QQ systems are ideal for strong interactions studies

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Heavy Quark Potentials at Zero Temperature
Nora Brambilla (U. Milano)

• QQ systems are ideal for strong interactions
  studies
• Scales and Effective Field Theoriessystematic
  approach
• pNRQCD the QQbar and QQQ potentials
• Applications of pNRQCD Potentials and Spectra,
  Decays, Transitions, SM parameters
• What at finite T?
• Whats more?

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Bound states of two (or more)heavy quarks
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QQ a multiscale System
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Non-relativistic bound states in QCD
The perturbative expansion breaks down when
Difficult also for the lattice!
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EFTs for Quarkonium
Hard
Soft (relative momentum)
Ultrasoft (binding energy)
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EFTs for Quarkonium
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EFTs for Quarkonium
The matching procedure enforces the EFT to be
equivalent to QCD
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pNRQCD for Quarkonium with small radius
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pNRQCD for Quarkonium with small radius
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pNRQCD for Quarkonium with small radius
Pineda, soto 97 Brambilla, Pineda, soto, Vairo
99-
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pNRQCD for Quarkonium with small radius
Pineda, soto 97 Brambilla, Pineda, soto, Vairo
99-
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pNRQCD for Quarkonium with small radius
Pineda, soto 97 Brambilla, Pineda, soto, Vairo
99-
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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.
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Static singlet potential at NNNNLO
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Pert. Static Energy versus lattice
Perfect agreement up to more than 0.2 fm!
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Pert. Static Energy versus lattice
No signal of short range-linear nonperturbative
effects
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Quarkonium energies at
low energy gluon
singlet
singlet
octet

• 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
  scalesmv2/mv, mv/m) RG correlated scales Luke
  and Savage Manohar and Stewart Pineda Soto
• The bottleneck are nonperturbative
  contributions (condensates) but they are
  suppressed

perturbative singlet potential
Precision calculations are possible
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Predictions of the
mass
In CDF 05 the
is found in
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The missing mesons
Under search at Fermilab and CLEO
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Present Knowledge of the QQ Potentials
--Vs known at four loops (no constants from 3
loop)
--Vo known at two loops
--V at order 1/m known at two loops
--V Spin dependent potential known one loop
--At order 1/m2 imaginary parts in the
potentials appear-gt describe inclusive decays at
order m alpha_s5
The RG improvement is also known for several
potentials
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Tree level QQQ potential

• Octets mixing between symmetric and antysimmetric
  octets
• aaantysimmetricantisimmetrico

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Strongly coupled pNRQCD (for systems with large
radius)
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strong pNRQCD Hitting
Bali et al. 98

• integrate out all scales above

• gluonic excitations develop a gap

and are integrated out

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Strong coupled pNRQCD
Brambilla Pineda Soto Vairo 00

• A potential description emerges from the EFT

• The potentials

from 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 90 93 95
97, Koma et al. 06,07
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The nonperturbative QCD potential

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QCD potential
Koma, koma, wittig 07

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

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Spin dependent potentials

Such data can distinguish different models for
the dynamics of low energy QCD
Differ from flux tube model prediction
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Exact relations on the Vs from Poincare
e. g.
Gromes relation
It is a check of the lattice calculation
many other such relations in pNRQCD, Brambilla et
al. 2003
Koma and Koma 2006
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QCD Spin independent potentials

Under calculation on the lattice Koma et al 07
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Good testing bed for QCD vacuum models
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Low energy (nonperturbative) QCD may be studied
in a systematic way
The potential is defined and calculated in all
the regimes
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backup slides
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