Chiral Quark Soliton Model: Applications in Experiments and Lattice Data

1. 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

2. 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

3. 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)

4. 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

5. 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

6. 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:

7. 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):

8. 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)

9. ChQSM - parameters

10. Chiral Quark Soliton  Practice Bound valence quarks Polarized Dirac Sea

11. Selfconsistent Soliton: Relativistic selfconsistent mean field

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

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

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

15. HERMES SIDIS-data for proton Favoured: positiv

16. COMPASS SIDIS-data for deuteron

17. BELLE

18. Transversity distribution: Facts Chiral Quark Soliton Model

19. Strange Formfactors

20. Parity violating electron scattering

21. Magnetic moments of octet baryons SU(3) particle ChQSM experiment

22. Strange Form Factors F1 and F2

23. Strange weak, electric, magnetic form factors

24. Experiment: 1.26 Axial and strange axial form factors

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

26. HAPPEX Parity violating asymmetries of proton SAMPLE A4

27. Prediction (backward angles) prediction Parity violating asymmetries: G0 forward angles

28. A4, G0: Parity violating e-scatt.

29. 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

30. 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

31. Data combined from parity-violating electron-scattering and neutrino- and anti-neutrino scattering (Pate et al.)

32. Data combined from parity-violating electron-scattering and neutrino- and anti-neutrino scattering (Pate et al.)

33. Data combined from parity-violating electron-scattering and neutrino- and anti-neutrino scattering (Pate et al.)

34. 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

35. ChQSM and Lattice Gauge theory

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

37. One fit parameter Nucleon mass: mp-dependence

38. Quenched vs. Unquenched

39. MILC LQCD-data

40. Extrapolation to small mp by ChPT and ChQSM

41. Extrapolation to small mp by ChPT and ChQSM

42. Spin-distribution, pressure, shear, surface tension, d-Term

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

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

45. Energy momentum tensor: Properties

46. 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

47. Angular momentum density rJ(r) of quarks (spin + orbital)

48. Pressure at r=0 is 10-100 times higher than in a neutron star Pressure and Shear Distribution inside the nucleon Integral =0

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

50. Form factors of the energy momentum tensor