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Chiral Quark Dynamics of Baryons

Chiral Quark Dynamics of Baryons. Amand Faessler, Tuebingen. Gutsche, Holstein, Lyubovitskij, + PhD students (Nicmorus, Kuckei, Cheedket, Pumsa-ard, Khosonthongkee, Giacosa). Chiral Quark Dynamics of Baryons. Quantum Chromodynamics: with:. Chiral Quark Dynamics of Baryons.

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Chiral Quark Dynamics of Baryons

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  1. Chiral Quark Dynamics of Baryons Amand Faessler, Tuebingen Gutsche, Holstein, Lyubovitskij, + PhD students (Nicmorus, Kuckei, Cheedket, Pumsa-ard, Khosonthongkee, Giacosa) Amand Faessler, Tuebingen

  2. Chiral Quark Dynamics of Baryons Quantum Chromodynamics: with: Amand Faessler, Tuebingen

  3. Chiral Quark Dynamics of Baryons Effective Lagrangian for low Energies with the same Symmetries as QCD: 1. P, C, T (exact) 2. Global (and local ) Gauge Invariance: (exact) for each flavorf Amand Faessler, Tuebingen

  4. Chiral Quark Dynamics of Baryons From this invariance follows: Conservation of the No quarks of flavor f; • baryon number • electric charge • Third compon. of Isospin • Strangeness • Charm … 3. ApproximateFlavor Sym. all the same u, d / SU(2) Isospin; u,d,s / SU(3) Amand Faessler, Tuebingen

  5. Chiral Quark Dynamics of Baryons 4. ApproximateChiral Symmetry: Current quark mass at QCD scale m ~ 1 GeV Current mass term: Current quark mass term violates Chiral Symmetry Amand Faessler, Tuebingen

  6. Chiral Quark Dynamics of Baryons Low energy effective Lagrangian with correct Symmetries Gluons and Quarks eliminated: -> Chiral Perturbation theory Gluons eliminated but with quarks: -> Perturbative Chiral Quark Model (Manohar and Georgi) Amand Faessler, Tuebingen

  7. Chiral Quark Dynamics of Baryons Perturbative Chiral Quark Model A. Manohar and H. Georgi: Nucl. Phys. B234 (1984) 189 Amand Faessler, Tuebingen

  8. Chiral Quark Dynamics of Baryons Danger of Double Counting in Chiral Quark Model : Pseudoscalar Mesons as Goldstone Bosons and as Quark-Antiquark States Investigated by A. Manohar and H. Georgi: Nucl. Phys. B234 (1984) 189 Goldstone Bosons are the low lying pseudoscalar Mesons. The quark-antiquark states lie very high. Amand Faessler, Tuebingen

  9. Chiral Quark Dynamics of Baryons Effective Lagrangian up to fourth order: • The quark functions q, the quark momenta, the constituent quark masses, and the chiral fields are of order 1: O(1). • Pseudoscalar meson masses, Meson momenta, electroweak potentials are of first order small. • Current quark masses, electric and magnetic field tensors Fmn are of second order small. Amand Faessler, Tuebingen

  10. Chiral Quark Dynamics of Baryons Up to fourth order in small quantities. With: Do not read this formula! On quark level suggested in leading order by Manohar and GeorgiNucl. Phys. B 234(1984)189. On hadron level formulated by Gasser, Leutwyler, Holstein, Meissner, Weise, Hemmert, Schererand others up to fourth order. Leading order Amand Faessler, Tuebingen

  11. Chiral Quark Dynamics of Baryons 10 Parameters: mu ;ms ;g ;c2 ;c4 ;c5 ;e7 ;e8 ;e10 ;d10 Compositeness condition: g( meson-quark) coupling; constituent quarks have mass in chiral limit Amand Faessler, Tuebingen

  12. Chiral Quark Dynamics of Baryons • Parameters and counterterms: c6 ,e7 ,e8 fitted to the magnetic moments: • Parameters: c2 , c4 ,e10 ,d10 fitted to electric and magnetic radii of protons and neutrons: With: Amand Faessler, Tuebingen

  13. Chiral Quark Dynamics of Baryons Nucleon expectation value of the bare constituent quark current. Formfactor of a single constituent bare quark q = u, d in the Nucleon at high energies can not calculated by chiral perturbation theory.

  14. Chiral Quark Dynamics of Baryons Alternative approach: We use a simple Gaussian Function for the bare quarks (I. V. Anikin et. al. Z. Phys. C65(1995) 681): k1E and k2E = Euclidian relative Jacobi momenta k1E k2E L B = 800 MeV Amand Faessler, Tuebingen

  15. Chiral Quark Dynamics of Baryons • We dress now the bare quark current by the pseudoscalar meson cloud of pions, kaons and etas. Amand Faessler, Tuebingen

  16. Chiral Quark Dynamics of Baryons More diagrams: Amand Faessler, Tuebingen

  17. Chiral Quark Dynamics of Baryons Diagrams with vector mesons: Amand Faessler, Tuebingen

  18. Chiral Quark Dynamics of Baryons Connection with Vector Dominance Model Amand Faessler, Tuebingen

  19. Chiral Quark Dynamics of Baryons g g - 18 such type of diagrams included: Correction smaller than about 15 % Single quark Counter terms g - Nucleon Pseudoscalar meson in flight not yet included. Small. Amand Faessler, Tuebingen

  20. Chiral Quark Dynamics of Baryons Dressed Baryon Current Amand Faessler, Tuebingen

  21. Chiral Quark Dynamics of Baryons • Effect of the pseudoscalar meson cloud on magnetic moments, • On electric and magnetic formfactors of protons and neutrons , • On the N-Delta M1 transition and the ratio E2/M1 and C2/M1 for N -> D. Amand Faessler, Tuebingen

  22. Magnetic Diagonal and Transition Moments of the Baryon Octet in units: [ nm] = Edelman; Blanpied et al. Fit Amand Faessler, Tuebingen

  23. Nucleon-Delta Transition LB = 0.8 GeV Data: S. Eidelman et al.; S. Stave et al.; G. Blanpied et al. Amand Faessler, Tuebingen

  24. Ratios of Coulomb and Electric Quadrupole over Magnetic Dipole for: Delta -> Nucleon + g Total: valence+cloud Total: valence+cloud Valence quarks Valence quarks Data: S. Stave et al.; N. F. Sparveris et al.; T. Popischil et al. ; D. Elsner et al. Eur. Phys. J. 27(2006) 91. Amand Faessler, Tuebingen

  25. Connection beween Dirac, Pauli F1/2 and Sachs GE/M Formfactors DIRAC Pauli With: Amand Faessler, Tuebingen

  26. Electron-Proton Scattering and Rosenbluth Separation of Sachs Formfactors: GpE and GpM Amand Faessler, Tuebingen

  27. Amand Faessler, Tuebingen

  28. Chiral Quark Dynamics of Baryons Ratio : Amand Faessler, Tuebingen

  29. Qualitative Explanation for the Electric Formfactor of the Proton: ~85 % ~15 % proton proton pion+ proton pion+ neutron = + = neutron proton proton Bessel Radius r Fourier –Transf. with spherical Bessel-fct.: Amand Faessler, Tuebingen

  30. Electric Formfactor of the Neutron neutron total proton pion- Valence quarks neutron Cloud Amand Faessler, Tuebingen

  31. Chiral Quark Dynamics of Baryons Magnetic Proton Formfactor. Amand Faessler, Tuebingen

  32. Chiral Quark Dynamics of Baryons Magnetic Formfactor of the Neutron over the Dipole Formfactor Amand Faessler, Tuebingen

  33. Electric over Magnetic Proton Formfactor Rosenbluth Separation Data: SLAC: Walker et al.Phys.Rev.D (1994); Jefferson Lab Hall A :Punjabi et al. Phys. Rev. C (2005) and Gayou et al.P.R.L. Polarised e-beam plus polarized recoil protons Amand Faessler, Tuebingen

  34. Chiral Quark Dynamics of Baryons Summary: • Chiral Dynamics on quark level up to fourth order • Parameters and Counter Terms fixed to Magnetic Moments (p, n, L), Radii and High Energy Behavior of Formfactors for Protons and Neutrons. • Calculated Meson cloud Effects on Magnetic Moments of Baryon Octet • Calculated meson cloud effects on N-D transition • Effects of Pseudoscalar Meson Cloud on Formfactors. The END Amand Faessler, Tuebingen

  35. PUBLICATIONS: 1. A. Faessler, Th. Gutsche, V. E. Lyubovitskij, K. Pumsa-ard: Prog. Part. Nucl. Phys. 55 ( 2005) 12. 2. A. Faessler, Th. Gutsche, V. E. Lyubovitskij, K. Pumsa-ard: Phys. Rev. D73 (2006)114021 3. A. Faessler, Th. Gutsche, B. R. Holstein, E. Lyubovitskij: Phys. Rev. D74 (2006) 074010 Amand Faessler, Tuebingen

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