Quark-gluon mixed matrix elements within the framework of
the nonlocal chiral quark model
Seung-il Nam*
Hyun-Chul Kim and Hui-Young Ryu
Department of Physics and Nuclear Physics & Radiation Technology Institute (NuRI), Pusan National University (PNU), Korea
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Introduction PNU & NuRI
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How the universe created?
What the universe made of?
Introduction PNU & NuRI
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Strong force
Prediction of mesons by Yukawa
Conception of partons
Group theoretical analyses of hadron families by Gell-Mann
String-like objects (~Reggization)
Advent of QCD: Confinment, Asymtotic freemdom
Transmutation of dimension ~ QCD
Chiral symmetry and its spontaneous breaking
Introduction PNU & NuRI
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Quantum ChromoDynamics: QCD
Quark and gluon degrees of freedom
Gluon interact in non-Abelain manner with quarks
Underlying theory for strong interaction
ARE WE HAPPY WITH THIS?
Highly nonlonear interaction
Running coupling depending on scale
Renormlaization group evolution
Lattice QCD simulation: descrete space-time
Perturbative QCD : high energy machinary
Introduction PNU & NuRI
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Low energy QCD
Perturbation: small coupling as a expamsion parameter
High energy s < 1 whereas low energy s > 1
Perturbative QCD, then what for the low energy?
As told, lattice QCD simulation works for all…..??
Still more sofistication necessary in lattice QCD
Time, machine power, large collaboration (matter of time??)
Introduction PNU & NuRI
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Effective low energy models for QCD
Relatively simple and easy “models” mimic QCD
Employment of different D.o.F.s treated easily
Guided by symmetries, constraints, LEC..
In case, several QCD conditions ignored
confinment, renormalizability, anomaly, etc.
Focusing on most relevant conditions
Depending much on “scale”
Better “QCD” like model building: understanding of QCD
Introduction PNU & NuRI
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Mass generation of quarks: broken symmetry
Flavor SU(3) symmetry: mu=md=ms (=0, chiral limit)
Broken flavor SU(3) symmetry: mu=md≠ms
mu=md=5 MeV and ms=150 MeV
Ex) Proton (uud) ~ 15 (940) MeV !?
Kaon (us,ds) ~ 155 (495) MeV !?
What happens for these mass differences?
Chiral doublet in the nature: N(940,1/2+) vs. N*(1535,1/2-)
Heavily broken chiral symmetry from the “beginning”
Spontaneous Chiral Symmetry Breaking (SSB)
Introduction PNU & NuRI
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Spontaneous Chiral Symmetry Breaking
Nontrivial vacuum: H|0≠0
Infinitely degenerated vacuua
Realization of SSB in hadron physics
Continuous symmetry breaking (SSB)
generation of the massless Goldstone boson
Pion (140 MeV) assigned to be the GS boson
must be crucial at the low energy hadron phyiscs !!
Model building with for the low energy effective models
Introduction PNU & NuRI
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Effective models related to pion
Hadron physics filled with pion due to its special natures
MIT bag model: naïve treatment of quarks
Chiral bag model: MIT bag + chiral symmetry with GS boson
Linear and nonlinear -models: Simple realization of SSB
Skyrme model: only GS boson in topological soliton
Nmabu-Jona-Lasinio (NJL): quark D.o.F. mesonic D.o.F.
Nonlocal NJL: nonlocal interaction plays a role
Instanton model: quark-instanton D.o.F. instead of gluon
Introduction PNU & NuRI
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Instanton vacuum configuration
Gluonic potential of QCD
Self-duality condition: minimizing the potential
Topological number realted to the ground state
Guage transformation of the ground state via
Instanton vacuum configuration
Winding number from homotopic SU(N) gaugetransformation
Tunneling between vacuua
Instanton solution for the self-duality condition
Natural mechanism for SSB
Introduction PNU & NuRI
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Introduction PNU & NuRI
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Merits in instanton model in the large Nc
All relevant QCD symmetries satisfied
Only two phenomenological parameters fixed in the model
Internstanton distance R ~ 1 fm and Instanton size ~ 1/3 fm
These values are supported from the lattice QCD simulations !!!
1/ ~ 600 MeV plays a role of the model scale parameter
“No adjustable free parameters”: highly constrained model
Intrinsic UV regulator from the quark-instanton interaction
Natural derivation of nonlocal interactions
Introduction PNU & NuRI
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Fermionic zero mode solution
A solution for the Dirac equation with the instanton
Fourier transformation of the wave function: Form factor
Natural UV regulator
Parameterization
Introduction PNU & NuRI
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Quark propagator in broken flavor SU(3)
Written in a iterative integral equation
Current quark mass dependent mass
Hadrons with strangeness quark being able to be studied
Then how we consturct the effective action from instanton?
The action generating the propagator from its Z-fucntion
SU(3) correction
Introduction PNU & NuRI
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Effective QCD partition function via instantonEffective QCD partition function via instanton
2Nf-multiquark interaction
Employing Lagrane multiplyer,
Introduction PNU & NuRI
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Effective QCD partition function via instantonEffective QCD partition function via instanton
Variation of Z about to
Self-consistent (saddle-point) equation
Phenomenological values
Gluon condensate
Introduction & Motivation PNU & NuRI
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Nonperturbative properties of QCD vacuuaNonperturbative properties of QCD vacuua
Nonzero vacuum expectation value (V.E.V.) of QCD operators
Quark (3Dim), gluon (4Dim), Mixed (5Dim) condensates….
Order parameter for the QCD phase transition
Order parameter for the SSB
Input parameter in QCD sumrules (OPE)
(0,x)=an’(x)
Various nonperturbative QCD vacuum properties
Resoponse of the V.E.V. to external EM-field
Results PNU & NuRI
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Gluon condensate Gluon condensate
Obvious flavor SU(3)
correction
Gluon blind for flavor symmetry : flat gluon condensate
Critical effects from the flavor SU(3) symmetry correction
With the correction
Without the correction
SiNam,H.-Ch.Kim arxiv:hep-ph/0605041Accepted for publication in Phys.Lett.B
Results PNU & NuRI
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Quark condensate Quark condensate
Well produced value
The ratio ~0.75 (0.8) With the correction
Without the correction
SiNam,H.-Ch.Kim arxiv:hep-ph/0605041Accepted for publication in Phys.Lett.B
Results PNU & NuRI
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Quark-gluon mixed condensate (5dim)Quark-gluon mixed condensate (5dim)
Quark-gluon Yukawa vertex
Factorization theorem with mass2-coefficient
Instanton: Classical solution for soft gluon
How we can treat gluon operator consistently???
Convolution of single quark-instnaton interaction and gluon OP
0| |0x
G(instanton) = dZ Y(quark,instanton) G
SiNam,H.-Ch.Kim arxiv:hep-ph/0605041Accepted for publication in Phys.Lett.B
Results PNU & NuRI
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Reconstructed gluon operatorReconstructed gluon operator
Single quark-instanton interaction
Gluon operator in terms of color orientation
Gluon operator as a quark-instanton interaction
This reconstructed operator used for
SiNam,H.-Ch.Kim arxiv:hep-ph/0605041Accepted for publication in Phys.Lett.B
Results PNU & NuRI
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Mixed condensateMixed condensate
Formula for the condensate
The SU(3) correction effect
manifeted
With the correction
Without the correction
SiNam,H.-Ch.Kim arxiv:hep-ph/0605041Accepted for publication in Phys.Lett.B
Results PNU & NuRI
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Factorzation coefficient mFactorzation coefficient m2200
Less sensitive effects from the SU(3) correction
Using expansion of
Bilocal quark operator and
QCD E.o.M.
With the correction
Without the correction
SiNam,H.-Ch.Kim arxiv:hep-ph/0605041Accepted for publication in Phys.Lett.B
Results PNU & NuRI
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Factorzation coefficient mFactorzation coefficient m2200
Relation between kand m20
k2 = 0.2 MeV2 vs. 0.23 MeV2 from pion DA
KK
w/ correctionw/o correction
SiNam et al, Phys.Rev.D74,014019(2006)SiNam et al, Phys.Rev.D74,076005(2006)
SiNam,H.-Ch.Kim arxiv:hep-ph/0605041Accepted for publication in Phys.Lett.B
Results PNU & NuRI
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Renormalization group evolutionRenormalization group evolution
Matching different scales between models
A ratio of the two different operators
Mixed condensate: 1/b = -2/27 ~ -0.07 (insensitive)
Quark condensate: 2/b = 4/9 ~ 0.44 (sensitive)
m20: (1- 2)/b = -14/27 ~ -0.52 (sensitive)
SiNam,H.-Ch.Kim arxiv:hep-ph/0605041Accepted for publication in Phys.Lett.B
Electtromagnetic properties of the QCD vacuumElecttromagnetic properties of the QCD vacuum
QCD vacuum response to the external EM-field
To obtain the operators, effective partition function given:
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H.Y.Ryu, SiNam, H.-Ch.Kimarxiv:hep-ph/0610348Submitted to Phys.Revt.D
Covariant derivative
H.-Ch.Kim,M.M.Musakhanov,M.SiddikovPhys.Lett.B608,95(2005)
Gluinic magnetic susceptibilitiesGluinic magnetic susceptibilities
Gauge invariant forms
and expanded in terms of the electric charges, e
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H.Y.Ryu, SiNam, H.-Ch.Kimarxiv:hep-ph/0610348Submitted to Phys.Revt.D
Gluonic magnetic susceptibilitiesGluonic magnetic susceptibilities
Absolute values decreasing as mf increases
Vacuum effects diminished as mf grows: general feature?!
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H.Y.Ryu, SiNam, H.-Ch.Kimarxiv:hep-ph/0610348Submitted to Phys.Revt.D
Comparison with othersComparison with others
Other model calcualtions moslty coming from QCDSR
Comparison via renormalization group evolution at 600 MeV
Inconsistent between the values even in the same scheme
Very different from
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H.Y.Ryu, SiNam, H.-Ch.Kimarxiv:hep-ph/0610348Submitted to Phys.Revt.D
Summary PNU & NuRI
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Strong interaction at nonperturbative regions
Difficulties in applicayion of QCD (lattice QCD?!)
Effective QCD-like models guided by relevant symmetries
SSB governing low-lying hadrons: critical role of
Nontrivial QCD vacuum: Instanton vacuum configuration
Relatively sophisticated model: highly constrained
Broken flavor SU(3) symmetry taken into account
Quark (3dim), gluon (4dim), mixed (5dim) studied
EM response of QCD vacuum considered
In principle, all kinds of hadronic matrix elements computed
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Thank you very much for your attention !!