INSTANTONAND

ITS APPLICATION

Nam, Seung-il

Yukawa Institute for Theoretical Physics (YITP), Kyoto University, Japan

YITP, Kyoto UniversityY

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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|00

It also effects on QCD phase structure, represented by qq, qq,…

Investigations on the vacuum itself: meron, dyon, vortex, instaton etc..

YITP, Kyoto UniversityY

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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 UniversityY

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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 UniversityY

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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 UniversityY

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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 U5

YITP, Kyoto UniversityY

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Pion EM form factor at finite density

VMD parameterization -meson mass shift

YITP, Kyoto UniversityY

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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 UniversityY

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Thank you very much for your attention

and

A bonus shot just for fun!

YITP, Kyoto UniversityY

ITP

Lun

ch S

emin

ar 1

9 D

ec 2

007

QuickTime¢‚∞˙ TIFF(LZW) æ–√‡ «ÿ¡¶±‚∞°

¿Ã ±◊∏≤¿ª ∫∏±‚ ¿ß«ÿ « ø‰«’¥œ¥Ÿ.