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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

- Quark Number Susceptibility with Finite Quark Mass in Holographic 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 region.

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Quark Number Susceptibility with Finite Quark Mass in Holographic QCD

AdS/QCD Model – Bottom-Up Approach

Ref. 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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Geometry

Confinement phase

Thermal AdS

Deconfinement phase

AdS Black Hole

The periodicity

The Hawking temperature

The black hole horizon

The Euclidean gravitational action

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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 approximation.

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The deformed AdS Black Hole

Ref. Y.Kim, T.Misumi, and I.j.Shin [arxiv 0911.3205]

<The back-reacted metric>

where,

<The Hawking temperature for black-hole>

where,

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<The 5D action for U(1) gauge field>

with gauge choice,

5D gauge coupling constant

The Fourier decomposition

<The equation of motion for A_t>

October 28th 2011

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<The quark susceptibility from hydrodynamic approach>

<The quark susceptibility from thermodynamics>

October 28th 2011

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Quark Number Susceptibility in D3/D7

<The black D3-brane background>

<The DBI action for D7 brane>

October 28th 2011

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<The quark mass and the density in D3/D7 model>

<The number of quarks>

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Quark Number Susceptibility in D3/D7

<The quark number susceptibility in D3/D7 Model>

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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 number 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.

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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>

q

u

q

Vs.

u

q

d

d

q

<Pentaquark>

q

u

u

d

s

<H Dibaryon>

Di-quark structure has a important rolein high density phase.

d

s

u

s

d

u

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<Two-point correlation function>

<The operator product expansion>

<Dispersion relation>

∼ Spectral Density

<Borel Transformation>

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d

u

s

Ref. PDG

<Current for Λ >

Scalar diquark field

Gauge invariant Lagrangian for diquarkfield

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Gauge invariant Lagrangian for diquarkfield

Propagator of diquark field

Free parameters!

The relation between diquark condensate and gluon condensate

OPE terms

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Neutron

u

d

d

Proton

d

u

u

Necleons doesn’t have “good” diquark structures inside.

-> We need to consider quark-diquark interactions.

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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 (tetraquark).
- We have reasonable results with “bad” diquark structures inside those particles.

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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.

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