Graduiertenkolleg Freiburg The nucleon as non- topological chiral soliton Klaus Goeke Ruhr-Universität Bochum, Theoretische Physik II Hadronenphysik Applications of the Chiral Quark Soliton Model to current topical experiments and lattice data Verbundforschung BMBF Transregio/SFB Bonn-Bochum-Giessen

Contents Chiral Quark Soliton Model Chiral Quark Soliton Model Quantum Chromodynamics Quantum Chromodynamics Relativistic Mean Field Description Relativistic Mean Field Description Parton distributions, transversity, magnetic moments (HERMES, COMPASS) Parton distributions, transversity, magnetic moments (HERMES, COMPASS) Strange magnetic form factors Strange magnetic form factors Experiments A4 G0 SAMPLE HAPPEX Experiments A4 G0 SAMPLE HAPPEX Lattice QCD and extrapolation to small m p Lattice QCD and extrapolation to small m p Form factors of energy momentum tensor Form factors of energy momentum tensor Distributions of (angular) momentum in nucleon Distributions of (angular) momentum in nucleon Distribution of pressure and shear in the nucleon Distribution of pressure and shear in the nucleon Summary and conclusions Summary and conclusions

Authors Anatoli Efremov (Dubna) Anatoli Efremov (Dubna) Hyun-Chul Kim (Busan) Hyun-Chul Kim (Busan) Andreas Metz (Bochum) Andreas Metz (Bochum) Jens Ossmann (Bochum) Jens Ossmann (Bochum) Maxim Polyakov (Bochum) Maxim Polyakov (Bochum) Peter Schweitzer (Bochum) Peter Schweitzer (Bochum) Antonio Silva (Coimbra) Antonio Silva (Coimbra) Diana Urbano (Coimbra/Porto) Diana Urbano (Coimbra/Porto) Gil-Seok Yang (Bochum/Busan) Gil-Seok Yang (Bochum/Busan)

Quantum Chromo dynamics Has problems with the chiral limit Constructed to work in the chiral limit Chiral Quark Soliton Model Nucleon Baryon – Octet – Decuplet - Antidecuplet SU(3)

QCD Lattice Techniques Lattice Techniques Aim: exact Aim: exact T  infinite T  infinite V  infinite V  infinite a  zero a  zero Pion mass > 500 GeV Pion mass > 500 GeV Wilson Clover Staggered Wilson Clover Staggered (Un)quenched (Un)quenched Extraction of dimensional quantities Extraction of dimensional quantities Expensive Expensive Effective Models Effective Models Approximate Approximate Certain physical region Certain physical region Pion mass = 140 MeV Pion mass = 140 MeV Identification of relevant degrees of freedom Identification of relevant degrees of freedom Inexpensive Inexpensive

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

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

Scattering of light quarks at randomly distributed Instantons (fluctuations of the gluon field with topological properties)  Instanton model of vacuum  Random matrix theory   Effective momentum dependent quark mass  ChQSM (Diakonov,Petrov) Similar to scattering of electrons at impurities in a solid state

ChQSM - parameters

Chiral Quark Soliton  Practice Bound valence quarks Polarized Dirac Sea

Relativistic selfconsistent mean field Selfconsistent Soliton:

ChQSM: Parton distributios Fitted to data Selfconsistently fulfilled: QCD-sum rules, positivity, Soffer-bounds, forward limits of GPDs, etc.

Azimuthal asymmetries transversal target Quark unpol quark Meson unpol Distr. Fragm. ChQSM: Transversity distribution

ChQSM: Transversity Parton Distribution Function Positive, close to Soffer bound

HERMES SIDIS-data for proton Favoured: positiv

COMPASS SIDIS-data for deuteron

BELLE

Transversity distribution: Facts Chiral Quark Soliton Model

Parity violating electron scattering

Magnetic moments of octet baryons SU(3) p n Lambda Sigma Sigma Sigma Xi Xi particleChQSMexperiment

Strange Form Factors F 1 and F 2

Strange weak, electric, magnetic form factors

Axial and strange axial form factors Experiment: 1.26

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

Parity violating asymmetries of proton SAMPLE HAPPEX A4

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

A4, G0: Parity violating e-scatt.

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.)

Strange Form factors Experiments: SAMPLE HAPPEX A4 G0 Experiments: SAMPLE HAPPEX A4 G0 Parity violating e-scatt Parity violating e-scatt n-scattering n-scattering ChQSM works well for all form factors ChQSM works well for all form factors 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

Experiment - Theory Experiment QCD Lattice Gauge QCD Chiral Perturb. Th. Chiral Quark soliton model

Nucleon mass: m p -dependence One fit parameter

Quenched vs. Unquenched

MILC LQCD-data

Extrapolation to small m p by ChPT and ChQSM

Energy Momentum Tensor of QCD: New form factors Lorentz decomposition:

DVCS and Form factors of energy- momentum tensor of QCD Sum rule of Ji

Energy momentum tensor: Properties

Energy density r E (r) in ChQSM At the physical point (m p =140 MeV) is the energy-density in the centre of the nucleon 13x the energy density of nuclear matter

Angular momentum density r J (r) of quarks (spin + orbital)

Pressure and Shear Distribution inside the nucleon Pressure at r=0 is times higher than in a neutron star Integral =0

Shear distribution (surface tension) of the nucleon Nucleon Liquid drop (softened) surface tension

Form factors of the energy momentum tensor

ChQSM vs. Lattice-QCD for M 2 Q (t) and extrapolation to small m p

Message of ChQSM: Linear extrapolation of Lattice-QCD data M 2 Q (t) and J Q (t) for M 2 Q (t) and J Q (t) works well

ChQSM vs. Lattice-QCD for d 1 Q (t) and extrapolation to small m p

Message of ChQSM: Linear extrapolation of Lattice-QCD data d 1 Q (t) does NOT for d 1 Q (t) does NOT work well

Summary and Conclusions Chiral Quark Soliton Model Chiral Quark Soliton Model Simplest quark model with proper global symmetries Simplest quark model with proper global symmetries Relativistic mean field approach Relativistic mean field approach Spontaneous chiral symmetry breaking Spontaneous chiral symmetry breaking Valence quarks and polarized Dirac sea Valence quarks and polarized Dirac sea Parton distributions: Transversity (HERMES, COMPASS, BELLE), Sivers-Function, Collins-Fragmentation-Function Parton distributions: Transversity (HERMES, COMPASS, BELLE), Sivers-Function, Collins-Fragmentation-Function Strange form factors Strange form factors Magnetic, electric, axial, etc., asymmetries Magnetic, electric, axial, etc., asymmetries Experiments A4 G0 SAMPLE HAPPEX Experiments A4 G0 SAMPLE HAPPEX Lattice QCD and extrapolation to small m p Lattice QCD and extrapolation to small m p Agreement with LQCD at large m p Agreement with LQCD at large m p Useful guideline for extrapolation to physical m p Useful guideline for extrapolation to physical m p Form factors of energy momentum tensor Form factors of energy momentum tensor Distributions of (angular) momentum in nucleon Distributions of (angular) momentum in nucleon Distribution of pressure and shear in the nucleon Distribution of pressure and shear in the nucleon