1

Description of Hadrons in the

Tuebingen Chiral Quark Model

Amand FaesslerUniversity 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:(1) P, C, T (exact)(2) Global Gauge Invariance:

(exact)for each flavor f

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

6

The Perturbative Chiral Quark Model

(Effective Lagrangian)

Chiral Perturbation Theory PT)

Gluons eliminatedQuarks eliminated

Perturbative Chiral Quark Model (PχQM)

Gluons eliminatedWith Quarks

8

Chiral Invariant Lagrangian for the

Quarks SU(2 or 3) Flavor

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

Gell-Mann-Oaks-Renner relat.:

Gell-Mann-Okubo relation:

with:

Current Algebra Relations

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)

054026

PION-NUCLEON Scattering:

time

Weinberg-Tomozawa

18

The Perturbative Chiral Quark Model

QCD:

Proton

20

Pion (Kaon, Eta)-Nucleon Sigma-Term

21

Pion-Nucleon Sigma Term in the Perturbative

Chiral Quark Model

3q K Tot. PT

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 0 4.5 0 33

4 13 69 9.4 96

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Scalar Formfactor of the Nucleon and the

Meson Cloud

23

The Perturbative Chiral Quark Model

+ counter terms

Electromagnetic Properties of Baryons:

Tuebingen group: Phys. Rev. C68, 015205(2003); Phys. Rev. C69, 035207(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

0 -.111 -.111 -.116

0.37 0.37 0.74 0.74

0.33 0.61 1.89 1.61

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Helicity Amplitudes for N – Transition at the Photon Point Q² = 0

A(1/2 ) A(3/2)

3quarks -78.3 -135.6

Loops

(ground q)-32.2 -55.7

Loops

(excited)-19.6 -33.9

Total -130 (3.4) -225 (6)

Exp[10**(-3) GeV**(-1/2) -135 (6) -255 (8)

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Strangeness in the Perturbative Chiral

Quark Model

Proton

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Strange Magnetic Moment and Electric and Magnetic Strange Mean

Square Radii

Approach

QCD Leinweber I

-0.16 (0.18)

QCD Leinweber II

-0.051 (0.021)

QCD

Dong-0.36 (0.20)

-0,16 (0.20)

CHPT Meissner

0.18 (0.34)

0.05 (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 -0.048 (0.012)

-0.011 (0.003)

0.024

(.003)

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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) 152001

32

Strangeness in the Nucleon

Approach

Q²[GeV²/c²]Gs(0.1)

SAMP §

Gs(0.48)

HAPP §

Gs(0.23)

Mainz*

PTMeissner

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

PQM -0.04

(0.01)

0.0018

(.0003)

0.00029

(.00005)

EXP 0.23 §

(0.76)

.025 §

(.034)

*

F. E. Maas et al. Phys. Rev. Lett. 94 (2005) 152001*

E. J. Beise et al. Prog. Part. Nucl. Phys. 54(2005)289 §

33

Compton Scattering N -> ´+ N´

and electric and magnetic Polarizabilities of the Nucleon.

Exp: Schumacher Prog. Part. Nucl. Phys. to be pub.55(2005)

35

Compton Scattering Diagrams for electric and magnetic Polarizabilities

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Compton Scattering diagrams for Spin Polarizabilities

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Electric and Magnetic Polarizabilities of the Nucleon [10**(-4) fm^3]

(p,E) (p, (n,E) (n,M)

DATA10**(-4) fm^3Schumacher

12.0

(0.6)

1.9

(0.6)

12.5

(1.7)

2.7

(1.8)

CHPTMeissner

7.9 -2.3 11.0 -2.0

CHPTBabusci

10.5

(2.0)

3.5

(3.6)

13.6

(1.5)

7.8

(3.6)

CHPTHemmert

12.6 1.26 12.6 1.26

CHPTLvov

7.3 -1.8 9.8 -0.9

PCQMTuebingen

10.9 5.1 10.9 1.15

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The Perturbative Chiral Quark Model

SUMMARYTheory of Strong Interaction:

Effective Lagrangian with correct chiral Symmetry without Gluons

with QuarksPerturbative Chiral Quark Model

40

The Perturbative Chiral Quark Model

(Effective Lagrangian)

Chiral Perturbation Theory:

Gluons eliminatedQuarks eliminated

Perturbative Chiral Quark Model (PχQM)

Gluons eliminatedWith 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

With:

Current Algebra

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: <r²>, g(A)