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

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.

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

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

  2. PNU & NuRI Introduction How the universe created? 2007 APCTP workshop at POSTECH 26~28 Feb. 2007 What the universe made of?

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

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

  5. PNU & NuRI Introduction 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??) 2007 APCTP workshop at POSTECH 26~28 Feb. 2007

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

  7. PNU & NuRI Introduction 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 (SSB) 2007 APCTP workshop at POSTECH 26~28 Feb. 2007

  8. PNU & NuRI Introduction Spontaneous Chiral Symmetry Breaking Nontrivial vacuum: H|0≠0 Infinitely degenerated vacuua Realization of SSB in hadron physics Continuous symmetry breaking (SSB)  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 2007 APCTP workshop at POSTECH 26~28 Feb. 2007

  9. PNU & NuRI Introduction 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 SSB 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 2007 APCTP workshop at POSTECH 26~28 Feb. 2007

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

  11. PNU & NuRI Introduction Instanton vacuum configuration Winding number from homotopic SU(N) gaugetransformation Tunneling between vacuua Instanton solution for the self-duality condition Natural mechanism for SSB 2007 APCTP workshop at POSTECH 26~28 Feb. 2007

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

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

  14. PNU & NuRI Introduction 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 2007 APCTP workshop at POSTECH 26~28 Feb. 2007 SU(3) correction

  15. PNU & NuRI Introduction Effective QCD partition function via instanton 2Nf-multiquark interaction Employing Lagrane multiplyer,  2007 APCTP workshop at POSTECH 26~28 Feb. 2007

  16. PNU & NuRI Introduction Effective QCD partition function via instanton Variation of Z about to  Self-consistent (saddle-point) equation Phenomenological values Gluon condensate 2007 APCTP workshop at POSTECH 26~28 Feb. 2007

  17. PNU & NuRI Introduction & Motivation Nonperturbative 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 SSB 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 2007 APCTP workshop at POSTECH 26~28 Feb. 2007

  18. PNU & NuRI Results SiNam,H.-Ch.Kim arxiv:hep-ph/0605041 Accepted for publication in Phys.Lett.B Gluon condensate Obvious flavor SU(3) correction Gluon blind for flavor symmetry : flat gluon condensate Critical effects from the flavor SU(3) symmetry correction Without the correction 2007 APCTP workshop at POSTECH 26~28 Feb. 2007 With the correction

  19. PNU & NuRI Results SiNam,H.-Ch.Kim arxiv:hep-ph/0605041 Accepted for publication in Phys.Lett.B Quark condensate Well produced value The ratio ~0.75 (0.8) Without the correction 2007 APCTP workshop at POSTECH 26~28 Feb. 2007 With the correction

  20. PNU & NuRI 0| |0 x Results SiNam,H.-Ch.Kim arxiv:hep-ph/0605041 Accepted for publication in Phys.Lett.B 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 2007 APCTP workshop at POSTECH 26~28 Feb. 2007 G(instanton) =  dZ Y(quark,instanton) G

  21. PNU & NuRI Results SiNam,H.-Ch.Kim arxiv:hep-ph/0605041 Accepted for publication in Phys.Lett.B Reconstructed 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 2007 APCTP workshop at POSTECH 26~28 Feb. 2007

  22. PNU & NuRI Results SiNam,H.-Ch.Kim arxiv:hep-ph/0605041 Accepted for publication in Phys.Lett.B Mixed condensate Formula for the condensate The SU(3) correction effect manifeted Without the correction 2007 APCTP workshop at POSTECH 26~28 Feb. 2007 With the correction

  23. PNU & NuRI Results SiNam,H.-Ch.Kim arxiv:hep-ph/0605041 Accepted for publication in Phys.Lett.B Factorzation coefficient m20 Less sensitive effects from the SU(3) correction Using expansion of Bilocal quark operator and QCD E.o.M. 2007 APCTP workshop at POSTECH 26~28 Feb. 2007 Without the correction With the correction

  24. PNU & NuRI w/o correction w/ correction   K K Results SiNam,H.-Ch.Kim arxiv:hep-ph/0605041 Accepted for publication in Phys.Lett.B Factorzation coefficient m20 Relation between kand m20 2007 APCTP workshop at POSTECH 26~28 Feb. 2007 SiNam et al, Phys.Rev.D74,014019(2006) SiNam et al, Phys.Rev.D74,076005(2006) k2 = 0.2 MeV2 vs. 0.23 MeV2 from pion DA

  25. PNU & NuRI Results SiNam,H.-Ch.Kim arxiv:hep-ph/0605041 Accepted for publication in Phys.Lett.B Renormalization 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) 2007 APCTP workshop at POSTECH 26~28 Feb. 2007

  26. PNU & NuRI Results H.Y.Ryu, SiNam, H.-Ch.Kim arxiv:hep-ph/0610348 Submitted to Phys.Revt.D Electtromagnetic properties of the QCD vacuum QCD vacuum response to the external EM-field To obtain the operators, effective partition function given: H.-Ch.Kim,M.M.Musakhanov,M.Siddikov Phys.Lett.B608,95(2005) 2007 APCTP workshop at POSTECH 26~28 Feb. 2007 Covariant derivative

  27. PNU & NuRI Results H.Y.Ryu, SiNam, H.-Ch.Kim arxiv:hep-ph/0610348 Submitted to Phys.Revt.D Gluinic magnetic susceptibilities Gauge invariant forms  and  expanded in terms of the electric charges, e 2007 APCTP workshop at POSTECH 26~28 Feb. 2007

  28. PNU & NuRI Results H.Y.Ryu, SiNam, H.-Ch.Kim arxiv:hep-ph/0610348 Submitted to Phys.Revt.D Gluonic magnetic susceptibilities Absolute values decreasing as mf increases Vacuum effects diminished as mf grows: general feature?! 2007 APCTP workshop at POSTECH 26~28 Feb. 2007

  29. PNU & NuRI Results H.Y.Ryu, SiNam, H.-Ch.Kim arxiv:hep-ph/0610348 Submitted to Phys.Revt.D Comparison 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  2007 APCTP workshop at POSTECH 26~28 Feb. 2007

  30. PNU & NuRI Summary Strong interaction at nonperturbative regions Difficulties in applicayion of QCD (lattice QCD?!) Effective QCD-like models guided by relevant symmetries SSB 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 2007 APCTP workshop at POSTECH 26~28 Feb. 2007

  31. PNU & NuRI Thank you very much for your attention !! 2007 APCTP workshop at POSTECH 26~28 Feb. 2007

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