Chiral Quark Dynamics of Baryons
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Amand Faessler, Tuebingen 1
Chiral Quark Dynamics of Baryons
Gutsche, Holstein, Lyubovitskij, + PhD students (Nicmorus,
Kuckei, Cheedket, Pumsa-ard, Khosonthongkee, Giacosa)
Amand Faessler, Tuebingen
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Amand Faessler, Tuebingen 2
Chiral Quark Dynamics of Baryons
Quantum Chromodynamics:
with:
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Amand Faessler, Tuebingen 3
Chiral Quark Dynamics of Baryons
1. P, C, T (exact)
2. Global (and local ) Gauge Invariance:
(exact)
for each flavor f
Effective Lagrangian for low Energies with the same Symmetries as QCD:
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Amand Faessler, Tuebingen 4
Chiral Quark Dynamics of Baryons
From this invariance follows:Conservation of the No quarks of flavor f;- baryon number- electric charge- Third compon. of Isospin- Strangeness- Charm …
3. Approximate Flavor Sym. all the same
u, d / SU(2) Isospin; u,d,s / SU(3)
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Amand Faessler, Tuebingen 5
Chiral Quark Dynamics of Baryons
4. Approximate Chiral Symmetry:
Current quark mass at QCD scale ~ 1 GeV
Current mass term:
Current quark mass term violates Chiral Symmetry
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Amand Faessler, Tuebingen 6
Chiral Quark Dynamics of Baryons
Low energy effective Lagrangian with correct Symmetries
Gluons and Quarks eliminated:
-> Chiral Perturbation theory
Gluons eliminated but with quarks:
-> Perturbative Chiral Quark Model (Manohar and Georgi)
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Amand Faessler, Tuebingen 7
Chiral Quark Dynamics of Baryons
Perturbative Chiral Quark Model A. Manohar and H. Georgi:
Nucl. Phys. B234 (1984) 189
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Amand Faessler, Tuebingen 8
Chiral Quark Dynamics of Baryons
Danger of Double Counting
in Chiral Quark Model :
Pseudoscalar Mesons as Goldstone
Bosons and as Quark-Antiquark States
Investigated by A. Manohar and H. Georgi:
Nucl. Phys. B234 (1984) 189Goldstone Bosons are the low lying pseudoscalar Mesons.
The quark-antiquark states lie very high.
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Amand Faessler, Tuebingen 9
Chiral Quark Dynamics of Baryons
Effective Lagrangian up to fourth order:The quark functions q, the quark momenta,
the constituent quark masses, and the chiral fields are of order 1: O(1).
Pseudoscalar meson masses, Meson momenta, electroweak potentials are of first order small.
Current quark masses, electric and magnetic field tensors Fare of second order small.
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Amand Faessler, Tuebingen 10
Chiral Quark Dynamics of Baryons
With:
Do not read this formula! On quark level suggested in leading order by Manohar and Georgi Nucl. Phys. B 234 (1984)189. On hadron level formulated by Gasser, Leutwyler,
Holstein, Meissner, Weise, Hemmert, Scherer and others up to fourth order.
Leading order
Up to fourth order in small quantities.
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Amand Faessler, Tuebingen 11
Chiral Quark Dynamics of Baryons
10 Parameters: mu ;ms ;g ;c2 ; c4 ;c5 ;e7 ;e8 ;e10 ;d10
Compositeness condition:
g( meson-quark) coupling;
constituent quarks
have mass in chiral limit
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Amand Faessler, Tuebingen 12
Chiral Quark Dynamics of Baryons
Parameters and counterterms: c6 ,e7 ,e8
fitted to the magnetic moments:
Parameters: c2 , c4 ,e10 ,d10 fitted to electric and magnetic radii of protons and neutrons:
With:
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Amand Faessler, Tuebingen 13
Chiral Quark Dynamics of Baryons
Formfactor of a single constituent bare quark q = u, d in the Nucleon at high energies can not calculated by chiral perturbation theory.
Nucleon expectation value of the bare constituent quark current.
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Amand Faessler, Tuebingen 15
Chiral Quark Dynamics of BaryonsAlternative approach: We use a simple Gaussian Function for the bare quarks (I. V. Anikin et. al. Z. Phys. C65(1995) 681):
k1E and k2E = Euclidian relative Jacobi momenta
B = 800 MeV
k1E
k2E
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Amand Faessler, Tuebingen 16
Chiral Quark Dynamics of Baryons
We dress now the bare quark current by the pseudoscalar meson cloud of pions, kaons and etas.
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Amand Faessler, Tuebingen 17
Chiral Quark Dynamics of Baryons
More diagrams:
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Amand Faessler, Tuebingen 18
Chiral Quark Dynamics of Baryons
Diagrams with vector mesons:
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Amand Faessler, Tuebingen 19
Chiral Quark Dynamics of Baryons
Connection with Vector Dominance Model
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Amand Faessler, Tuebingen 20
Chiral Quark Dynamics of Baryons
-
-
18 such type of diagrams included: Correction smaller than about 15 %
Pseudoscalar meson in flight not yet included. Small.
Counter terms
Single quark
Nucleon
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Amand Faessler, Tuebingen 21
Chiral Quark Dynamics of Baryons
Dressed Baryon Current
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Amand Faessler, Tuebingen 22
Chiral Quark Dynamics of Baryons
Effect of the pseudoscalar meson cloud on magnetic moments,
On electric and magnetic formfactors of protons and neutrons ,
On the N-Delta M1 transition and the ratio E2/M1 and C2/M1 for N -> .
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Amand Faessler, Tuebingen 23
Magnetic Diagonal and Transition Moments of the Baryon Octet in units: [ nm] =
FitEdelman; Blanpied et al.
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Amand Faessler, Tuebingen 24
Nucleon-Delta Transition GeV Data: S. Eidelman et al.; S.
Stave et al.; G. Blanpied et al.
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Amand Faessler, Tuebingen 25
Ratios of Coulomb and Electric Quadrupole over Magnetic Dipole for: Delta -> Nucleon +
Data: S. Stave et al.; N. F. Sparveris et al.; T. Popischil et al. ; D. Elsner et al. Eur. Phys. J. 27(2006) 91.
Valence quarks
Total: valence+cloud
Valence quarks
Total: valence+cloud
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Amand Faessler, Tuebingen 26
Connection beween Dirac, Pauli F1/2 and Sachs GE/M Formfactors
With:
DIRAC
Pauli
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Amand Faessler, Tuebingen 27
Electron-Proton Scattering and Rosenbluth
Separation of Sachs Formfactors: GpE and Gp
M
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Amand Faessler, Tuebingen 28
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Amand Faessler, Tuebingen 29
Chiral Quark Dynamics of Baryons Ratio :
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Amand Faessler, Tuebingen 30
Qualitative Explanation for the Electric Formfactor of the Proton:
+
proton proton
proton
proton
=
proton
=neutron
neutron
pion+
pion+
Fourier –Transf. with spherical Bessel-fct.:
Radius r
~85 % ~15 %
Bessel
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Amand Faessler, Tuebingen 31
Electric Formfactor of the Neutron
Cloud
Valence quarks
total
pion-
neutron
neutron
proton
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Amand Faessler, Tuebingen 32
Chiral Quark Dynamics of BaryonsMagnetic Proton Formfactor.
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Amand Faessler, Tuebingen 33
Chiral Quark Dynamics of BaryonsMagnetic Formfactor of the Neutron over the Dipole Formfactor
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Amand Faessler, Tuebingen 35
Electric over Magnetic Proton Formfactor
Rosenbluth Separation
Polarised e-beam plus polarized recoil protons
Data: SLAC: Walker et al.Phys.Rev.D (1994); Jefferson Lab Hall A :Punjabi et al. Phys. Rev. C (2005) and Gayou et al.P.R.L.
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Amand Faessler, Tuebingen 36
Summary:- Chiral Dynamics on quark level up to fourth order- Parameters and Counter Terms fixed to Magnetic
Moments (p, n, ), Radii and High Energy Behavior of Formfactors for Protons and Neutrons.
- Calculated Meson cloud Effects on Magnetic Moments of Baryon Octet
- Calculated meson cloud effects on N-transition- Effects of Pseudoscalar Meson Cloud on Formfactors.
Chiral Quark Dynamics of Baryons
The END
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Amand Faessler, Tuebingen 37
PUBLICATIONS:
1. A. Faessler, Th. Gutsche, V. E. Lyubovitskij, K. Pumsa-ard: Prog. Part. Nucl. Phys. 55 ( 2005) 12.
2. A. Faessler, Th. Gutsche, V. E. Lyubovitskij, K. Pumsa-ard: Phys. Rev. D73 (2006)114021
3. A. Faessler, Th. Gutsche, B. R. Holstein, E. Lyubovitskij: Phys. Rev. D74 (2006) 074010