1. Relating holographic QCD models to hidden local symmetry models Property of X(3872) as a hadronic molecule with negative parity Masayasu Harada “New Hadons” Workshop 2010 @RIKEN (February 28, 2011) MH, S.Matsuzaki, K.Yamawaki, PRD82, 076010 (2010) MH and M. Rho,. arXiv:1010.1971 MH and Y.L. Ma, arXiv:1010.3607

2. Relating Holographic QCD Models to Hidden Local Symmetry Models MH, S.Matsuzaki, K.Yamawaki, PRD82, 076010 (2010) MH and M. Rho,. arXiv:1010.1971

3. ◎ A possible V-A mixing term violates charge conjugation but conserves parity generates a mixing between transverse  and A 1 ☆ Motivation : V-A mixing in dense baryonic matter M.H. and C.Sasaki, Phys. Rev. C 80, 054912 (2009) ◎ Dispersion relations  meson A 1 meson

4. ☆ Determination of mixing strength C ◎ An estimation from  dominance e-e- e+e+ A1  ρ + C  ～ 0.1 GeV × (n B / n 0 ) n 0 : normal nuclear matter density ◎ An estimation in a holographic QCD (AdS/QCD) model ・ Infinite tower of vector mesons ( ,  ’,  ”, …) in AdS/QCD models ・ These effects of infinite  mesons can generate V-A mixing ・ This summation was done in an AdS/QCD model S.K.Domokos, J.A.Harvey, PRL99 (2007) a very rough estimation

5. Can infinite tower of  mesons contribute ? This is related to a long-standing problem of QCD not clearly understood: Why does the  /  meson dominance work well ? ・ In our works, MH, S.Matsuzaki, K.Yamawaki, PRD82, 076010 (2010) MH and M. Rho,. arXiv:1010.1971 we developed ways to relate holographic models to hidden local symmetry (HLS) models for pi and rho for handling infinite number of vector mesons.

6. Example 1:  EM form factor In Sakai-Sugimoto model infinite tower of  mesons contributes. k=1 :  meson k=2 :  ’ meson k=3 :  ” meson … = 1.31 + (-0.35) + (0.05) + (-0.01) + … ’’   ’’  ’’’  meson dominance ⇒ ; In the Hidden Local Symmetry  EM form factor is parameterized as ・ Reduction of Sakai-Sugimoto model ⇒

7. Example 1:  EM form factor  meson dominance  2 /dof = 226/53=4.3 ; SS model :  2 /dof = 147/53=2.8 best fit in the HLS :  2 /dof=81/51=1.6 Exp data : NA7], NPB277, 168 (1996) J-lab F(pi), PRL86, 1713(2001) J-lab F(pi), PRC75, 055205 (2007) J-lab F(pi)-2, PRL97, 192001 (2006) Infinite tower works well as the  meson dominance ! MH, S.Matsuzaki, K.Yamawaki, PRD82, 076010 (2010) cf : MH, K.Yamawaki, Phys.Rept 381, 1 (2003)

8. Example 2:  transition form factor MH, S.Matsuzaki, K.Yamawaki, arXiv:1007.4715 cf : MH, K.Yamawaki, Phys.Rept 381, 1 (2003) best fit in the HLS :  2 /dof=24/30=0.8 Sakai-Sugimoto model :  2 /dof=45/31=1.5  meson dominance :  2 /dof=124/31=4.0

9. Example 3: Proton EM form factor M.H. and M.Rho, arXiv:1010.1971 [hep-ph]  meson dominance :  2 /dof=187 best fit in the HLS :  2 /dof=1.5 a = 4.55 ; z = 0.55 Violation of  /  meson dominance may indicate existence of the contributions from the higher resonances. Contribution from heavier vector mesons actually exists in several physical processes even in the low-energy region Sakai-Sugimoto: Hong-Rho-Yi-Yee model :  2 /dof=20.2 a = 3.01 ; z = -0.042

10. Property of X(3872) as a Hadronic Molecule with Negative Parity MH and Y.L. Ma, arXiv:1010.3607

11. X(3872) was first observed by Belle Collaboration: S. K. Choi et al. [Belle Collaboration], Phys. Rev. Lett.91, 262001 (2003) [arXiv: hep-ex/0309032]. Confirmed by the CDF, the D0 and the BaBar. Possible structures for X(3872)  Hybrid state, F.E.Close ;B.A.Li,…  Tetraquark state, J.Vijande, …  Chrmonium-molecule mixing state, E.Braaten, Y.b.Dong, S.Takeuchi,...  Molecular state with J PC = 1 ++, N.A.Tornqvist, Y.b.Dong, M.B.Voloshin, E.S.Swanson, Y.L. Ma, …… ☆ Observation of X(3872)

12. ☆ Recent Observation of X(3872) BaBar ; arXiv:1005.5190 The 3π mass distribution strongly favors P-wave ⇒ J PC = 2 -+ In our work, we regard X(3872) with J PC =2 -+ as DD* molecule, and study its properties.

13. ◎ Good point for J PC = 2 -+ Is explained naturally. ( no need of large isospin violation ) from phase space factor ⇒ X(3872) is dominantly I = 0 state. ◎ Bad point : J = 2 ⇒ DD* with L = 1 ・・・ L = 0 bound state ? We do not specify the origin of binding force, And just assume that X(3872) is L = 1 bound state.

14. ☆ Wave function of X(3872) as a DD* molecule ☆ Compositeness Condition = 0 m X input ⇒ A relation between φ and Λ X

15. ☆ Fit φ = 9 degree X = 99% ( I = 0 state) + 1% ( I = 1 state ) ☆ A typical prediction