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

PION & NUCLEON FORM FACTORS IN (NON-PERTURBATIVE) QCD. C.A. Dominguez Centre for Theoretical Physics & Astrophysics University of Cape Town. UTFSM 2008. M.Loewe M.Fetea J.Rozowski C.van Gend H.Castillo R.Rontsch B.Willers J.Jonker. M.Shifman, A.Vainshtein, V.Zakharov

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

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  1. PION & NUCLEON FORM FACTORS IN (NON-PERTURBATIVE) QCD C.A. Dominguez Centre for Theoretical Physics & Astrophysics University of Cape Town UTFSM 2008

  2. M.Loewe M.Fetea J.Rozowski C.van Gend H.Castillo R.Rontsch B.Willers J.Jonker M.Shifman, A.Vainshtein, V.Zakharov B.Ioffe, A.Radyushkin V.Braun et al. A.Lenz et al. V.Belyaev & I. Kogan Credits

  3. PION & NUCLEON FF • QCD SUM RULES (π, N) • DUAL-LARGE NC QCD (π, N)

  4. QCD SUM RULES (SVZ)

  5. QUARK-HADRON DUALITY

  6. FINITE ENERGY SUM RULES

  7. PION FORM FACTOR

  8. VECTOR MESON DOMINANCE

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

  10. 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)  

  11. 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 

  12. 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

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

  14. QCD SUM RULES F1,2(-q2)

  15. QCD Sum Rules SUMMARY • Fπ(q2) : Reasonable fit for -1 GeV2 ≤ q2 ≤ - 10 GeV2 • F1 (q2) : Reasonable fit for -1 GeV2 ≤ q2 ≤ - 30 GeV2 • F2 (q2) : → 1/(q2) DISASTER !!!

  16. DUAL – LARGE Nc QCDQCD∞

  17. QCD • Lim Nc  (Nc = 3) ( t’Hooft ’74 & Witten ’79) • Spectrum:  number of zero width resonances Im  M2

  18. Real Spectral Function Im  E2

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

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

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

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

  23. PION FORM FACTOR Dual-Large Nc QCD

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

  25. SUMMARY • QCD sum rules: FπOK F1OK F2NOT • DUAL – Nc ∞ : Fπ, F1 & F2 + GE / GM PERFECT FITS

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