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C.A. Dominguez Centre for Theoretical Physics & Astrophysics University of Cape Town

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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C.A. Dominguez Centre for Theoretical Physics & Astrophysics University of Cape Town

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  1. 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

  2. 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 (QCD∞) Realization of QCD∞ inspired in the Dual Resonance Model (Veneziano) NOT an expansion in Nc. Nc =∞ ab initio, although finite-width corrections can be incorporated NOT the Veneziano model for hadronic scattering Two different Quantum Field Theory (QFT) Models

  3. VECTOR MESON DOMINANCE • Abelian, TREE-LEVEL model • No truly QFT platform • Not subject to PERTURBATION THEORY improvement

  4. KROLL – LEE – ZUMINO (KLZ)QFT MODEL

  5. 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 = M2ρ

  6. Gounaris-Sakurai empirical width

  7. KLZ: Strong coupling theory • g ≈ 5 & 1/(4 π)2 per loop • Hence: well defined (convergent) perturbative expansion

  8. DUAL – LARGE Nc QCD QCD ∞

  9. QCD ∞ • Lim Nc→∞ (Nc = 3) ( t’Hooft ’74 & Witten ’79) • Spectrum: ∞ number of zero width resonances Im G M2

  10. Real Spectral Function Im G E2

  11. CORRECTIONS to 1/Nc  / M  10 %

  12. RESONANCES •  - p+ coupling :  - 0 - p+ •  0 : JPC = 1- - • M 770 MeV • M’  1340 MeV • M,,  1720 MeV • M,,,  2034 MeV

  13. Dual - QCD ∞ • Dual Resonance Model Veneziano (1968) • ∞ number of zero width resonances, equally spaced • Masses & couplings fixed to give an Euler Beta Function

  14. M= 769 MeV M’  1340 MeV [EXP.: 1465  25 MeV] M’’  1720 MeV [EXP.: 1700  20 MeV] M’’’  2034 MeV [EXP.: 2149  17 MeV]

  15. PION FORM FACTOR Dual-Large Nc QCD

  16. PROTONELECTRIC & MAGNETIC FORM FACTORS • <Pf | J(p+) | Pi>  <Pf |  F1(q2) • + i μν q ν a F2 (q2)/M | Pi>

  17. 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)  

  18. ROSENBLUTH METHOD • Unpolarized e- p+ scattering • Measure R for constant q2 varying  • Determine GM (q2) from intercept • Determine GE (q2) from slope • Assume ScalingLaw : GE /GM = 1   GE/GM 1 - q2 

  19. 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

  20. Reconciliation between Rosenbluth & PolarizationMeasurementsSecond order correction more important in Rosenbluth than in Polarization

  21. Nucleon Form FactorsDual-Large Nc QCD • F1 (q2) • F2 (q2) • GM (q2) • GE (q2) • GE (q2) / GM (q2)

  22. FORM FACTORS OF Δ(1236) G*M (q2) , G*E (q2) , G*C (q2)

  23. SUMMARY • KLZ: Fπ • DUAL – Nc ∞ : Fπ, F1 & F2 + GE / GM , GM* , G*E , G*C PERFECT FITS

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