New Frontiers in QCD, October 28th, 2011 Based on K. Kim, D. Jido, S.H. Lee PRC 84(2011) K. Kim, Y. Kim, S. Takeuchi, T. Tsukioka PTP 126(2011)735

Introduction 2/32October 28 th 2011

Introduction 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. 3/32October 28 th 2011

AdS/CFT Correspondence 4D generating functional5D classical effective action Operator5D bulk field [Operator]5D mass Current conservationGauge symmetry ResonancesKlauza-Klein states 5 5/32October 28 th 2011

AdS/QCD Model – Bottom-Up Approach Ref. Erlich, Katz, Son, Stephanov PRL 95(2005) 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 6/32October 28 th 2011

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 7/32October 28 th 2011

Quark Number Susceptibility Ref. Cheng et al. PRD 79, (2009) = Grand potential Under conditions met in RHIC and LHC the net baryon number is small and QCD at vanishing chemical potential provides a good approximation. 8/32October 28 th 2011

Deformed AdS Space The deformed AdS Black Hole where, where, 9/32October 28 th 2011 Ref. Y.Kim, T.Misumi, and I.j.Shin [arxiv ]

Quark Number Susceptibility 5D gauge coupling constant with gauge choice, The Fourier decomposition 10/32October 28 th 2011

Quark Number Susceptibility 11/32October 28 th 2011

Quark Number Susceptibility 12/32October 28 th 2011

Quark Number Susceptibility in D3/D7 13/32October 28 th 2011

Quark Number Susceptibility 14/32October 28 th 2011

Quark Number Susceptibility in D3/D7 15/32October 28 th 2011

Summary & Conclusion 16/32October 28 th 2011 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.

Motivation : Di-quark Structures in Hadrons SHLee and S.Yasui : EPJ C (2009) 18/32October 28 th 2011

Motivation : Di-quark Structures in Hadrons u d q q Vs. u q dq u d q u s u d s u d s Di-quark structure has a important role in high density phase. 19/32October 28 th 2011

Introduction: QCD Sum Rules ∼ Spectral Density 20/32October 28 th 2011

Λ Baryons u d s Ref. PDG Scalar diquark field Gauge invariant Lagrangian for diquark field 21/32October 28 th 2011

Λ Baryons Gauge invariant Lagrangian for diquark field Propagator of diquark field Free parameters! The relation between diquark condensate and gluon condensate OPE terms 22/32October 28 th 2011

QCDSR with Di-quark fields OPE Result 23/32October 28 th 2011

Λ Baryons Diquark Mass (GeV)Ratio(λ) Parameter Set ( m s =0.12GeV, m Λ =1.115GeV) Parameter Set ( m s =0.12GeV, m Λ =1.115GeV) 24/32October 28 th 2011

Λ Baryons 25/32October 28 th 2011

Nucleons u d d d u u Neutron Proton Necleons doesn’t have “good” diquark structures inside. -> We need to consider quark-diquark interactions. 26/32October 28 th 2011

Scalar meson q Scalar meson as a tetraquark (ud-diquark field) 27/32October 28 th 2011 q q q

Summary & Conclusion 28/32October 28 th 2011 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.

Summary 30/32October 28 th 2011 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 31/32October 28 th 2011