instanton and its application nam, seung-il yukawa institute for theoretical physics (yitp), kyoto...
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INSTANTONAND
ITS APPLICATION
Nam, Seung-il
Yukawa Institute for Theoretical Physics (YITP), Kyoto University, Japan
YITP, Kyoto UniversityY
ITP
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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
ITP
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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
ITP
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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
ITP
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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
ITP
Lun
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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
ITP
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Pion EM form factor at finite density
VMD parameterization -meson mass shift
YITP, Kyoto UniversityY
ITP
Lun
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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
ITP
Lun
ch S
emin
ar 1
9 D
ec 2
007
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