QQ systems are ideal for strong interactions studies Scales and Effective Field Theories:systematic approach pNRQCD: the QQbar and QQQ potentials Applications of pNRQCD: Potentials and Spectra, Decays, Transitions, SM parameters What at finite T? What’s more? Heavy Quark Potentials at Zero Temperature Nora Brambilla (U. Milano)

Bound states of two (or more)heavy quarks

QQ: a multiscale System

Non-relativistic bound states in QCD Difficult also for the lattice! The perturbative expansion breaks down when

EFTs for Quarkonium Hard Soft (relative momentum) Ultrasoft (binding energy)

EFTs for Quarkonium

The matching procedure enforces the EFT to be equivalent to QCD

EFTs for Quarkonium In QCD another scale is relevant

pNRQCD for Quarkonium with small radius

Pineda, soto 97; Brambilla, Pineda, soto, Vairo 99- pNRQCD for Quarkonium with small radius

Pineda, soto 97; Brambilla, Pineda, soto, Vairo 99- pNRQCD for Quarkonium with small radius

Pineda, soto 97; Brambilla, Pineda, soto, Vairo 99- pNRQCD for Quarkonium with small radius

Static singlet QCD QQ potential The potential is a Wilson coefficient of an EFT. In general, it undergoes renormalization, develops scale dependence and satisfies renormalization group equations, which allow to resum large logarithms.

Static singlet potential + :calculated in the matching up to two loops: The mu dependence cancels between the two terms V contains log mu r

Static singlet potential at NNNNLO

Pert. Static Energy versus lattice Perfect agreement up to more than 0.2 fm!

Pert. Static Energy versus lattice No signal of short range-linear nonperturbative effects

Summing large beta0 (removing the renormalon of the series) Beneke et al., Hoang et al., Summing the logs of v (coming from the ratio of scales:mv^2/mv, mv/m) RG correlated scales Luke and Savage; Manohar and Stewart; Pineda Soto The bottleneck are nonperturbative contributions (condensates) but they are suppressed Precision calculations are possible perturbative singlet potential singlet octet low energy gluon Quarkonium energies at

b and c mass extraction from Y(1S) and J\psi Quarkonium energies at QWG Cern YR 2005 averages:

mass In CDF 05 theis found in Predictions of the

The missing mesons Under search at Fermilab and CLEO

Present Knowledge of the QQ Potentials --Vs known at four loops (no constants from 3 loop) --Vo known at two loops --V Spin dependent potential known one loop --V at order 1/m known at two loops --At order 1/m^2 imaginary parts in the potentials appear-> describe inclusive decays at order m alpha_s^5 The RG improvement is also known for several potentials

QQQ states: pNRQCD for small radii up to two loops: Recent calculation of the potential at order g^4, three body contribution at order g^6 Brambilla, Ghiglieri, Vairo 08

Tree level QQQ potential color factor perturbative diagram calculation

Tree level QQQ potential Octets mixing between symmetric and antysimmetric octets aaantysimmetricantisimmetrico

One loop QQQ potential Esponentiation The potential is still two body

One loop QQQ potential The first three body potential appears at g^6

Strongly coupled pNRQCD (for systems with large radius)

strong pNRQCD: Hitting integrate out all scales above Bali et al. 98 gluonic excitations develop a gap and are integrated out

Strong coupled pNRQCD Brambilla Pineda Soto Vairo 00 A potential description emerges from the EFT The potentialsfrom QCD in the matching V to be calculated on the lattice or in QCD vacuum models Creutz et al 82, Campostrini 85, Michael 85, Born et al 94, Bali et al 97, Brambilla et al , Koma et al. 06,07

The nonperturbative QCD potential

QCD potential Koma, koma, wittig 07

QCD Spin dependent potentials -Factorization; Power counting; Quantum mechanical divergences absorbed by NRQCD matching coefficients

Spin dependent potentials Differ from flux tube model prediction Such data can distinguish different models for the dynamics of low energy QCD

Exact relations on the V’s from Poincare e. g. It is a check of the lattice calculation Koma and Koma 2006 Gromes relation many other such relations in pNRQCD, Brambilla et al. 2003

QCD Spin independent potentials Under calculation on the lattice Koma et al 07

Good testing bed for QCD vacuum models

Low energy (nonperturbative) QCD may be studied in a systematic way The potential is defined and calculated in all the regimes

Quarkonium at Finite T more scales ? Debye mass Screening Scale see A. Vairo talk this afternoon!

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Lattice calculation of the QQQ potential