Pion Form Factor in the KrollLeeZumino

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• Pion Form Factor in the Kroll-Lee-Zumino
  
• Model
• C. A. Dominguez and B. Willers
• University of Cape Town, South Africa
• J. I. Jottar and M. Loewe
• Pontificia Universidad Católica de Chile

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• This talk is based on the article Pion form
  factor in the
• Kroll-Lee-Zumino model, Phys. Rev. D 76 (2007)
  095002.
• This work has been supported by
• FONDECYT, Centro de Estudios Subatómicos (CHILE)
• and NRF (South Africa)

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Two different Quantum Field Theory (QFT) Models

• Kroll-Lee-Zumino Model
• Abelian, Renormalizable QFT
• Platform to justify extend beyond tree-level
  the well known Vector Meson Dominance (VMD)
  Model
• A viable alternative to non-renormalizable QFT
  (effective) models (e.g. Chiral Perturbation
  Theory)

• Dual Large Nc QCD (QCD8)
• Realization of QCD8 inspired in the Dual
  Resonance Model (Veneziano)
• NOT an expansion in Nc. Nc 8 ab initio, although
  finite-width corrections can be incorporated
• NOT the Veneziano model for hadronic scattering

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VECTOR MESON DOMINANCE

• Abelian, TREE-LEVEL model
• No truly QFT platform
• Not subject to PERTURBATION THEORY improvement

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KROLL LEE ZUMINO (KLZ)QFT MODEL

• N. M. Kroll T. D. Lee, and B. Zumino, Physical
  Review 157 (1967) 1376
• Phenomenological Applications Gale and Kapusta.
  ?-meson self energy to one loop order.

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CALCULATING IN KLZ

• Regularization using DIMENSIONAL REGULARIZATION
• Renormalization (fields, masses, couplings)
• Renormalization subtraction point for vertex
  diagram q2 0
• Renormalization subtraction point for vacuum
  polarization diagram
• q2 M2?

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No free Parameters
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• Finally

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Gounaris-Sakurai empirical width
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Conclusions and Outlook

• KLZ Strong coupling theory
• g 5 1/(4 p)2 per loop
• Hence well defined (convergent) perturbative
  expansion
• KLZ is a complement to Chiral Perturbation Theory
  which is valid only in a neighbourhood of
  thresholds
• The calculation of the thermal behaviour of the
  pion form factor is in progress. Relevant for the
  central rapidity region in heavy ion collisions.