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INSTANTON AND ITS APPLICATION Nam, Seung-il Yukawa Institute for Theoretical Physics (YITP), Kyoto University, Japan YITP, Kyoto University YITP Lunch Seminar 19 Dec 2007
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Introduction Strongly interacting particles governed by QCD Difficulties in QCD in low energy region Developing models guided in terms of symmetries A powerful guidance: Spontaneous Breakdown of Chiral Symmetry SBCS Nambu-Goldstone (NG) bosons (pion) Chiral bag, NJL, Skyrmion, HLS etc… But… what is the origin of this interesting phenomena? Highly nontrivial QCD vacuum: H|0 0 It also effects on QCD phase structure, represented by qq , qq ,… Investigations on the vacuum itself: meron, dyon, vortex, instaton etc.. YITP, Kyoto University YITP Lunch Seminar 19 Dec 2007
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Instanton Named by t’Hooft (cf:Euclidean Gauge Soliton) Classical ground state solution of the QCD in Euclidean space Analogy: QED electron & phonon vs. QCD quark & instanton Minimizing the QCD YM action: Self-dual condition (Singular gauge) instanton solution Nonperturbative part of gluons replaced by instantons (Anti)quarks moving around this effective potential-like ensemble YITP, Kyoto University YITP Lunch Seminar 19 Dec 2007
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Instanton Quark propagator in the instanton effects Momentum-dependent quark mass Playing a role of a intrinsic UV regularator Non-zero chiral condensate ( qq ) natural interpretation of SBCS YITP, Kyoto University YITP Lunch Seminar 19 Dec 2007
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Instanton Advantageous features of this approach Preserving all relevant QCD symmetries U(1) A included via nonzero topological susceptibility Natural scale parameter: average instanton size & inter-distance No adjustable free parameters (at least for light quarks in leading Nc ) Natural UV regulator: M(k) Highgly nonlocal interaction between quarks Natural derivations of (almost) NJL and Skyrme mode No confinement… (a PNJL-like approach possible?) YITP, Kyoto University YITP Lunch Seminar 19 Dec 2007
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Applications For baryonic sector: Chiral Quark Soliton Model For mesonic sector: Nonlocal Chiral Quark Model Quark + Instanton Quark + NG boson by bosonization Effective chiral action at finite density: Nonlocal pseudoscalar meson background field For mesonic sector, we pick up meson fields directly by expanding U 5 YITP, Kyoto University YITP Lunch Seminar 19 Dec 2007
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Pion EM form factor at finite density VMD parameterization -meson mass shift YITP, Kyoto University YITP Lunch Seminar 19 Dec 2007
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Summary and outlook Nontrivial QCD vacuum configuration: instanton Beautiful interpretations on nonperturbative hadronic properties Widely applied to various problems Next steps extension to baryonic sector extension to finite temperature A possible relation with the hQCD?: and 5th z -direction Confinement in the instanton model?: eff. thermodynamic potential? Complex constituent quark mass: bounded at time-like region? YITP, Kyoto University YITP Lunch Seminar 19 Dec 2007
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Thank you very much for your attention and A bonus shot just for fun! YITP, Kyoto University YITP Lunch Seminar 19 Dec 2007
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