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Studying Strong Interactions at Densities
Kyungil Kim
New Frontiers in QCD, October 28th, 2011
Based on K. Kim, D. Jido, S.H. Lee PRC 84(2011)025204 K. Kim, Y. Kim, S. Takeuchi, T. Tsukioka PTP 126(2011)735
Introduction
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<The QCD Phase Diagram>
Introduction
Quark Number Susceptibility with Finite Quark Mass in Holo-graphic QCD
Sudden increase of quark number fluctuation near phase transition
Quark number susceptibility is suppressed by finite quark mass.
Diquarks in Hadron Structures
Using QCD sum rules, we will study properties of diquark structure in hadrons.
It will give a chance to glance at extremely high density re-gion.
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Quark Number Susceptibility with Finite Quark Mass in Holographic
QCD
5
AdS/CFT Correspondence
4D generating functional 5D classical effective action
Operator 5D bulk field
[Operator] 5D mass
Current conservation Gauge symmetry
Resonances Klauza-Klein states
<AdS metric in 5D>
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AdS/QCD Model – Bottom-Up ApproachRef. Erlich, Katz, Son, Stephanov PRL 95(2005)261602 Rold and Pomarol NPB 721(2005)79 Domokos and Harvey, Phys.Rev.Lett.99:141602(2007)
The action of model,
where,
AdS5 space is compactified such that
Solving the vector field equation of motion at zero momentum yields
must be proportional to the quark chemical potential
In generalized gauge symmetry to
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The Hawking-Page Transition
Confinement phase
Thermal AdS
Deconfinement phase
AdS Black Hole
Geometry
The Euclidean gravitational action
The periodicity The Hawking temperature
The black hole horizon
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Quark Number Susceptibility
Ref. Cheng et al. PRD 79, 074505 (2009)
<The pressure>
= Grand potential
<The definition of susceptibility for various charge>
Under conditions met in RHIC and LHC the net baryon number is small and QCD at vanishing chemical potential provides a good ap-proximation.
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Deformed AdS Space
The deformed AdS Black Hole
<The back-reacted metric>
where,
<The Hawking temperature for black-hole>
where,
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Ref. Y.Kim, T.Misumi, and I.j.Shin [arxiv 0911.3205]
Quark Number Susceptibility
<The 5D action for U(1) gauge field>
5D gauge coupling constant
with gauge choice,
The Fourier decomposition
<The equation of motion for A_t>
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Quark Number Susceptibility
<The quark susceptibility from hydrodynamic approach>
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<The quark susceptibility from thermodynamics>
Quark Number Susceptibility
<The quark number susceptibility in deformed AdS>
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Quark Number Susceptibility in D3/D7
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<The black D3-brane background>
<The DBI action for D7 brane>
Quark Number Susceptibility
<The quark mass and the density in D3/D7 model>
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<The number of quarks>
Quark Number Susceptibility in D3/D7
<The quark number susceptibility in D3/D7 Model>
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Summary & Conclusion
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We can have similar results in holographic QCD with lattice calculation in quark number susceptibility calculations.
At bottom-up approach, two ways to obtain the quark num-ber susceptibility give us same result.
Both the bottom-up approach and the top-down approach give the same behavior that the quark number fluctuation is suppressed by the finite quark mass.
Diquarks in Hadron Struc-
tures
Motivation : Di-quark Structures in Hadrons
SHLee and S.Yasui : EPJ C (2009)
<Diquark inside baryons>
<Quark-antiquark inside mesons>
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Motivation : Di-quark Structures in Hadrons
<Tetraquark> ud
qq Vs.
u q
d q
<H Dibaryon>
<Pentaquark>
ud
q us
ud
su
ds
Di-quark structure has a im-portant role in high density phase.
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Introduction: QCD Sum Rules
<Two-point correlation function>
<The operator product expansion>
<Dispersion relation>
∼ Spectral Density
<Borel Transformation>
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Λ Baryons
u d
s
Ref. PDG<Current for Λ >
Scalar diquark field
Gauge invariant Lagrangian for diquark field
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Λ Baryons
Gauge invariant Lagrangian for diquark field
Propagator of diquark field
Free parameters!
The relation between diquark condensate and gluon condensate
OPE terms
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QCDSR with Di-quark fields
OPE Result
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Λ BaryonsDiquark Mass
(GeV)Ratio(λ)
0.2 -0.5
0.3 -0.2
0.4 -0.013
0.41 0
Parameter Set ( ms=0.12GeV, mΛ =1.115GeV)
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Λ Baryons
<Lambda_c sum rule> <Lambda_b sum rule>
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Nucleons
u
dd
d
u u
Neutron
Proton
Necleons doesn’t have “good” diquark structures inside. -> We need to consider quark-diquark interactions.
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Scalar meson
q
Scalar meson as a tetraquark(ud-diquark field)
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q q
q
Summary & Conclusion
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The QCD sum rule approach with a diquark field gives a good result for Lambda.
We can have a diquark mass and condensate values from Lambda.
These parameters give good masses for Lmabda_c and Lambda_b.
We tried this approach to nucleon and scalar meson (te-traquark).
We have reasonable results with “bad” diquark structures in-side those particles.
Summary&
Outlook
Summary
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The AdS/QCD model is useful to study the physics near phase transition.
We can have similar results in holographic QCD with lattice calculation in quark number susceptibility calculations.
Diquark pictures for hadrons are successful.
We now try to apply this approach to other particles which are expected to have “good” diquark structure. (tetraqaurk, pentaquark, H-dibaryon, …)
By extended work to H-dibaryon, we expect to glance at high density region.
Outlook
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<FAIR at GSI>
<KoRIA Project>
Thank you very much!!