1. Structure of the exotic heavy mesons Makoto Takizawa (Showa Pharmaceutical Univ.) Collaborators Sachiko Takeuchi (Japan College of Social Work) Kiyotaka Shimizu (Sophia University) Heavy Quark Hadrons at J-PARC, Tokyo Institute of Technology, June 22, 2012 arXiv:1206.4877

2. Contents X(3872): experimental status -> Prof. Olsen’s talk X(3872): How exotic X(3872) is? Structure of the X(3872): Charmonium- hadronic molecule hybrid Z b1 and Z b2 Consistency between X(3872) and Z b

3. X(3872): experimental status First observation: 2003, Belle, KEKB Mass: (3871.57 ± 0.25) MeV (PDG 2011) 0.16 MeV below D 0 D *0 -bar thresold 3871.73MeV PDG2012 (3871.68 ± 0.17) MeV Charged B decays: (3871.4 ± 0.6 ± 0.1 ) MeV (BABAR) Neutral B decays: : (3868.7 ± 1.5 ± 0.4 ) MeV (BABAR) B decays: (3871.85 ± 0.27 ± 0.19 ) MeV (Belle) p p bar collisions: (3871.61 ± 0.16 ± 0.19 ) MeV (CDF) p p collisions: (3871.95 ± 0.48 ± 0.12 ) MeV (LHCB) Width: less than 1.2 MeV Quantum Number: J PC = 1 ++, 2 -+ ?

4. B + → K + + J/ψ + ππ(π) B + → X(3872) ＋ K + → J/ψ ＋ vector meson →π’s 11 Sep 2010 jps fall meeting @ 九州工業大学

5. X(3872) : How exotic X(3872) is? 1.Not CC bar Estimated energy of 2 3 P 1 c c-bar state by the potential model is 3950 MeV, which is about 80 MeV higher than the observed mass of X(3872). 1.Large isospin symmetry breaking If X(3872) is c c-bar state, it is isoscalar. X(3872) → ρ 0 J/ψ → π + π - J/ψ : isovector This decay means large isospin breaking.

6. (0.8 ± 0.3) by BABAR Isovector component is smaller than isoscalar component : 10~30% Estimation of isospin component from this value is an issue of the discussion

7. 3.Not D 0 D* 0 -bar Molecule D 0 D *0 -bar is 50% isovector and 50% isoscalar: Too big the isovector component Why are there no charged X(3872)? D + D *0 -bar, D 0 D *- molecules The production rate of such molecular-like state may be too small.

8. Charmonium D 0 D* 0 -bar, D + D *- molecule hybrid Structure of X(3872): c c-bar core state (charmonium) is coupling to D 0 D* 0 -bar and D + D *- states Effect of the isospin symmetry breaking is introduced by the mass differences between neutral and charged D, D* mesons

9. Coupling between C C-bar core and D 0 D* 0 -bar, D + D *- c c-bar core D* 0 -bar D0D0 D+D+ D* - +.....

10. Coupling between C C-bar core, D 0 D* 0 -bar and D + D *- cc-bar core state: D 0 D *0 -bar state : D + D *- state : in the center of mass frame q is the conjugate momentum of the relative coordinate

11. Coupling between C C-bar core, D 0 D* 0 -bar and D + D *- Charge conjugation + state is assumed Interaction: Isospin symmetric

12. Coupling between C C-bar core, D 0 D* 0 -bar and D + D *- X(3872) is a mixed state: Isospin base: Isospin symmetric case: c 2 = c 3 No isovector component

13. Coupling between C C-bar core, D 0 D* 0 -bar and D + D *- Schroedinger Equation

14. Numerical results: Mass Mass of the cc-bar core: 3.95 GeV from S. Godfrey, N. Isgur, Phys. Rev. D 32 (1985) 189. Cutoff: 0.3GeV and 0.5 GeV Lambda = 0.5 GeV, Calculated bound state energy is 3.87157 GeV with coupling strength g = 0.05115 Lambda = 0.3 GeV, Calculated bound state energy is 3.87157 GeV with coupling strength g = 0.05440

15. Numerical results: Wavefunction Lambda = 0.5 GeV, B.E. = 0.16 MeV Lambda = 0.3 GeV Large isospin symmetry breaking Cutoff dependence is small

16. Why so large isospin symmetry breaking? m D0 + m D*0 = 3871.73 MeV m D+ + m D*- = 3879.79 ± 0.37 MeV m X = 3871.57 MeV Binding Energy Neutral D case: 0.16 MeV Charged D case: 8.22 MeV Large difference

17. Numerical results: Wavefunction Lambda = 0.5 GeV, B.E. = 0.16 MeV

18. Case of m x = 3868.7 MeV from Neutral B decay data Lambda = 0.5 GeV, B.E. = 3.03 MeV

20. Energy spectrum We consider c c-bar core state is produced in the production process Transition strength S(E): B K E=Energy transfer X(3872)

21. Numerical results: Energy spectrum Lambda = 0.3 GeV, B.E. = 0.16 MeV X(3872) bound state CC-bar state

22. Numerical results: Energy spectrum Lambda = 0.5 GeV, B.E. = 0.16 MeV X(3872) bound state CC-bar state disappears

23. Interaction between D and D * c c-bar core D* 0 -bar D0D0 D+D+ D* - +..... c c-bar core

24. Interaction between D 0 and D* 0bar, D + and D* - Interaction:

25. Numerical results: Mass of the cc-bar core: 3.95 GeV from S. Godfrey, N. Isgur, Phys. Rev. D 32 (1985) 189. Cutoff: 0.5 GeV Determination of the interaction strengths First, we set λ=0, then g is fixed so as to reproduce mass of X(3872) to be 3.8715 GeV Then, we change the value of g from 0.9g, 0.8g, 0.7g, … and determine the value of λ so as to reproduce mass of X(3872) to be 3.8715 GeV

26. Numerical results: X(3872) components Λ=0.5 GeV, m X = 3.87157 GeV

27. Numerical results: X(3872) components Λ=0.5 GeV, m X = 3.87157 GeV

28. Numerical results: X(3872) components Λ=0.5 GeV, m X = 3.8687 GeV

29. Summary of X(3872) Charmonium- hadronic molecule haybrid Λ=0.5 GeV, B.E. = 3.03 MeV, g/g 0 = 0.5 7% cc-bar core: good for production rate size of the isospin symmetry breaking is OK no charged partnar of X(3872) because cc bar cannot couple to the charged state cc-bar core state: decay width is large -> not observed

30. ZbZb M(Z b1 ) = 10607.2 ± 2.0 MeV/c 2 Γ 1 = 18.4 ± 2.4 MeV BB *bar threshold: 10604 MeV/c 2 BB *bar molecule M(Z b2 ) = 10652.2 ± 1.5 MeV/c 2 Γ 2 = 11.5 ± 2.2 MeV B * B *bar threshold: 10650 MeV/c 2 B * B *bar molecule I G (J P ) = 1 + (1 + )

31. Interaction between B and B * is similar to that between D and D * because of the heavy quark symmetry In the case of X (3872), about 60% of the attraction is coming from coupling to cc bar core state and rest (40%) is interaction between D and D * -> JUST FOR Z b interaction -> Ohkoda-san’s talk yesterday

32. Charmonium above the open charm threshold exprimentally observed states are L >=1 decay modes Charmonium with L =0 open cham decay mode have not been observed