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

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. 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. 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)
With Perturbative Chiral Quark Model
(PχQM)

6. The Perturbative Chiral Quark Model (Effective Lagrangian)
Chiral Perturbation
Theory (cPT):
Gluons eliminated
Quarks eliminated
Perturbative Chiral Quark Model (PχQM)
Gluons eliminated
With Quarks

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

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

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

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

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

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

13. The Perturbative Chiral Quark Model
Seagull Term

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

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

16. The Perturbative Chiral Quark Model

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. The Perturbative Chiral Quark Model
QCD:
Proton

19. The Perturbative Chiral Quark Model

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

21. Pion-Nucleon Sigma Term in the Perturbative Chiral Quark Model
Tot.
cPT 13 39
2.1
0.1 55
45(8) 1 12 .3
.02 14
15(.4) .1
1.4
.04
.002
1.5
1.6 85
256 40
4.5
386
395 28 33 4 69
9.4 96

22. Scalar Formfactor of the Nucleon and the Meson Cloud

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

24. Magnetic Moments and Electric and Magnetic Radii of Protons and Neutrons [in units of Nulear Magnetons and fm²] 3q
loops
Total
Exp.
1.8
0.80
2.60
2.79
-1.2
-0.78
-1.98
-1.91
0.60
0.12
0.72
0.76
-.111
-.116
0.37
0.74
0.33
0.61
1.89
1.61

25. Helicity Amplitudes for N – D Transition at the Photon Point Q² = 0
3quarks
-78.3
-135.6
Loops
(ground q)
-32.2
-55.7
(excited)
-19.6
-33.9
Total
-130 (3.4)
-225 (6)
Exp[10**(-3) GeV**(-1/2)
-135 (6)
-255 (8)

26. The Perturbative Chiral Quark Model

27. The Perturbative Chiral Quark Model

28. Strangeness in the Perturbative Chiral Quark Model
Proton

29. Strange Magnetic Moment and Electric and Magnetic Strange Mean Square Radii
Approach
QCD Leinweber I
-0.16 (0.18)
QCD Leinweber II
(0.021)
QCD
Dong
-0.36 (0.20)
-0,16 (0.20)
CHPT Meissner
0.18 (0.34)
(0.09)
-0.14
NJL Weigel
0.10 (0.15)
-0,15 (0.05)
CHQSM Goeke
0.115
-0.095
0.073
CQM Riska
-0.046
~0.02
PCHQM
(0.012)
(0.003)
0.024
(.003)

30. Strangeness in the nucleon E. J. Beise et al. Prog. Part. Nucl. Phys
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. The Perturbative Chiral Quark Model
THEORY (Pert. χ Quark M)
+ SAMPLE + HAPPEX:
Approach
Gs (0.1) SAMP
Gs (0,48)
HAPP
Gs ( )
MAMI
χ PT
Meissner
Goeke
Shyrme
Riska
PχQM
Tuebingen
Exp
0.23 ± 0.44
0.09
- 0.06
- (3.7±1.2) 10-2
0.14 ± 0.6
0.023 ± 0.048
fit
0.087 ± 0.016
- 0.08
(1.8±0.3) 10-3
0.025 ± 0.034
0.007 ± 0.127
0.14 ± 0.03
(2.9±0.5) 10-4 ?
MIT
CEBAF
Mainz

32. 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) *
Approach
Q²[GeV²/c²]
Gs(0.1)
SAMP §
Gs(0.48)
HAPP §
Gs(0.23)
Mainz*
cPT
Meissner
0.023 (0.44)
0.023 fit
(0.048)
0.007
(0.127)
Skyrme
Goeke
0.09
0.087
(0.016)
0.14
(0.03)
Riska
-0.06
-0.08
PcQM
-0.04
(0.01)
0.0018
(.0003)
(.00005)
EXP
0.23 §
(0.76)
.025 §
(.034) *

33. Exp: Schumacher Prog. Part. Nucl. Phys. to be pub.55(2005)
Compton Scattering g + N -> g´+ N´ and electric a and magnetic b Polarizabilities of the Nucleon.
Exp: Schumacher Prog. Part. Nucl. Phys. to be pub.55(2005)

34. Compton Scattering g + N -> g´+ N´ and electric a and magnetic b Polarizabilities.

35. Compton Scattering Diagrams for electric a and magnetic b Polarizabilities

36. Compton Scattering diagrams for Spin Polarizabilities g

37. Electric a and Magnetic b Polarizabilities of the Nucleon [10
Electric a and Magnetic b Polarizabilities of the Nucleon [10**(-4) fm^3]
a(p,E)
b(p,M)
a(n,E)
b(n,M)
DATA
10**(-4) fm^3
Schumacher
12.0
(0.6)
1.9
12.5
(1.7)
2.7
(1.8)
CHPT
Meissner
7.9
-2.3
11.0
-2.0
Babusci
10.5
(2.0)
3.5
(3.6)
13.6
(1.5)
7.8
Hemmert
12.6
1.26
Lvov
7.3
-1.8
9.8
-0.9
PCQM
Tuebingen
10.9
5.1
1.15

38. Electric and Magnetic Polarizabilities: Data and Theories

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. The Perturbative Chiral Quark Model (Effective Lagrangian)
Chiral Perturbation Theory:
Gluons eliminated
Quarks eliminated
Perturbative Chiral Quark Model (PχQM)
Gluons eliminated
With Quarks

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

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

43. The Perturbative Chiral Quark Model
Current Algebra
With:

44. The Perturbative Chiral Quark Model

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

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

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

48. The Perturbative Chiral Quark Model
Two Parameters only: <r²>, g(A)
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

49. The Perturbative Chiral Quark Model
The danger of trouble counting in chiral
Perturbation Theory (χPT)
and in the perturbative chiral Quark Model
(PχQM)

50. The Perturbative Chiral Quark Model
Covariance: