chiral quark dynamics of baryons

Amand Faessler, Tuebingen 1

Chiral Quark Dynamics of Baryons

Gutsche, Holstein, Lyubovitskij, + PhD students (Nicmorus,

Kuckei, Cheedket, Pumsa-ard, Khosonthongkee, Giacosa)

Amand Faessler, Tuebingen

Amand Faessler, Tuebingen 2

Chiral Quark Dynamics of Baryons

Quantum Chromodynamics:

with:

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:

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)

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

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)

Amand Faessler, Tuebingen 7

Chiral Quark Dynamics of Baryons

Perturbative Chiral Quark Model A. Manohar and H. Georgi:

Nucl. Phys. B234 (1984) 189

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.

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.

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.

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

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:

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.

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

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.

Amand Faessler, Tuebingen 17

Chiral Quark Dynamics of Baryons

More diagrams:

Amand Faessler, Tuebingen 18

Chiral Quark Dynamics of Baryons

Diagrams with vector mesons:

Amand Faessler, Tuebingen 19

Chiral Quark Dynamics of Baryons

Connection with Vector Dominance Model

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

Amand Faessler, Tuebingen 21

Chiral Quark Dynamics of Baryons

Dressed Baryon Current

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 -> .

Amand Faessler, Tuebingen 23

Magnetic Diagonal and Transition Moments of the Baryon Octet in units: [ nm] =

FitEdelman; Blanpied et al.

Amand Faessler, Tuebingen 24

Nucleon-Delta Transition GeV Data: S. Eidelman et al.; S.

Stave et al.; G. Blanpied et al.

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

Amand Faessler, Tuebingen 26

Connection beween Dirac, Pauli F1/2 and Sachs GE/M Formfactors

With:

DIRAC

Pauli

Amand Faessler, Tuebingen 27

Electron-Proton Scattering and Rosenbluth

Separation of Sachs Formfactors: GpE and Gp

M

Amand Faessler, Tuebingen 28

Amand Faessler, Tuebingen 29

Chiral Quark Dynamics of Baryons Ratio :

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

Amand Faessler, Tuebingen 31

Electric Formfactor of the Neutron

Cloud

Valence quarks

total

pion-

neutron

neutron

proton

Amand Faessler, Tuebingen 32

Chiral Quark Dynamics of BaryonsMagnetic Proton Formfactor.

Amand Faessler, Tuebingen 33

Chiral Quark Dynamics of BaryonsMagnetic Formfactor of the Neutron over the Dipole Formfactor

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.

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

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