leading non-vanishing order epsilon^3. We fix the b-quark MSbar mass $\bar{m}_b \equiv m_b^{\bar{\rm MS}}(m_b^{\bar{\rm MS}})$ on Upsilon(1S) and compute the higher levels. The effect of the charm mass decreases $\bar{m}_b$ by about 11 MeV and increases the n=2 and n=3 levels by about 70--100 MeV and 240--280 MeV, respectively. We provide an extensive quantitative analysis. The size of non-perturbative and higher order contributions is discussed by comparing the obtained predictions with the experimental data. An agreement of the perturbative predictions and the experimental data depends crucially on the precise value (inside the present error) of alpha_s(M_Z). We obtain $m_b^{\bar{\rm MS}}(m_b^{\bar{\rm MS}}) = 4190 \pm 20 \pm 25 \pm 3 ~ {\rm MeV}$.Comment: 33 pages, 21 figures; v2: Abstract modified; Table7 (summary of errors) added; Version to appear in Phys.Rev.