Recovering QCD at large NC: Twopoint Greenfunctions

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Recovering QCD at large NCTwo-point
Green-functions

• J. J. Sanz Cillero, IN2P3 - Orsay

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Outline

• DUALITY
• QCD at large NC (QCD8) ? Resonance Theory
  (RcT8)

• Analysis of QCD correlators
• a)- Physical QCD content
• b)- Relation RcT Sum-rules
• c)- Truncated RcT pQCD Continuum
• Conclusions

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Duality in QCD
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QCD8
Infinite resonance Regularization
CUT-OFF Regularization

RcT8
RcT(n)
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pQCD
pQCD
LOCAL DUALITY RcT8 ?QCD8

Local Duality NOT POSSIBLE at LO in 1/NC !
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QCD Green-functions NOT BEING order-parameters
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Left-left correlator in QCD8
AA correlator VV correlator

• Short distance behaviour in pQCD for (VA)

Shiftman et al. 76
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• Resonance description

Resonance Effective Theory
with q2 -Q2 lt 0
RcT at Large NC
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Peris et al. 98 Beane 01
Golterman Peris 01

• Integral representation of discrete series

From series to integral ?
with the function
and the interspacing
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Relation with sum-rules
QCD dispersion relations
Infinite series from RcT
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High mass resonances Origin of the Continuum
Convergence of H(t) around
Truncated RcT
CONTINUUM
pQCD Continuum
s
Mc2
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High and low energy Hierarchies
Analytical
pQCD
Non-analytical
DOMINANT
cPT
Analytical
DOMINANT
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Phenomenology VA Adler-function
NO CONTINUUM
(without pion pole)
Truncated RcT CONTINUUM
(without pion pole)
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Conclusions
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• Duality QCD RcT (local
  global)
• QCD at large NC
• Infinite resonance summation
• Hierarchy
• Truncated RcT
• pQCD continuum

Logarithmic UV behaviour
Short distances Continuum dominance Long
distances Lightest resonances
Phenomenological success
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• OUTLOOK
• Form-factors (Correlators at NLO in 1/NC)
• Other non-order-parameter Green-funtions
• Scattering amplitudes

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• In addition

LOCAL DUALITY
AVERAGED (GLOBAL) DUALITY
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High and low energy Hierarchies
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Phenomenology Vector Adler-function
NO CONTINUUM
(without pion pole)
Truncated RcT CONTINUUM
(without pion pole)