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Graduiertenkolleg Freiburg 24-02-2007 The nucleon as non-topological chiral soliton. Klaus Goeke. Applications of the Chiral Quark Soliton Model to current topical experiments and lattice data. Ruhr-Universität Bochum, Theoretische Physik II Hadronenphysik.
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Graduiertenkolleg Freiburg 24-02-2007 The nucleon as non-topological chiral soliton Klaus Goeke Applications of the Chiral Quark Soliton Model to current topical experiments and lattice data Ruhr-Universität Bochum, Theoretische Physik II Hadronenphysik Verbundforschung BMBF Transregio/SFB Bonn-Bochum-Giessen
Contents • Chiral Quark Soliton Model • Quantum Chromodynamics • Relativistic Mean Field Description • Parton distributions, transversity, magnetic moments (HERMES, COMPASS) • Strange magnetic form factors • Experiments A4 G0 SAMPLE HAPPEX • Lattice QCD and extrapolation to small mp • Form factors of energy momentum tensor • Distributions of (angular) momentum in nucleon • Distribution of pressure and shear in the nucleon • Summary and conclusions
Authors • Anatoli Efremov (Dubna) • Hyun-Chul Kim (Busan) • Andreas Metz (Bochum) • Jens Ossmann (Bochum) • Maxim Polyakov (Bochum) • Peter Schweitzer (Bochum) • Antonio Silva (Coimbra) • Diana Urbano (Coimbra/Porto) • Gil-Seok Yang (Bochum/Busan)
Quantum Chromo dynamics SU(3) Has problems with the chiral limit Constructed to work in the chiral limit Baryon –Octet –Decuplet -Antidecuplet Nucleon Chiral Quark Soliton Model
Lattice Techniques Aim: exact T infinite V infinite a zero Pion mass > 500 GeV Wilson Clover Staggered (Un)quenched Extraction of dimensional quantities Expensive Effective Models Approximate Certain physical region Pion mass = 140 MeV Identification of relevant degrees of freedom Inexpensive QCD
Multiplets: 8, 10, 10 No multipletts Symmetry spontaneousl broken Dynamic mass generation Pions as massless Goldstone bosons Chiral Symmetry of QCD Light Systems: QCD in chiral Limit, QCD-Quarkmasses zero ~ 0 Global QCD-Symmetries Lagrangean invariant under:
Simplest effective Lagrangean Invariant: flavour vector transformation Not invariant: flavour axial transformation Invariant: flavour vector transformation and axial transformation U(x) must transform properly U(x) exists Pseudo-scalar pion- Kaon-Goldstone field Chiral Quark Soliton Model (ChQSM):
Scattering of light quarks at randomly distributed Instantons (fluctuations of the gluon field with topological properties) Similar to scattering of electrons at impurities in a solid state • Instanton model of vacuum Random matrix theory • Effective momentum dependent quark mass ChQSM (Diakonov,Petrov)
Chiral Quark Soliton Practice Bound valence quarks Polarized Dirac Sea
Selfconsistent Soliton: Relativistic selfconsistent mean field
Fitted to data Fitted to data ChQSM: Parton distributios Selfconsistently fulfilled: QCD-sum rules, positivity, Soffer-bounds, forward limits of GPDs, etc.
Azimuthal asymmetries transversal target Quark unpol Distr. Meson unpol Fragm. quark ChQSM: Transversity distribution
Positive, close to Soffer bound ChQSM: Transversity Parton Distribution Function
HERMES SIDIS-data for proton Favoured: positiv
Transversity distribution: Facts Chiral Quark Soliton Model
Strange Formfactors
Magnetic moments of octet baryons SU(3) particle ChQSM experiment
Experiment: 1.26 Axial and strange axial form factors
Parity violating asymmetries Polarized eP-scattering, circularly polarized electrons, positive and negative helicities
HAPPEX Parity violating asymmetries of proton SAMPLE A4
Prediction (backward angles) prediction Parity violating asymmetries: G0 forward angles
The World data for GsM and GsE from A4, HAPPEX and SAMPLE 19) ChQSM 21) Lewis et al. 20) Lyubovitskij et al. 16) Park + Weigel 17) Hammer et al. 22) Leinweber et al. 18) Hammer + Musolf
The World data for GsM and GsE from A4, HAPPEX and SAMPLE + HAPPEX(2005) 19) ChQSM 21) Lewis et al. 20) Lyubovitskij et al. 16) Park + Weigel 17) Hammer et al. 22) Leinweber et al. 18) Hammer + Musolf preliminary
Data combined from parity-violating electron-scattering and neutrino- and anti-neutrino scattering (Pate et al.)
Data combined from parity-violating electron-scattering and neutrino- and anti-neutrino scattering (Pate et al.)
Data combined from parity-violating electron-scattering and neutrino- and anti-neutrino scattering (Pate et al.)
Strange Form factors • Experiments: SAMPLE HAPPEX A4 G0 • Parity violating e-scatt • n-scattering • ChQSM works well for all form factors • Only approach with ms>0 • Experiments with large error bars • Clear predictions for A4, G0 • Theory with large error bars
ChQSM and Lattice Gauge theory
Experiment - Theory Experiment QCD Chiral Perturb. Th. QCD Lattice Gauge Chiral Quark soliton model
One fit parameter Nucleon mass: mp-dependence
Spin-distribution, pressure, shear, surface tension, d-Term
Energy Momentum Tensor of QCD: New form factors Lorentz decomposition:
DVCS and Form factors of energy-momentum tensor of QCD Sum rule of Ji
At the physical point (mp=140 MeV) is the energy-density in the centre of the nucleon 13x the energy density of nuclear matter Energy density rE(r) in ChQSM
Pressure at r=0 is 10-100 times higher than in a neutron star Pressure and Shear Distribution inside the nucleon Integral =0
Shear distribution (surface tension) of the nucleon Liquid drop (softened) surface tension Nucleon