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

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

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

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

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)

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

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

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

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

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

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

The Perturbative Chiral Quark Model with: SU2: SU3:

The Perturbative Chiral Quark Model Seagull Term

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

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

The Perturbative Chiral Quark Model

The Perturbative Chiral Quark Model The PION-NUCLEON Sigma Term: Gutsche, Lyubovitskij, Faessler; P. R. D63 (2001) 054026 PION-NUCLEON Scattering: time Weinberg-Tomozawa

The Perturbative Chiral Quark Model QCD: Proton

The Perturbative Chiral Quark Model

Pion (Kaon, Eta)-Nucleon Sigma-Term

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

Scalar Formfactor of the Nucleon and the Meson Cloud

The Perturbative Chiral Quark Model Electromagnetic Properties of Baryons: + counter terms Tuebingen group: Phys. Rev. C68, 015205(2003); Phys. Rev. C69, 035207(2004) ….

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

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)

The Perturbative Chiral Quark Model

The Perturbative Chiral Quark Model

Strangeness in the Perturbative Chiral Quark Model Proton

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)

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) 152001

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

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* 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) 0.00029 (.00005) EXP 0.23 § (0.76) .025 § (.034) *

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)

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

Compton Scattering Diagrams for electric a and magnetic b Polarizabilities

Compton Scattering diagrams for Spin Polarizabilities g

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

Electric and Magnetic Polarizabilities: Data and Theories

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

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

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

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

The Perturbative Chiral Quark Model Current Algebra With:

The Perturbative Chiral Quark Model

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

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

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

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

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

The Perturbative Chiral Quark Model Covariance: