Charmonium and QCD

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Charmonium spectroscopy and
QCD
Nora Brambilla (U. Milano)

• Charmonium and QCD
• The new Charmonium Revolution
• Effective Field Theories for Quarkonium
• Potential Non-Relativistic QCD
• Applications potentials, spectra, SM parameters,
  hybrids and gluelumps, decay and transitions
• Open challenges and future experiments
• Whats more?

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Charmonium at the beginning

• With the November 1974 revolution also the
  traditional quarkonium spectroscopy started
• huge impact on the QCD development
• c quark discovery
• asymptotic freedom
• confinement.
• few conventional charmonium states
• limited production mechanisms
• limited statistics
• potential model.

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QCD and Charmonium
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QCD and Charmonium
Bali et al. 95
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Charmonium and qcd a difficult problem
Progress driven by
New data
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The new Charmonium Revolution
New data
N e w s t a t e s
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Progress driven by
New data
New Theory
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Systems made by two quarks become golden
systems for strong interactions
They can provide us with

• Precision determinations of QCD parameters (of
  interest for SM and BSM physics)
• information on QCD vacuum and low energy
  properties (of interest for theories beyond QCD)
• information on the transition region from high
  energy to low energy (of interest for the
  behaviour of perturbative series)

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Low energy (nonperturbative) QCD may be studied
in a systematic way
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Scales and EFTs
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QQ scales
and
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Non-relativistic bound states
Difficult also for the lattice!
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EFTs for Quarkonium
Hard
Soft (relative momentum)
Ultrasoft (binding energy)
In QCD another scale is relevant
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EFTs for Quarkonium
Caswell, Lepage 86, Lepage, Thacker 88
Bodwin, Braaten, Lepage 95......
Pineda, Soto 97, Brambilla et al. 99--06, Kniehl,
Penin et al. 99... Luke Manohar 97, Luke Savage
98, Beneke Smirnov 98 Labelle 98, Grinstein
Rothstein 98 Manohar Stewart 00, Hoang et al, 01
....... --gtvNRQCD
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EFTs for Quarkonium
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Charmonium Scales
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NRQCD
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Weakly coupled pNRQCD
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Potentials and Spectra
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Static singlet potential
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Static singlet potential
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Pert. Static potential versus lattice
Perfect agreement up to more than 0.2 fm!
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Spectrum of ccbar with small radius
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J/psi energy at

• Removing the renormalon of the series
• Summing the logs RG correlated scales

Brambilla, Pineda, Soto, Vairo 99
Beneke et al., Hoang et al., Pineda
Luke and Savage Manohar and Stewart Pineda,
Nonperturbative nonlocal condensates set the
precision of calculation---gt in some situations
they are suppressed
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J/psi energy at
We can obtain a precision determination of m_c
N. B. Sumino Vairo 01
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Precise determination of at 2m_b and 2m_c
from Y radiative decay
N. B. Garcia Soto Vairo 07
Extraction of alpha_s(2m_c) from J/psi radiative
decays?
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Still a challenge for lattice QCD --excited
charmonium states -hyperfine
charmonium separation -unquenched charmonium
spetra
Good understanding of some lowest spin averaged
levels
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Charmonium spectrum in the Fermilab formulation
Gottlieb et al. 05
Tree matching coefficients
Work in progress anisotropic lattice quenched
(Dudek et al 06), anisotropic unquenched (Juge et
al 06)
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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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Strongly coupled pNRQCD
Brambilla Pineda Soto Vairo 00

• A potential (quark model like) description
  emerges from the EFT

from QCD in the matching

• The potentials

it contains hard and soft contributions

• V to be calculated on the lattice or in QCD
  vacuum models

Calculate once for ever the potential and get the
full charmonium specroscopy
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The nonperturbative QCD potential

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QCD potential

if it counts as V_0 we have flavor dependence at
LO
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QCD Spin dependent potentials

-factorization power counting QM divergences
absorbed by NRQCD matching coefficients
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Spin dependent potentials

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Spin dependent potentials

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 Koma, Koma and wittig
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States close to threshold
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Hybrids and Gluelumps
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QQ Static spectrum with gluons
hybrid
L a t t i c e
Juge Kuti Mornigstar 98-06
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Gluelumps and hybrids in pNRQCD
l a t t i c e
Juge Kuti Morningstar 00 03
for small r pNRQCD applies
Brambilla Pineda Soto Vairo 00
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Gluelumps and hybrids in pNRQCD more symmetry!
l a t t i c e
Juge Kuti Morningstar 00 03
Brambilla Pineda Soto Vairo 00
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Gluelumps Masses
Magnetic gluelump mass
Electric gluelump mass
is the fundamental object in many models of QCD
vacuum Stochastic Vacuum Model, Dosch et al Dual
QCD Baker et al Brambilla et al 97, 98,00
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Gluelumps Masses
Magnetic gluelump mass
Electric gluelump mass
it gives also the leading nonperturbative
correction to spectra and decay It needs better
lattice calculation!
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Transitions and Decays
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radiative transitions
Magnetic Dipole transitions
In potential models
Eichten QWG 02
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EFTheory of radiative transitions
pNRQCD with singlet, octet, US gluons and photons
Brambilla, Jia, Vairo 05

• No nonperturbative physics at order

• Exact relations from Poincare invariance

• No large anomalous magnetic moment

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I n c l u s i v e
d e c a y s
pNRQCD factorization nonperturbative effects in
condensates

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we need precision measurements of diverse
elements of the spectra and transitions with good
luminosity and resolution

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Open Challengeccbar spectroscopy at finite T
QQbar singlet Free energy at finite T
Spectral density above and below Tc
EFT approach for the scale T, gT, g2 T

Sequential dissociation depending on the ccbar
radius
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Open challenge Confinement mechanism
Boryakov et al. 04

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Outlook
Heavy quark bound states are a unique lab for
the study of the strong interactions from the
high energy scales where precision studies can be
made to the low energy region use all the
present and future data to test/develop our
theory tools on the way to the hadron structure
and dynamics need ppbar experiments
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Reviews