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Parity violating asymmetries: Milos (Greece) May 2006 Solitonic approach to strange Form Factors Klaus Goeke Bochum University Transregio/SFB Bonn, Bochum, Giessen Verbundforschung BMFT Hadronen und Kerne COSY-Project Jülich Applications of the Chiral Quark Soliton Model to SAMPLE, HAPPEX, G0 and A4

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Contents Chiral Quark Soliton Model Chiral Quark Soliton Model Quantum Chromodynamics Quantum Chromodynamics Relativistic Mean Field Description Relativistic Mean Field Description Strange magnetic form factors Strange magnetic form factors Experiments A4 G0 SAMPLE HAPPEX Experiments A4 G0 SAMPLE HAPPEX Asymmetries Asymmetries Global data Global data Form factors, Parton distributions etc. Form factors, Parton distributions etc. Chiral Symmetry breaking, Instantons Chiral Symmetry breaking, Instantons

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Silva et al. Hyun-Chul Kim (Busan) Hyun-Chul Kim (Busan) Antonio Silva (Coimbra) Antonio Silva (Coimbra) Diana Urbano (Porto) Diana Urbano (Porto) K. G. (Bochum) K. G. (Bochum)

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Parity violating electron scattering

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SAMPLE HAPPEX A4 A good theory must be able to describe several form factors simultaneously and generalized form factors (i.e. generalized parton distributions) and parton distributions and anti-parton distributions

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QCD Lattice Techniques Lattice Techniques Aim: exact Aim: exact T infinite T infinite V infinite V infinite a zero a zero Pion mass 140 GeV Pion mass 140 GeV Wilson Clover Staggered Wilson Clover Staggered (Un)quenched (Un)quenched Extraction of dimensional quantities Extraction of dimensional quantities Effective Models Effective Models Certain physical region Certain physical region Aim: Relevant degrees of freedom Aim: Relevant degrees of freedom approximate approximate

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ChQSM: Effective rel. QFT Stationary state of this lagrangean calculated by relativistic mean field techniques Projection on angular momentum quantum numbers by semiclassical methods

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Strange weak and magnetic form factor SAMPLE (JLAB)

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HAPPEX

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Parity violating asymmetries Polarized eP-scattering, circularly polarized electrons, positive and negative helicities

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Proton electroweak neutral axial vector form factors

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Parity violating asymmetries of proton SAMPLE HAPPEX A4

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Parity violating asymmetries: G0 forward angles Prediction (backward angles)

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Parity violating e-scatt.

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Effect of strante quarks Difference between the parity violating asymmetries including strange quark effects (A-phys) and the asymmetry assuming strange form factors to vanish (A-0). The lines represent the ChQSM

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The World data for GsM and GsE from A4, HAPPEX and SAMPLE and ChQSM

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Hydrogen and deuterium data for GsM and GeA(T=1) from HaPPEX at Q2=0.1GeV2ext Data plot from Beise, Pitt and Spayde

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Magnetic moments of octet baryons SU(3) p(1.759)2.4002.793 n(-1.210)-1.651-1.913 Lambda(-0.478)-0652-0.613 Sigma-(-0.702)-0.958-1.16 Sigma-0(+0.495)0.675- Sigma+(+1.692)2.3092.458 Xi-(-0.444)-0.606-0.651 Xi-0(-1.030)-1.450-1.250 particleChQSMexperiment(ChQSM)

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Magnetic transition moments

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Chiral quark soliton model Fitted to data Selfconsistently fulfilled: QCD-sum rules, positivity, Soffer-bounds, forward limits of GPDs, etc.

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d-bar minus u- bar Antiquark distributions: unpolarized flavourasymmetr y Chiral Quark Soliton Model E866: Drell-Yan:

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Bochum prediction Antiquark isovector polarized

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HERMES: DVCS - SSA Our Prediction including Tw-3

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HERMES: DVCS – CA With D-Term and tw-3 Prediction Without D-Term Prediction Charge asymmetry vs.

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ChQSM: Strange unpol. quark distribution Wakamatsu

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ChQSM: Strange polarized quark distribution

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Wakamatsu ChQSM: SU(3) SU2 ChQS SU3 ChQS Exp G-A-31.411.201.257 G-A-8-0.590.579 G-A-00.350.360.31(7) Delta-u0.880.820.82(3) Delta-d-0.53-0.38-0.44(3) Delta-s0-0.08-0.11(3) F-0.450.459(8) D-0.760.798(8) F/D-0.590.575(16)

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Nucleon mass: m p -dependence

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Scattering of light quarks at randomly distributed Instantons (fluctuations of the gluon field with topological properties) Instanton model of vacuum Effective momentum dependent quark mass ChQSM (Diakonov,Petrov)

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Chiral Symmetry of QCD Light Systems: QCD in chiral Limit, QCD-Quarkmasss zero ~ 0 Globa QCD-Symmetries Lagrangean invariant under: Multiplets: 8, 10, 10 No multipletts Symmetry spontaneousl broken Dynamic mass generation Pions as massless Goldstone bosons

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Simplest effective Lagrangean Chiral Quark Soliton Model (ChQSM): Pseudo-scalar pion- Kaon-Goldstone field Invariant: flavour vector transformation Not invariant: flavour axial transformation Invariant: flavour vector transformation and axial transformation U(x) must transform properly U(x) exists

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Chiral Quark Soliton Practice Selfconsistent Soliton:

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Chiral Quark Soliton Practice Bound valence quarks Polarized Dirac Sea

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Summary Chiral Quark Soliton Model Chiral Quark Soliton Model Simplest Quark model with spont.chir.symm.breaking Simplest Quark model with spont.chir.symm.breaking Relativistic Mean Field Description Relativistic Mean Field Description Collective Quantization Collective Quantization Strange magnetic form factors Strange magnetic form factors Experiments A4 G0 SAMPLE HAPPEX-II Experiments A4 G0 SAMPLE HAPPEX-II Asymmetries Asymmetries Octet- and Decuplet- form factors Octet- and Decuplet- form factors Parton distributions, GPDs Parton distributions, GPDs

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JLAB-animation

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Parity violating electron scattering

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Strange Form factors ChQSM works well ChQSM works well Only approach with m s >0 Only approach with m s >0 Experiments with large error bars Experiments with large error bars Clear predictions for A4, G0 Clear predictions for A4, G0 Theory with large error bars Theory with large error bars

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Strange Form Factors F 1 and F 2

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HAPPEX

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A4-Experiment Mainz: Q2=0.108 GeV 2 cQSM

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Hydrogen and deuterium data for GsM and GeA(T=1) from HaPPEX at Q2=0.1GeV2ext Data plot from Beise, Pitt and Spayde

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Text

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World data vs. cQSM

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Quantumnumbers Quantum-No. coherent:1p-1h,2p-2h,.... In natural way small quark and anti-quark admixtures Coupling of spins and iso- spins of 3 quarks Mean Field non-linear System Soliton Rotation of Soliton in space and iso-space Projektion In natural way exotic baryonic states 3-quark models quark soliton model

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formalism

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Magn. moments scaled with the mass of the nucleon Magnetic moments, electric radii, axial coupling constant

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Predictions: G0-Experiment

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Magnetic moments of octet baryons SU(3) p(1.759)2.4002.793 n(-1.210)-1.651-1.913 Lambda(-0.478)-0652-0.613 Sigma-(-0.702)-0.958-1.16 Sigma-0(+0.495)0.675- Sigma+(+1.692)2.3092.458 Xi-(-0.444)-0.606-0.651 Xi-0(-1.030)-1.450-1.250 particleChQSMexperiment(ChQSM)

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Electric and magnetic radii of octet baryons SU(3) (fm 2 ) Baryon R 2 -E Exp R 2 -M Exp P0.7280.729(24)0.6490.699(18) N-0.097-0.113(7)0.6770.776(20) Lambda0.039-0.457- Sigma-0.662 0.6 0.9 0.718- Sigma-00.075-0.550- Sigma+0.811-0.619- Xi-0.546-0.318- Xi-00.102-0.535- ChQSM

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Parity violating electron scattering SAMPLE HAPPEX A4 A good theory must be able to describe several form factors simultaneously and generalized form factors (i.e. generalized parton distributions) and parton distributions and anti-parton distributions

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Quantum Chromo dynamics Has problems with small quark masses Constructed to work in the region of small quark masses Chiral Quark Soliton Model Nucleon Baryon – Octet – Decuplet - Antidecuplet SU(3)

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QCD: Spontaneous breakdown of chiral symm. Chiral Quark Soliton Model (ChQSM): Pseudo-scalar pion field Invariant: flavour vector transformation Not invariant: flavour axial transformation Invariant: flavour vector transformation and axial transformation U(x) must transform properly U(x) exists Simplest effective Lagrangean for quarks: Mean field Baryon in Large N c -Limit of QCD Mean Field

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QCD in Large N c - Limit

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Fock-State: Valence and Polarized Dirac Sea NOT up up down

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Form Factors Adopt the Sachs FF: G Z E /M provide an important new benchmark for testing non-perturbative QCD structure of the nucleon

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Magnetic moments of octet baryons SU(3) p2.4002.793 n-1.651-1.913 Lambda-0652-0.613 Sigma--0.958-1.16 Sigma-00.675- Sigma+2.3092.458 Xi--0.606-0.651 Xi-0-1.450-1.250 particleChQSMexperiment

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