Transcript The Perturbative Chiral Quark Model - uni

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
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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
u, d / SU(2) Isospin
(4) Approximate Chiral Sym.
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The Perturbative Chiral
Quark Model
(Effective Lagrangian)
Chiral Perturbation
Theory (cPT):
Gluons eliminated
Quarks eliminated
Perturbative Chiral Quark
Model (PχQM)
Gluons eliminated
With 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
Current Algebra Relations
Gell-Mann-Oaks-Renner relat.:
Gell-Mann-Okubo relation:
with:
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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 p
K
13 39
2.1 0.1
55
45(8)
1
.3
14
15(.4)
12
h
.02
Tot. cPT
.1 1.4 .04 .002 1.5 1.6
85 256 40
4.5
386 395
28 0
4.5 0
33
4
69
96
13
9.4
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Scalar Formfactor of
the Nucleon and the
Meson Cloud
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The Perturbative Chiral
Quark Model
Electromagnetic Properties of Baryons:
+ counter terms
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
2.79
2.60
-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
– D Transition at the
Photon Point Q² = 0
A(1/2 )
A(3/2)
3quarks -78.3
-135.6
Loops
(ground q)
Loops
(excited)
-32.2
-55.7
-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)
NJL Weigel
0.10
(0.15)
-0,15
(0.05)
CHQSM
Goeke
0.115
-0.095
CQM Riska
-0.046
PCHQM
-0.048 -0.011 0.024
(0.012) (0.003) (.003)
-0.14
0.073
~0.02
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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
E. J. Beise et al. Prog. Part. Nucl. Phys. 54(2005)289 §
F. E. Maas et al. Phys. Rev. Lett. 94 (2005) 152001*
Approach
Gs(0.1)
Q²[GeV²/c²] SAMP §
Gs(0.48) Gs(0.23)
HAPP § Mainz*
cPT
Meissner
0.023 fit
(0.048)
0.023
(0.44)
0.007
(0.127)
Skyrme 0.09
Goeke
0.087
0.14
(0.016) (0.03)
Riska
-0.06
-0.08
PcQM
-0.04
(0.01)
0.0018 0.00029
(.0003) (.00005)
EXP
0.23 §
(0.76)
.025 §
(.034)
*
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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)
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Compton Scattering
Diagrams for electric a and
magnetic b Polarizabilities
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Compton Scattering
diagrams for Spin
Polarizabilities g
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Electric a and Magnetic b
Polarizabilities of the
Nucleon [10**(-4) fm^3]
DATA
10**(-4)
fm^3
a(p,E)
b(p,M) a(n,E)
b(n,M)
12.0
(0.6)
1.9
(0.6)
12.5
(1.7)
2.7
(1.8)
-2.3
11.0
-2.0
3.5
(3.6)
1.26
13.6
(1.5)
12.6
7.8
(3.6)
1.26
-1.8
9.8
-0.9
5.1
10.9
1.15
Schumacher
CHPT 7.9
Meissner
CHPT 10.5
Babusci
(2.0)
CHPT 12.6
Hemmert
CHPT 7.3
Lvov
PCQM 10.9
Tuebingen
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The Perturbative Chiral
Quark Model
SUMMARY
Theory of Strong Interaction:
Effective Lagrangian with correct chiral
Symmetry without Gluons with Quarks
Perturbative Chiral Quark Model
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The Perturbative Chiral
Quark Model
(Effective Lagrangian)
Chiral Perturbation Theory:
Gluons eliminated
Quarks eliminated
Perturbative Chiral Quark
Model (PχQM)
Gluons eliminated
With Quarks
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Chiral Invariant
Lagrangian for the
Quarks SU(2 or 3) Flavor
41
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
Current Algebra
With:
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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
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