Chiral Symmetry and the partonic structure of the nucleon

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Chiral Symmetry and the partonic structure of
the nucleon
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Chiral Symmetry and the Partonic Structure of the
Nucleon
Klaus Goeke, Bochum

• QCD and Chiral Symmetry
• Chiral Quark Soliton Model
• Form Factors
• Parton Distributions
• Anti-Quark Distributions
• Transversity Distributions
• Generalized Parton Distributions
• Higher Twists
• New Particle Z
• Instanton Vacuum of QCD

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HERMES (DESY) COMPASS (CERN)CLAS
(JLAB)MAMI (Mainz), ELSA (Bonn)COSY (Jülich),
SPRING8 (Japan)
Experiments

• DIS Inclusive Deep Inelastic Scattering
• SIDIS Semi-inclusive DIS (Pion- and Kaon prod.)
• DVCS Deeply Virtual Compton Scattering
• HEMP Hard Exclusive Meson Production
• SPRING8 Real Photon scattering
• COSY Proton-Proton-Scattering
• MAMI, ELSA Low Energy Electron scattering

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Objective of the talk
Chiral Quark Soliton Model
Quantum Chromo Dynamics
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Collaborators

• Bochum
• Maxim Polyakov
• Pavel Pobylitsa
• Birgit Dressler
• Andreas Metz
• Regensburg
• Christian Weiss
• Nikolai Kivel
• St. Petersburg
• Dimiter Diakonov
• Victor Petrov
• Pusan
• Hyun-Chul Kim

• Mainz
• Marc Vanderhaeghen
• Pavia
• Peter Schweitzer
• Dubna
• Anatoli Efremov
• Penn. State
• Mark Strikman
• Tel Aviv
• Leonid Frankfurt
• Coimbra
• Diana Urbano
• Antonio Silva

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QCD and the Chiral Quark Soliton Model
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Objective of this section is

• To remind you of QCD and its chiral limit
• To remind you of global Symmetries of QCD
• To show you how a chiral effective Lagrangean can
  be formulated
• To introduce you to the Chiral Quark Soliton
  Model as the simplest possible effective model
• To sketch the solution of the ChQSM

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Quantum Chromo dynamics
Nucleon
Chiral Quark Soliton Model
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Quantum Chromo dynamics
Baryon Octet Decuplet -Antidecuplet
Nucleon
Chiral Quark Soliton Model
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Global Symmetries of QCD
Light quark systems QCD in Chiral limit, i.e.
Quarkmasses ? 0
Global Symmetries
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Effective Lagrangean of QCD
Light quark systems QCD in Chiral limit, i.e.
Quarkmassen ? 0
Global Symmetries
Requires all current quark masses to be equal in
order to be exactly fulfilled
Requires all current quark masses to be zero in
order to be exactly fulfilled
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Multiplet structure of QCD

• Vector SU(3)
• Octet
• Decuplet
• Antidecuplet

• Axial-Vector SU(3)
• No multiplets
• spontaneous breakdown of chiral symmetry
• dynamically generated quark mass m?M
• constituent mass M(350-400) MeV
• Massless Goldstone Bosons (pions)
• Chiral quark condensate

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Simplest effective Lagrangean
Does not work
Does work
Chiral Quark Soliton Model (ChQSM)
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QCD and Instantons
Derivation of ChQSM from QCD via Instantons by
Diakonov and Petrov
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QCD and Instantons
The M in the ChQSM is partially a constituent
mass and partially a coupling constant between
quark fields and a non-linear pion field
As coupling constant M should be momentum
dependent M(p)
Derivation from QCD by Diakonov Petrov Dilute
interacting Instanton Gas ? M(p)
The M(k) is the Fourier transform of the
zero-mode of a quark interacting with an
instanton.
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Non-local dynamical mass M
Non-locality of M in coordinate space is
equivalent to a k- dependence of M in momentum
space.
M(k) is the Fourier transform of the
eigenfunction of the zero mode of a quark
interacting with an instanton
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Chiral Quark Soliton Model - Basics

• Effective relativistic field theory for quarks.
• Has been derived from Instanton gas of QCD
• Minimally chiral invariant interaction of quarks
  with Goldstone bosons
• Incorporates spontaneous chiral symmetry breaking
• Incorporates Weinberg Lagrangean
• Incorporates Wess-Zumino-Term
• Yields low energy coefficients of effective
  chiral Lagrangean used e.g. in chiral
  perturbation theory
• Fulfills QCD sum rules, positivity bounds,
  Soffer-inequalities
• Fulfills QCD equations of motion for quarks and
  gluons

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Chiral Quark Soliton Model Formalism
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Variational procedure
Stationary phase approximation
Bound valence quarks
Polarized Dirac Sea
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Variation Selfconsistent mean field
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Selfconsistent Mean Field Hartree-Fock
Analogous to the mean field of an atom
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Nucleon observables
Example Elastic electromagnetic form factor
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ChQSM - numerics
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ChQSM - parameters
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Summary ChQSM

• Chiral Quark Soliton Model Simplest
  quark-Goldstone interaction
• Derived from QCD Instanton Liquid
• SU(2) 3 parameters, once and forever adjusted
• to pion-dacay constant, pion mass, nucleon radius
• Variational approach, large Nc-limit 1/Nc-corr.
• Consistency checks and sum rules fulfilled

• Properties of nucleon (and octet decuplet
  antidecuplet)
• Mass splittings
• Electric and magnetic and axial and strange form
  factors
• Quark distributions, unpolarized, helicity,
  transversity
• Anti-Quark distributions, flavour asymmetry
• Generalized parton distributions
• Higher Twist Effects

• FF and transition FF at MAMI, ELSA, JLAB
• DIS and SIDIS at HERMES, COMPASS
• DVCS at HERMES, JLAB
• Hard exclusive meson prod. at HERMES, JLAB
• Single spin and azimuthal asymmetries at HERMES,
  COMPASS
• Double spin asymmetries, RHIC
• Antidecuplet Z COSY, SPRING8, JLAB

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Though this be madness,yet there is method in it.
Thank you !