Holographic approach to Exotic Hadrons K G FIT

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Holographic approach to Exotic Hadrons K. G (FIT), A. Nakamura, M. Ishihara, T. Taminato,

Holographic approach to Exotic Hadrons K. G (FIT), A. Nakamura, M. Ishihara, T. Taminato, F. Toyoda based on JHEP 08(2010)007, 04(2009)041 1. 2. 3. 4. Introduction Model Baryon and vertex Various vertex solutions Baryonium, Penta and Hepta quark 5. Summary

1. Introduction  based on Type IIB superstring •   Holographic “QCD” (YM Fields + Quarks)

1. Introduction  based on Type IIB superstring •   Holographic “QCD” (YM Fields + Quarks)   a) SU(Nc) Yang-Mills Theory       10 D gravity with D 3 branes              Closed strings Open Strings (=Large)

Maldacena ‘ 98 From the sol of 10 D Einstein Eqs. Partition func. of

Maldacena ‘ 98 From the sol of 10 D Einstein Eqs. Partition func. of Semi-classical 10 D Gravity SYM(CFT) generating functional of 4 D SYM (CFT) strong coupling, non-perturbative

 • b) Quarks (by flavor branes, probe = Quenched Approxi. ) Karch-Katz JHEP 2003

• b) Quarks (by flavor branes, probe = Quenched Approxi. ) Karch-Katz JHEP 2003 Nf<<Nc flavor Color ・Color superconductor n. B large Nc ≈ Nf

c) Hadrons; (1) Mesons Kruczenski et al JHEP 2003 Fifth Coordinate r Large spins

c) Hadrons; (1) Mesons Kruczenski et al JHEP 2003 Fifth Coordinate r Large spins x, y, z Fluctuations of fields on D 7 and in bulk

(2)Baryons: Vertex (D 5 Brane)+ Nc Strings Witten 1998 Nc-string as U(1) flux Exotic

(2)Baryons: Vertex (D 5 Brane)+ Nc Strings Witten 1998 Nc-string as U(1) flux Exotic Hadorons appear through the structure of D 5

2. Set up of model Gauge = bulk BG (by imposing Confinement ) Freund-Rubin

2. Set up of model Gauge = bulk BG (by imposing Confinement ) Freund-Rubin Ansatz With this Solve the Eom as 1) (Susy) Kehagias-Sfetsos, Liu-Tseytlin 1999 2) And Non-susy sol (dilaton only)

3. Baryon = Vertex + Quarks; i) Vertex = D 5 brane on S^5

3. Baryon = Vertex + Quarks; i) Vertex = D 5 brane on S^5 Callan et al hep-th/9902197 = For  

Energy density U After Legendre tr. W. r. t. to D Solution has generally

Energy density U After Legendre tr. W. r. t. to D Solution has generally two cusps at (north and south poles)

Meaning of ν : separation of outgoing flux (1 -ν)N strings νN strings :

Meaning of ν : separation of outgoing flux (1 -ν)N strings νN strings : for a unit string

ii) Quarks ; Add Strings (and No Force condition) • S=SD 5 +N SF

ii) Quarks ; Add Strings (and No Force condition) • S=SD 5 +N SF Strings rc Valence of tensions at the cusp at rc

No force condition at rc for a point (x’=0) baryon config. For D 5

No force condition at rc for a point (x’=0) baryon config. For D 5 : For SF :

4. Various solutions of D 5 Branes: G, Ishihara; 2008 G, Nakamura, Toyoda; 2009

4. Various solutions of D 5 Branes: G, Ishihara; 2008 G, Nakamura, Toyoda; 2009 G, Nakamura, Taminato, Toyoda; 2011

Numerical solution for Baryonium L

Numerical solution for Baryonium L

Tension of vertex Minimum Not clash

Tension of vertex Minimum Not clash

Construction of New Baryonic states

Construction of New Baryonic states

No force condition at θ=0 In r-x plane for extended D 5 vertex where

No force condition at θ=0 In r-x plane for extended D 5 vertex where At θ=π, similar condition is given

Important relation Exterior tension is stronger than inner one

Important relation Exterior tension is stronger than inner one

Penta Quark (for N=3) Consider a configuration of At θ=0 θ=π r=0 Infinite energy

Penta Quark (for N=3) Consider a configuration of At θ=0 θ=π r=0 Infinite energy Difficult to realize this type (Penta-Quark)

Possible multi-quark state For finite energy N+3 Quark state is possible Sample of numerical

Possible multi-quark state For finite energy N+3 Quark state is possible Sample of numerical results Hepta

Counting rule for baryonic states Mass of nq quark state Lowest energy of the

Counting rule for baryonic states Mass of nq quark state Lowest energy of the multiquark states

State with extended vertex : split type Energy is given by two kinds of

State with extended vertex : split type Energy is given by two kinds of tensions; 1. String 2. Vertex energy is approximated as τD 5=  For Hepta

In other models • We find the similar quark states and similar qualitative consequences

In other models • We find the similar quark states and similar qualitative consequences i) Non-susy background in IIB ii) Type IIA D 4 back ground model

5. Summary • • • Baryonic penta quark may be excluded Hepta quark is

5. Summary • • • Baryonic penta quark may be excluded Hepta quark is possible Baryonium –tetra quark state is stable Their mass obey the quark counting rule +vertex tension would be seen for extended vertex state (evidence of String theory)