Parity violating asymmetries: Milos (Greece) May 2006 Solitonic approach to strange Form Factors
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Transcript of Parity violating asymmetries: Milos (Greece) May 2006 Solitonic approach to strange Form Factors
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
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