ELECTROMAGNETIC FORM FACTORS IN QUANTUM FIELD THEORIES

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Electromagnetic Form Factors of Hadrons in
Quantum Field Theories
C.A. Dominguez Centre for Theoretical Physics
Astrophysics University of Cape Town This
talk draws on work done in collaboration with
J.I. Jottar, M. Loewe, R. Röntsch, B. Willlers,
Y.Zhang
ICTP 2008
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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
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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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Gounaris-Sakurai empirical width
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• KLZ Strong coupling theory
• g 5 1/(4 p)2 per loop
• Hence well defined (convergent) perturbative
  expansion

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DUAL LARGE Nc QCD QCD 8
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QCD 8

• Lim Nc ? 8 (Nc 3) ( tHooft 74 Witten 79)
• Spectrum 8 number of zero width resonances

Im G
M2
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Real Spectral Function
Im G
E2
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CORRECTIONS to 1/Nc

• ? / M ? 10

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RESONANCES

• ? - p coupling
• ? - ?0 - p
• ? 0 JPC 1- -
• M? ? 770 MeV
• M? ? 1340 MeV
• M?,, ? 1720 MeV
• M?,,, ? 2034 MeV

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Dual - QCD 8

• Dual Resonance Model Veneziano (1968)
• 8 number of zero width resonances, equally spaced
• Masses couplings fixed to give an Euler Beta
  Function

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M? 769 MeV     M? ? 1340 MeV
EXP. 1465 ? 25 MeV     M? ? 1720 MeV
EXP. 1700 ? 20 MeV     M? ? 2034 MeV
EXP. 2149 ? 17 MeV        
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PION FORM FACTOR

• Dual-Large Nc QCD

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PROTONELECTRIC MAGNETIC FORM FACTORS

• ltPf J?(p) Pigt ? ltPf ?? F1(q2)
• i ?µ? q ? a F2
  (q2)/M Pigt

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e- p CROSS SECTION

• GE (q2) F1(q2) (a q2/4M2) F2(q2)
• GM (q2) F1(q2) a F2(q2)
• ?R (- q2/4M2) G2M (q2) ? G2E (q2)

?
?
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ROSENBLUTH METHOD

• Unpolarized e- p scattering
• Measure ?R for constant q2 varying ?
• Determine GM (q2) from intercept
• Determine GE (q2) from slope
• Assume Scaling Law ?GE /GM 1

?
? GE/GM
1
- q2
?
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Polarized e- p ScatteringJefferson Lab

• Measure longitudinal transverse polarizations
  of the recoil proton Pl, Pt
• . ? GE /GM ? Pt / Pl
• . ? GE /GM ? 1 0.13 q2
• A zero at q2 ? 8 GeV2

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Reconciliation between Rosenbluth
PolarizationMeasurementsSecond order correction
more important in Rosenbluth than in Polarization
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Nucleon Form Factors Dual-Large Nc QCD

• F1 (q2)
• F2 (q2)
• GM (q2)
• GE (q2)
• GE (q2) / GM (q2)

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FORM FACTORS OF ?(1236)

• GM (q2) , GE (q2) , GC (q2)

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SUMMARY

• KLZ Fp
• DUAL Nc 8 Fp , F1 F2 GE / GM ,
• GM , GE , GC
• 
  PERFECT FITS