2007 APCTP workshop at POSTECH 2628 Feb 2007
2007 APCTP workshop at POSTECH 26~28 Feb. 2007 PNU & Nu. RI 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 (Nu. RI), Pusan National University (PNU), Korea
Introduction 2007 APCTP workshop at POSTECH 26~28 Feb. 2007 How the universe created? What the universe made of? PNU & Nu. RI
2007 APCTP workshop at POSTECH 26~28 Feb. 2007 Introduction PNU & Nu. RI 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 2007 APCTP workshop at POSTECH 26~28 Feb. 2007 Quantum Chromo. Dynamics: 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 PNU & Nu. RI
Introduction PNU & Nu. RI 2007 APCTP workshop at POSTECH 26~28 Feb. 2007 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 & Nu. RI 2007 APCTP workshop at POSTECH 26~28 Feb. 2007 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 & Nu. RI 2007 APCTP workshop at POSTECH 26~28 Feb. 2007 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 Me. V and ms=150 Me. V Ex) Proton (uud) ~ 15 (940) Me. V !? Kaon (us, ds) ~ 155 (495) Me. V !? 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)
Introduction PNU & Nu. RI 2007 APCTP workshop at POSTECH 26~28 Feb. 2007 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 Me. V) 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 & Nu. RI 2007 APCTP workshop at POSTECH 26~28 Feb. 2007 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
Introduction 2007 APCTP workshop at POSTECH 26~28 Feb. 2007 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 PNU & Nu. RI
Introduction PNU & Nu. RI 2007 APCTP workshop at POSTECH 26~28 Feb. 2007 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
Introduction PNU & Nu. RI 2007 APCTP workshop at POSTECH 26~28 Feb. 2007 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 Me. V 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 & Nu. RI 2007 APCTP workshop at POSTECH 26~28 Feb. 2007 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 & Nu. RI 2007 APCTP workshop at POSTECH 26~28 Feb. 2007 Quark propagator in broken flavor SU(3) Written in a iterative integral equation Current quark mass dependent mass SU(3) correction 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
Introduction PNU & Nu. RI 2007 APCTP workshop at POSTECH 26~28 Feb. 2007 Effective QCD partition function via instanton 2 Nf-multiquark interaction Employing Lagrane multiplyer,
Introduction PNU & Nu. RI 2007 APCTP workshop at POSTECH 26~28 Feb. 2007 Effective QCD partition function via instanton Variation of Z about to Self-consistent (saddle-point) equation Phenomenological values Gluon condensate
Introduction & Motivation PNU & Nu. RI 2007 APCTP workshop at POSTECH 26~28 Feb. 2007 Nonperturbative properties of QCD vacuua Nonzero vacuum expectation value (V. E. V. ) of QCD operators Quark (3 Dim), gluon (4 Dim), Mixed (5 Dim) 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
Results PNU & Nu. RI Si. Nam, H. -Ch. Kim arxiv: hep-ph/0605041 Accepted for publication in Phys. Lett. B 2007 APCTP workshop at POSTECH 26~28 Feb. 2007 Gluon condensate Without the correction Obvious flavor SU(3) correction With the correction Gluon blind for flavor symmetry : flat gluon condensate Critical effects from the flavor SU(3) symmetry correction
Results PNU & Nu. RI Si. Nam, H. -Ch. Kim arxiv: hep-ph/0605041 Accepted for publication in Phys. Lett. B 2007 APCTP workshop at POSTECH 26~28 Feb. 2007 Quark condensate Without the correction Well produced value The ratio ~0. 75 (0. 8) With the correction
Results PNU & Nu. RI Si. Nam, H. -Ch. Kim arxiv: hep-ph/0605041 Accepted for publication in Phys. Lett. B 2007 APCTP workshop at POSTECH 26~28 Feb. 2007 Quark-gluon mixed condensate (5 dim) Quark-gluon Yukawa vertex 0| x |0 Factorization theorem with mass 2 -coefficient Instanton: Classical solution for soft gluon How we can treat gluon operator consistently? ? ? Convolution of single quark-instnaton interaction and gluon OP G (instanton) = d. Z Y(quark, instanton) G
Results Si. Nam, H. -Ch. Kim arxiv: hep-ph/0605041 Accepted for publication in Phys. Lett. B 2007 APCTP workshop at POSTECH 26~28 Feb. 2007 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 PNU & Nu. RI
Results PNU & Nu. RI Si. Nam, H. -Ch. Kim arxiv: hep-ph/0605041 Accepted for publication in Phys. Lett. B 2007 APCTP workshop at POSTECH 26~28 Feb. 2007 Mixed condensate Formula for the condensate Without the correction The SU(3) correction effect manifeted With the correction
Results PNU & Nu. RI Si. Nam, H. -Ch. Kim arxiv: hep-ph/0605041 Accepted for publication in Phys. Lett. B 2007 APCTP workshop at POSTECH 26~28 Feb. 2007 Factorzation coefficient m 20 Less sensitive effects from the SU(3) correction Using expansion of Without the correction Bilocal quark operator and QCD E. o. M. With the correction
Results 2007 APCTP workshop at POSTECH 26~28 Feb. 2007 Factorzation coefficient m 20 Relation between k and m 2 Si. Nam, H. -Ch. Kim arxiv: hep-ph/0605041 Accepted for publication in Phys. Lett. B w/o correction 0 PNU & Nu. RI w/ correction K K Si. Nam et al, Phys. Rev. D 74, 014019(2006) Si. Nam et al, Phys. Rev. D 74, 076005(2006) k 2 = 0. 2 Me. V 2 vs. 0. 23 Me. V 2 from pion DA
Results Si. Nam, H. -Ch. Kim arxiv: hep-ph/0605041 Accepted for publication in Phys. Lett. B Renormalization group evolution 2007 APCTP workshop at POSTECH 26~28 Feb. 2007 PNU & Nu. RI 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) m 20: ( 1 - 2)/b = -14/27 ~ -0. 52 (sensitive)
Results H. Y. Ryu, Si. Nam, H. -Ch. Kim arxiv: hep-ph/0610348 Submitted to Phys. Revt. D PNU & Nu. RI 2007 APCTP workshop at POSTECH 26~28 Feb. 2007 Electtromagnetic properties of the QCD vacuum response to the external EM-field H. -Ch. Kim, M. M. Musakhanov, M. Siddikov Phys. Lett. B 608, 95(2005) To obtain the operators, effective partition function given: Covariant derivative
Results H. Y. Ryu, Si. Nam, H. -Ch. Kim arxiv: hep-ph/0610348 Submitted to Phys. Revt. D 2007 APCTP workshop at POSTECH 26~28 Feb. 2007 Gluinic magnetic susceptibilities Gauge invariant forms and expanded in terms of the electric charges, e PNU & Nu. RI
Results H. Y. Ryu, Si. Nam, H. -Ch. Kim arxiv: hep-ph/0610348 Submitted to Phys. Revt. D PNU & Nu. RI 2007 APCTP workshop at POSTECH 26~28 Feb. 2007 Gluonic magnetic susceptibilities Absolute values decreasing as mf increases Vacuum effects diminished as mf grows: general feature? !
Results H. Y. Ryu, Si. Nam, H. -Ch. Kim arxiv: hep-ph/0610348 Submitted to Phys. Revt. D PNU & Nu. RI 2007 APCTP workshop at POSTECH 26~28 Feb. 2007 Comparison with others Other model calcualtions moslty coming from QCDSR Comparison via renormalization group evolution at 600 Me. V Inconsistent between the values even in the same scheme Very different from
Summary PNU & Nu. RI 2007 APCTP workshop at POSTECH 26~28 Feb. 2007 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 (3 dim), gluon (4 dim), mixed (5 dim) 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 PNU & Nu. RI Thank you very much for your attention !!
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