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Recovering QCD at large N C : Two-point Green-functions

Recovering QCD at large N C : Two-point Green-functions. J. J. Sanz Cillero, IN2P3 - Orsay. DUALITY QCD at large N C (QCD ∞ )  Resonance Theory (R c T ∞ ). Outline:. Analysis of QCD correlators: a)- Physical QCD content b)- Relation R c T Sum-rules

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Recovering QCD at large N C : Two-point Green-functions

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  1. Recovering QCD at large NC:Two-point Green-functions J. J. Sanz Cillero, IN2P3 - Orsay

  2. DUALITY QCD at large NC (QCD∞) Resonance Theory (RcT∞) Outline: • Analysis of QCD correlators: • a)- Physical QCD content • b)- Relation RcT Sum-rules • c)- Truncated RcT + “pQCD Continuum” • Conclusions

  3. Duality in QCD

  4. QCD∞ Infinite resonance Regularization CUT-OFF Regularization …… RcT∞ RcT(n)

  5. pQCD pQCD LOCAL DUALITY RcT∞QCD∞ … Local Duality NOT POSSIBLE at LO in 1/NC !

  6. QCD Green-functions NOT BEING order-parameters

  7. UV divergent • Scale dependent • Logarithmic behaviour • Physical & finite • m independent • Logs within as Left-left correlator inQCD∞ & AA correlator & VV correlator • Short distance behaviour inpQCDfor (V+A): [ Shiftman et al. ’76 ]

  8. UV DIVERGENT when M∞2∞ UV finite when M∞2∞ • Resonance description: Resonance Effective Theory with q2= -Q2 < 0 RcT at Large NC

  9. [ Peris et al. ´98 ] [ Beane ’ 01 ] [ Golterman & Peris ‘ 01 ] … • Integral representation of discrete series: From series to integral with the function and the interspacing

  10. Short distance QCD : Information about higher multiplets pQCD Relation with sum-rules: QCDdispersion relations Infinite series fromRcT

  11. High mass resonances: Origin of the “Continuum” Convergence of H(t) around Truncated RcT “CONTINUUM” “pQCD Continuum” s Mc2

  12. High and low energy Hierarchies Analytical pQCD: DOMINANT Non-analytical cPT: Analytical DOMINANT

  13. Phenomenology: V+A Adler-function NO “CONTINUUM” (without pion pole) Truncated RcT + “CONTINUUM” (without pion pole)

  14. Conclusions

  15. Duality: QCDRcT (local & global) QCDat large NC : Infinite resonance summation Hierarchy Truncated RcT + pQCD continuum Logarithmic & UV behaviour Short distances: Continuum dominance Long distances: Lightest resonances Phenomenological success

  16. OUTLOOK: • Form-factors (Correlators at NLO in 1/NC) • Other non-order-parameter Green-funtions • Scattering amplitudes ? ? ?

  17. In general: Example  for the scalar correlator • In addition: LOCAL DUALITY AVERAGED (GLOBAL) DUALITY

  18. High and low energy Hierarchies

  19. Phenomenology: Vector Adler-function NO CONTINUUM (without pion pole) Truncated RcT + CONTINUUM (without pion pole)

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