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1 Description of Hadrons in the Tuebingen Chiral Quark Model Amand Faessler University of Tuebingen Gutsche, Lyubovitskij, Yupeng Yan, Dong, Shen + PhD.

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Presentation on theme: "1 Description of Hadrons in the Tuebingen Chiral Quark Model Amand Faessler University of Tuebingen Gutsche, Lyubovitskij, Yupeng Yan, Dong, Shen + PhD."— Presentation transcript:

1 1 Description of Hadrons in the Tuebingen Chiral Quark Model Amand Faessler University of Tuebingen Gutsche, Lyubovitskij, Yupeng Yan, Dong, Shen + PhD students: Kuckei, Chedket, Pumsa-ard, Kosongthonkee, Giacosa, Nicmorus

2 2 The Perturbative Chiral Quark Model Quantum Chromodynamic (QCD) with: (Approximate) Symmetries: (1) P, C, T(exact) (2) Global Gauge Invariance: (exact) for each flavor f

3 3 The Perturbative Chiral Quark Model Conservation of the No quarks of flavor f: - baryon number - electric charge - Third component of Isospin - Strangeness - Charme … (3) Approximate Flavor Sym. all the same (4) Approximate Chiral Sym. u, d / SU(2) Isospin

4 4 The Perturbative Chiral Quark Model Conservation of the No quarks of flavor f: - baryon number - electric charge - Third component of Isospin - Strangeness - Charme … (3) Approximate Flavor Sym. all the same (4) Approximate Chiral Sym. u, d / SU(2) Isospin

5 5 The Perturbative Chiral Quark Model Chiral Symmetry: (The non-linear Sigma Model) Low energy effective Lagrangian with correct Symmetries: No Gluons (eliminated) No or with Quarks No Hadrons only: Chiral Perturbation Th. (many free parameters) WithPerturbative Chiral Quark Model (P χ QM)

6 6 The Perturbative Chiral Quark Model (Effective Lagrangian) Chiral Perturbation Theory  PT)  Gluons eliminated Quarks eliminated Perturbative Chiral Quark Model (P χ QM) Gluons eliminated With Quarks

7 7 The Perturbative Chiral Quark Model SU(2) or:SU(3) Invariance under: Isospin

8 8 Chiral Invariant Lagrangian for the Quarks SU(2 or 3) Flavor

9 9 The Perturbative Chiral Quark Model Mass (or scalar Poten.) ≠ 0: Gell-Mann (SU2: )

10 10 The Perturbative Chiral Quark Model = scalar + pseudoscalar (1) Linear σ -Model: weak π decay const.

11 11 The Perturbative Chiral Quark Model (2) Non-Linear σ -Model: SU(2): invariant since: Invariant Lagrangian: with Scalar- and Vector-Potential.

12 12 The Perturbative Chiral Quark Model with: SU2: SU3:

13 13 The Perturbative Chiral Quark Model Seagull Term

14 14 The Perturbative Chiral Quark Model Gell-Mann-Oaks-Renner relat.: Gell-Mann-Okubo relation: with: Current Algebra Relations

15 15 The Perturbative Chiral Quark Model NUCLEON Wave Functions and Parameters: Quark Wave Function: Potential:

16 16 The Perturbative Chiral Quark Model

17 17 The Perturbative Chiral Quark Model The PION-NUCLEON Sigma Term: Gutsche, Lyubovitskij, Faessler; P. R. D63 (2001) PION-NUCLEON Scattering: time Weinberg-Tomozawa

18 18 The Perturbative Chiral Quark Model QCD: Proton

19 19 The Perturbative Chiral Quark Model

20 20 Pion (Kaon, Eta)- Nucleon Sigma-Term

21 21 Pion-Nucleon Sigma Term in the Perturbative Chiral Quark Model 3q  K  Tot.  PT (8) (.4)

22 22 Scalar Formfactor of the Nucleon and the Meson Cloud

23 23 The Perturbative Chiral Quark Model + counter terms Electromagnetic Properties of Baryons: Tuebingen group: Phys. Rev. C68, (2003); Phys. Rev. C69, (2004) ….

24 24 Magnetic Moments and Electric and Magnetic Radii of Protons and Neutrons [ in units of Nulear Magnetons and fm² ] 3qloopsTotalExp

25 25 Helicity Amplitudes for N –  Transition at the Photon Point Q² = 0 A(1/2 )A(3/2) 3quarks Loops (ground q) Loops (excited) Total -130 (3.4)-225 (6) Exp[10**(-3) GeV**(-1/2) -135 (6)-255 (8)

26 26 The Perturbative Chiral Quark Model

27 27 The Perturbative Chiral Quark Model

28 28 Strangeness in the Perturbative Chiral Quark Model Proton

29 29 Strange Magnetic Moment and Electric and Magnetic Strange Mean Square Radii Approach QCD Leinweber I (0.18) QCD Leinweber II (0.021) QCD Dong (0.20) -0,16 (0.20) CHPT Meissner 0.18 (0.34) 0.05 (0.09) NJL Weigel 0.10 (0.15) -0,15 (0.05) CHQSM Goeke CQM Riska ~0.02 PCHQM (0.012) (0.003) (.003)

30 30 Strangeness in the nucleon E. J. Beise et al. Prog. Part. Nucl. Phys. 54(2005)289 F. E. Maas et al. Phys. Rev. Lett. 94 (2005)

31 31 The Perturbative Chiral Quark Model THEORY (Pert. χ Quark M) + SAMPLE + HAPPEX: ApproachG s (0.1) SAMP G s (0,48) HAPP G s ( ) MAMI χ PT Meissner Goeke Shyrme Riska P χ QM Tuebingen Exp 0.23 ± (3.7±1.2) ± ± fit ± (1.8±0.3) ± ± ± 0.03 (2.9±0.5) ? MITCEBAFMainz

32 32 Strangeness in the Nucleon Approach Q²[GeV²/c²] Gs(0.1) SAMP § Gs(0.48) HAPP § Gs(0.23) Mainz*  PT Meissner (0.44) fit (0.048) (0.127) Skyrme Goeke (0.016) 0.14 (0.03) Riska P  QM (0.01) (.0003) (.00005) EXP0.23 § (0.76).025 § (.034) * F. E. Maas et al. Phys. Rev. Lett. 94 (2005) * E. J. Beise et al. Prog. Part. Nucl. Phys. 54(2005)289 §

33 33 Compton Scattering  N ->  ´+ N´ and electric  and magnetic  Polarizabilities of the Nucleon. Exp: Schumacher Prog. Part. Nucl. Phys. to be pub.55(2005)

34 34 Compton Scattering  N ->  ´+ N´ and electric  and magnetic  Polarizabilities.

35 35 Compton Scattering Diagrams for electric  and magnetic  Polarizabilities

36 36 Compton Scattering diagrams for Spin Polarizabilities 

37 37 Electric  and Magnetic  Polarizabilities of the Nucleon [10**(-4) fm^3]  (p,E)  (p,  (n,E)  (n,M) DATA 10**(-4) fm^3 Schumacher 12.0 (0.6) 1.9 (0.6) 12.5 (1.7) 2.7 (1.8) CHPT Meissner CHPT Babusci 10.5 (2.0) 3.5 (3.6) 13.6 (1.5) 7.8 (3.6) CHPT Hemmert CHPT Lvov PCQM Tuebingen

38 38 Electric and Magnetic Polarizabilities: Data and Theories

39 39 The Perturbative Chiral Quark Model SUMMARY Theory of Strong Interaction: Effective Lagrangian with correct chiral Symmetry without Gluons with Quarks Perturbative Chiral Quark Model

40 40 The Perturbative Chiral Quark Model (Effective Lagrangian) Chiral Perturbation Theory: Gluons eliminated Quarks eliminated Perturbative Chiral Quark Model (P χ QM) Gluons eliminated With Quarks

41 41 Chiral Invariant Lagrangian for the Quarks SU(2 or 3) Flavor

42 42 The Perturbative Chiral Quark Model (2) Non-Linear σ -Model: SU(2): invariant since: Invariant Lagrangian: with Scalar- and Vector-Potential.

43 43 The Perturbative Chiral Quark Model With : Current Algebra

44 44 The Perturbative Chiral Quark Model

45 45 The Perturbative Chiral Quark Model Effective Low Energy L Chiral symmetry: Goldstone Bosons (m PS = 0) Pseudo-Scalar Octet

46 46 The Perturbative Chiral Quark Model Chiral Symmetry Breaking: Restore Symmetry:

47 47 The Perturbative Chiral Quark Model Perturbation Theory around in powers of up to second order: Perturbative Chiral Quark Model: P χ QM Parameters adjusted: Ansatz for Quark fct.: Gasser Leutwhyler

48 48 The Perturbative Chiral Quark Model Radii and Magnetic Moments of p, n Electric and Magnetic p,n Form factors Strangeness in N π -Nucleon- σ Term Electric and Magnetic Polarizabilities of the Nucleon The End Two Parameters only:, g(A)

49 49 The Perturbative Chiral Quark Model The danger of trouble counting in chiral Perturbation Theory ( χ PT) and in the perturbative chiral Quark Model (P χ QM)

50 50 The Perturbative Chiral Quark Model Covariance:


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