Parity violating asymmetries: Milos (Greece) May 2006 Parity violating asymmetries: Milos (Greece) May 2006

Solitonic approach to Solitonic approach to strange Form Factors strange Form Factors

Klaus Goeke Klaus Goeke Bochum University

Transregio/SFB Bonn, Bochum, Giessen

Verbundforschung BMFT Hadronen und Kerne

COSY-Project Jülich

Applications of the Chiral Quark Soliton Modelto SAMPLE, HAPPEX , G0 and A4

ContentsContents Chiral Quark Soliton ModelChiral Quark Soliton Model

Quantum ChromodynamicsQuantum Chromodynamics Relativistic Mean Field DescriptionRelativistic Mean Field Description

Strange magnetic form factorsStrange magnetic form factors Experiments A4 G0 SAMPLE HAPPEXExperiments A4 G0 SAMPLE HAPPEX AsymmetriesAsymmetries Global dataGlobal data

Form factors, Parton distributions etc.Form factors, Parton distributions etc. Chiral Symmetry breaking, InstantonsChiral Symmetry breaking, Instantons

Silva et al.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)

Parity violating electron Parity violating electron scatteringscattering

0( )Z q

Parity violating electron Parity violating electron scatteringscattering

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

QCDQCD

Lattice TechniquesLattice Techniques Aim: exactAim: exact T T infinite infinite V V infinite infinite a a zero zero Pion mass Pion mass 140 GeV 140 GeV Wilson Clover Wilson Clover

StaggeredStaggered (Un)quenched(Un)quenched Extraction of Extraction of

dimensional quantitiesdimensional quantities

Effective ModelsEffective Models Certain physical Certain physical

regionregion Aim: Relevant degrees Aim: Relevant degrees

of freedomof freedom approximateapproximate

ChQSM: Effective rel. QFTChQSM: Effective rel. QFT

0 5( ) ( ) exp( ( ) )A Aeff

iL i m MU U x x

f

0

2

Regularization: Proper Time, Pauli-Villars regularization

SU(2): Lagrangean: , ,

SU(2): Physics: 93 , 139 ,

(3) : In addition 180 and Witten's embedding (2) (3)

a

cutoff

c proton

s

m M

f MeV m MeV r

SU m MeV SU SU

nd perturbative treatment in collective quantization

0

Numbers:

420 , 15 , 600cutoffM MeV m MeV MeV

3(250 )MeV

Stationary state of this lagrangean calculated by relativistic mean field techniquesProjection on angular momentum quantum numbers by semiclassical methods

Strange weak and magnetic Strange weak and magnetic form factorform factor

SAMPLE (JLAB)

2(1 4sin )Z p n sM W M M MG G G G

HAPPEX HAPPEX

2 20.477

12.3

Q GeV

QSM QSM

Parity violating asymmetriesParity violating asymmetries

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

PVA

Proton electroweak neutral axial Proton electroweak neutral axial vector form factorsvector form factors

1 (3) 0

1 0

1(1 )

2

0.41 0.24 0.06 0.14 (Zhu et al.)

e p NC sA A A A A A A

A A

G G G R G R G

R R

Parity violating Parity violating asymmetries of asymmetries of

proton proton

SAMPLE

HAPPEX

A4

Parity violating Parity violating asymmetries: G0 forward asymmetries: G0 forward

anglesangles

Prediction (backward

angles)

Parity violating e-scatt.Parity violating e-scatt.

Effect of strante quarksEffect 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

The World data for GsM and GsE from The World data for GsM and GsE from A4, HAPPEX and SAMPLE and ChQSMA4, HAPPEX and SAMPLE and ChQSM

Hydrogen and deuterium data for Hydrogen and deuterium data for GsM and GeA(T=1) from HaPPEX GsM and GeA(T=1) from HaPPEX

at Q2=0.1GeV2extat Q2=0.1GeV2ext

Data plot from Beise, Pitt and Spayde

Magnetic moments of octet baryons Magnetic moments of octet baryons SU(3) SU(3)

pp (1.759)(1.759) 2.4002.400 2.7932.793

nn (-(-1.210)1.210)

-1.651-1.651 -1.913-1.913

LambdLambdaa

(-(-0.478)0.478)

-0652-0652 -0.613-0.613

Sigma-Sigma- (-(-0.702)0.702)

-0.958-0.958 -1.16-1.16

Sigma-Sigma-00

(+0.49(+0.495)5)

0.6750.675 --

SigmaSigma++

(+1.69(+1.692)2)

2.3092.309 2.4582.458

Xi-Xi- (-(-0.444)0.444)

-0.606-0.606 -0.651-0.651

Xi-0Xi-0 (-(-1.030)1.030)

-1.450-1.450 -1.250-1.250

particle ChQSM experiment(ChQSM)

Magnetic transition Magnetic transition momentsmoments

0

( ) 5.33 . .

( ) 2.70 . .

( ) 0.14 . .

n m

n m

n m

Chiral quark soliton modelChiral quark soliton model

Fitted to data Fitted to data

Selfconsistently fulfilled: QCD-sum rules, positivity, Soffer-bounds, forward limits of GPDs, etc.

d-bar d-bar minus u-minus u-

barbar

Antiquark Antiquark distributions: distributions: unpolarized unpolarized

flavourasymmflavourasymmetryetry

Chiral Quark

Soliton Model

E866: Drell-Yan:

( ) ( )d x u x

Bochum prediction

Antiquark Antiquark isovector isovector polarized polarized

HERMES: DVCS - SSAHERMES: DVCS - SSA

Our Prediction including Tw-3

Single-Spin-Asymmetrie plotted vs.

Single Spin Asymmetry ( , , ) etc.H t

HERMES: DVCS – CA HERMES: DVCS – CA

With D-Term and tw-3 Prediction

Without D-Term Prediction

Charge asymmetry vs.

ChQSM: Strange unpol. quark distribution

Wakamatsu

Wakamatsu

ChQSM: Strange polarized quark distribution

( ( ) ( ))x s x s x

Wakamatsu

ChQSM: SU(3)

SU2 ChQSSU2 ChQS SU3 ChQSSU3 ChQS ExpExp

G-A-3G-A-3 1.411.41 1.201.20 1.2571.257

G-A-8G-A-8 -- 0.590.59 0.5790.579

G-A-0G-A-0 0.350.35 0.360.36 0.31(7)0.31(7)

Delta-uDelta-u 0.880.88 0.820.82 0.82(3)0.82(3)

Delta-dDelta-d -0.53-0.53 -0.38-0.38 -0.44(3)-0.44(3)

Delta-sDelta-s 00 -0.08-0.08 -0.11(3)-0.11(3)

FF -- 0.450.45 0.459(8)0.459(8)

DD -- 0.760.76 0.798(8)0.798(8)

F/DF/D -- 0.590.59 0.575(16)0.575(16)

Nucleon mass: mNucleon mass: m--dependencedependence

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)

Chiral Symmetry of QCDChiral Symmetry of QCD

(2) : ' expu uA AV

d d

SU i

Light Systems: QCD in chiral Limit, QCD-Quarkmasss zero ~ 0

QCD 2

1( )

4a aL F F i A

g

5(2) : ' expu uA AA

d d

SU i

Globa QCD-Symmetries Lagrangean invariant under:

Multiplets: 8, 10, 10

No multipletts Symmetry

spontaneousl broken

Dynamic mass generation Pions as massless Goldstone bosons

Simplest effective LagrangeanSimplest effective Lagrangean

( )effL i MU

( )effL i M

5( ) ( ) exp( ( ) )A Aeff

iL i MU U x x

f

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

† 4

Partition function :

exp ( )QSMZ DU D D d xL x

Chiral Quark Soliton Chiral Quark Soliton Practice Practice

5( ) exp( ( ) )A AiU x x

f ( )effL i MU

5( ) ~

i i i

A Ai i

i occ

i MU

x

5( ) exp( ( ) )A AiU x x

f

Selfconsistent Soliton:

Partition Function:

exp totaleffZ D S

Stationary phase approx ( ) : 0

Iterative procedure, yields selfconsistent solution ( )

totaleff

c c

c

SN

x

Chiral Quark Soliton Chiral Quark Soliton Practice Practice

5( ) exp( ( ) )A AiU x x

f ( )effL i MU

Partition Function:

exp totaleffZ D S

Stationary phase approx ( ) : 0

Iterative procedure, yields selfconsistent solution ( )

totaleff

c c

c

SN

x

Bound valence quarks

Polarized Dirac Sea

SummarySummary Chiral Quark Soliton ModelChiral Quark Soliton Model

Simplest Quark model with Simplest Quark model with spont.chir.symm.breakingspont.chir.symm.breaking

Relativistic Mean Field DescriptionRelativistic Mean Field Description Collective QuantizationCollective Quantization

Strange magnetic form factorsStrange magnetic form factors Experiments A4 G0 SAMPLE HAPPEX-II Experiments A4 G0 SAMPLE HAPPEX-II AsymmetriesAsymmetries

Octet- and Decuplet- form factorsOctet- and Decuplet- form factors Parton distributions, GPDsParton distributions, GPDs

JLAB-animationJLAB-animation

Parity violating electron Parity violating electron scatteringscattering

Strange Form factorsStrange Form factors

ChQSM works wellChQSM works well Only approach with Only approach with ss>0>0 Experiments with large error barsExperiments with large error bars Clear predictions for A4, G0Clear predictions for A4, G0 Theory with large error barsTheory with large error bars

Strange Form Factors FStrange Form Factors F11 and F and F22

HAPPEXHAPPEX

2 20.477

12.3

Q GeV

A4-Experiment Mainz: A4-Experiment Mainz: Q2=0.108 GeVQ2=0.108 GeV22

QSM

Hydrogen and deuterium data for Hydrogen and deuterium data for GsM and GeA(T=1) from HaPPEX GsM and GeA(T=1) from HaPPEX

at Q2=0.1GeV2extat Q2=0.1GeV2ext

Data plot from Beise, Pitt and Spayde

TextText

World data vs. World data vs. QSMQSM

QuantumnumbQuantumnumb

ersers Quantum-No.

Quantum-No.

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

formalismformalism

Magn. moments scaled with the mass of the nucleon

Magnetic moments, electric Magnetic moments, electric radii, axial coupling constantradii, axial coupling constant

Predictions: G0-ExperimentPredictions: G0-Experiment

Magnetic moments of octet baryons Magnetic moments of octet baryons SU(3) SU(3)

pp (1.759)(1.759) 2.4002.400 2.7932.793

nn (-(-1.210)1.210)

-1.651-1.651 -1.913-1.913

LambdLambdaa

(-(-0.478)0.478)

-0652-0652 -0.613-0.613

Sigma-Sigma- (-(-0.702)0.702)

-0.958-0.958 -1.16-1.16

Sigma-Sigma-00

(+0.49(+0.495)5)

0.6750.675 --

SigmaSigma++

(+1.69(+1.692)2)

2.3092.309 2.4582.458

Xi-Xi- (-(-0.444)0.444)

-0.606-0.606 -0.651-0.651

Xi-0Xi-0 (-(-1.030)1.030)

-1.450-1.450 -1.250-1.250

particle ChQSM experiment(ChQSM)

Electric and magnetic radii of octet Electric and magnetic radii of octet baryons SU(3) (fmbaryons SU(3) (fm22))

BaryonBaryon RR22-E-E ExpExp RR22-M-M ExpExp

PP 0.7280.728 0.729(240.729(24))

0.6490.649 0.699(180.699(18))

NN -0.097-0.097 --0.113(7)0.113(7)

0.6770.677 0.776(200.776(20))

LambdaLambda 0.0390.039 -- 0.4570.457 --

Sigma-Sigma- 0.6620.662 0.6 0.90.6 0.9 0.7180.718 --

Sigma-0Sigma-0 0.0750.075 -- 0.5500.550 --

Sigma+Sigma+ 0.8110.811 -- 0.6190.619 --

Xi-Xi- 0.5460.546 -- 0.3180.318 --

Xi-0Xi-0 0.1020.102 -- 0.5350.535 --ChQSM ChQSM

Parity violating electron Parity violating electron scatteringscattering

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

Quantum Quantum Chromo Chromo

dynamicsdynamics

Has problems with small quark masses

Constructed to work in the region of small quark masses

Chiral Quark Soliton ModelNucleon

Baryon –Octet –

Decuplet -Antidecuplet

SU(3)

QCD: Spontaneous breakdown of QCD: Spontaneous breakdown of chiral symm.chiral symm.

( )effL i MU

( )effL i M

5( ) ( ) exp( ( ) )A Aeff

iL i MU U x x

f

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:Massless QCD: Invariant under

* flavour vector transformation

* flavour axial transformation

Mean field

Baryon in Large Nc-Limit of QCD Mean Field

0

3c

axial charges:

0.27 1~

1.26 NA

A

g

g

QCD in QCD in Large NLarge Ncc--

LimitLimit

Fock-State: Valence and Fock-State: Valence and Polarized Dirac SeaPolarized Dirac Sea

i i ii MU 5( ) ( ) exp( ( ) )A A

eff

iL i MU U x x

f

NOT up up down

Form FactorsForm Factors

NFM

qiFNNuuNJ

Nqq

qq

EM

21 2

Q

2121 FFGFFG ME Adopt the Sachs FF:

sME

dME

uMEME GGGG //// 3

1

3

1

3

2

sMEW

dMEW

uMEW

ZME GGGG /

2/

2/

2/ sin

3

41sin

3

41sin

3

81

GZE/M provide an important new benchmark for testing

non-perturbative QCD structure of the nucleon

Magnetic moments of octet baryons Magnetic moments of octet baryons SU(3) SU(3)

pp 2.4002.400 2.7932.793

nn -1.651-1.651 -1.913-1.913

LambdLambdaa

-0652-0652 -0.613-0.613

Sigma-Sigma- -0.958-0.958 -1.16-1.16

Sigma-Sigma-00

0.6750.675 --

SigmaSigma++

2.3092.309 2.4582.458

Xi-Xi- -0.606-0.606 -0.651-0.651

Xi-0Xi-0 -1.450-1.450 -1.250-1.250

particle ChQSM experiment