1 description of hadrons in the tuebingen chiral quark model amand faessler university of tuebingen...
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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
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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
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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
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The Perturbative Chiral Quark Model
(Effective Lagrangian)
Chiral Perturbation Theory PT)
Gluons eliminatedQuarks eliminated
Perturbative Chiral Quark Model (PχQM)
Gluons eliminatedWith Quarks
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Chiral Invariant Lagrangian for the
Quarks SU(2 or 3) Flavor
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The Perturbative Chiral Quark Model
(2) Non-Linear σ-Model:SU(2):
invariant since:
Invariant Lagrangian:with Scalar- and Vector-Potential.
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The Perturbative Chiral Quark Model
with:
SU2:
SU3:
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The Perturbative Chiral Quark Model
Seagull Term
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The Perturbative Chiral Quark Model
Gell-Mann-Oaks-Renner relat.:
Gell-Mann-Okubo relation:
with:
Current Algebra Relations
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The Perturbative Chiral Quark Model
NUCLEON Wave Functions and Parameters:
Quark Wave Function:
Potential:
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The Perturbative Chiral Quark Model
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The Perturbative Chiral Quark Model
The PION-NUCLEON Sigma Term:Gutsche, Lyubovitskij, Faessler; P. R. D63 (2001)
054026
PION-NUCLEON Scattering:
time
Weinberg-Tomozawa
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The Perturbative Chiral Quark Model
QCD:
Proton
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Pion (Kaon, Eta)-Nucleon Sigma-Term
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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
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The Perturbative Chiral Quark Model
+ counter terms
Electromagnetic Properties of Baryons:
Tuebingen group: Phys. Rev. C68, 015205(2003); Phys. Rev. C69, 035207(2004) ….
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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
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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 §
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Compton Scattering N -> ´+ N´
and electric and magnetic Polarizabilities of the Nucleon.
Exp: Schumacher Prog. Part. Nucl. Phys. to be pub.55(2005)
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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
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The Perturbative Chiral Quark Model
(Effective Lagrangian)
Chiral Perturbation Theory:
Gluons eliminatedQuarks eliminated
Perturbative Chiral Quark Model (PχQM)
Gluons eliminatedWith Quarks
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Chiral Invariant Lagrangian for the
Quarks SU(2 or 3) Flavor
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The Perturbative Chiral Quark Model
(2) Non-Linear σ-Model:SU(2):
invariant since:
Invariant Lagrangian:with Scalar- and Vector-Potential.
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The Perturbative Chiral Quark Model
With:
Current Algebra
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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)