quark-gluon mixed matrix elements within the framework of the nonlocal chiral quark model

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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 PNU & NuRI 2007 APCTP workshop at POSTECH 26~28 Feb. 2007

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PNU & NuRI. Quark-gluon mixed matrix elements within the framework of the nonlocal chiral quark model Seung-il Na m* Hyun-Chul Kim and Hui-Young Ryu Department of Physics and Nuclear Physics & Radiation Technology Institute (NuRI), Pusan National University (PNU), Korea. - PowerPoint PPT Presentation

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Page 1: Quark-gluon mixed matrix elements within the framework of the nonlocal chiral quark model

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

PNU & NuRI2

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Page 2: Quark-gluon mixed matrix elements within the framework of the nonlocal chiral quark model

Introduction PNU & NuRI

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How the universe created?

What the universe made of?

Page 3: Quark-gluon mixed matrix elements within the framework of the nonlocal chiral quark model

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

Page 4: Quark-gluon mixed matrix elements within the framework of the nonlocal chiral quark model

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

Page 5: Quark-gluon mixed matrix elements within the framework of the nonlocal chiral quark model

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??)

Page 6: Quark-gluon mixed matrix elements within the framework of the nonlocal chiral quark model

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

Page 7: Quark-gluon mixed matrix elements within the framework of the nonlocal chiral quark model

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)

Page 8: Quark-gluon mixed matrix elements within the framework of the nonlocal chiral quark model

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

Page 9: Quark-gluon mixed matrix elements within the framework of the nonlocal chiral quark model

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

Page 10: Quark-gluon mixed matrix elements within the framework of the nonlocal chiral quark model

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

Page 11: Quark-gluon mixed matrix elements within the framework of the nonlocal chiral quark model

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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Page 12: Quark-gluon mixed matrix elements within the framework of the nonlocal chiral quark model

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

Page 13: Quark-gluon mixed matrix elements within the framework of the nonlocal chiral quark model

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

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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

Page 15: Quark-gluon mixed matrix elements within the framework of the nonlocal chiral quark model

Introduction PNU & NuRI

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Effective QCD partition function via instantonEffective QCD partition function via instanton

2Nf-multiquark interaction

Employing Lagrane multiplyer,

Page 16: Quark-gluon mixed matrix elements within the framework of the nonlocal chiral quark model

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

Page 17: Quark-gluon mixed matrix elements within the framework of the nonlocal chiral quark model

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

Page 18: Quark-gluon mixed matrix elements within the framework of the nonlocal chiral quark model

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

Page 19: Quark-gluon mixed matrix elements within the framework of the nonlocal chiral quark model

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

Page 20: Quark-gluon mixed matrix elements within the framework of the nonlocal chiral quark model

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

Page 21: Quark-gluon mixed matrix elements within the framework of the nonlocal chiral quark model

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

Page 22: Quark-gluon mixed matrix elements within the framework of the nonlocal chiral quark model

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

Page 23: Quark-gluon mixed matrix elements within the framework of the nonlocal chiral quark model

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

Page 24: Quark-gluon mixed matrix elements within the framework of the nonlocal chiral quark model

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

Page 25: Quark-gluon mixed matrix elements within the framework of the nonlocal chiral quark model

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

Page 26: Quark-gluon mixed matrix elements within the framework of the nonlocal chiral quark model

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)

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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

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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

Page 29: Quark-gluon mixed matrix elements within the framework of the nonlocal chiral quark model

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

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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 !!