1. The charmonium-molecule hybrid structure of the X(3872) Makoto Takizawa (Showa Pharmaceutical Univ.) Sachiko Takeuchi (Japan College of Social Work) Kiyotaka Shimizu (Sophia University) International conference on the structure of baryons, BARYONS’10, Osaka, Japan. Dec. 8, 2010 Ref: M. Takizawa and S. Takeuchi, EPJ web of conference 3, (2010) 03026; Prog. Theor. Phys. Suppl. 186 (2010) 160.

2. Contents Problems of X(3872) as C C-bar state Problems of X(3872) as D 0 D* 0 -bar molecule Coupling between C C-bar core state, D 0 D* 0 -bar state and D + D *- state Interaction between D and D* Wavefunction and isospin symmetry breaking Energy spectrum Numerical results Discussion Summary

3. About X(3872) First observation: 2003, Belle, KEKB cited more than 500 times B - → K - π + π - J/ ψ decay Sharp peak of the invariant mass distribution of π + π - J/ ψ Mass: (3871.5 ± 0.19) MeV about 0.3 MeV below D 0 D *0 -bar thresold Width: less than 3.0 MeV Quantum Number: J PC = 1 ++ ? Other decay mode: X(3872) → γ J/ ψ 、 γψ (2S) X(3872) → π + π - π 0 J/ ψ International Journal of Theoretical Physics

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

5. Problems of X(3872) as C C-bar State 1. 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. 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. Is X(3872) isospin mixed state?

6. Isovector component is smaller than isoscalar component : 10~20% Estimation of isospin component from this value is an issue of the discussion D. Gamermann and E. Oset, Phys. Rev. D80:014003,2009. M. Kerliner and H. J. Lipkin, arXiv:1008.0203. K. Terasaki, Prog. Theor. Phys. 122:1205,2010.

7. X(3872) as D 0 D* 0 -bar Molecule m D0 + m D*0 = (3871.81 ± 0.36) MeV m X(3872) = (3871.50 ± 0.19) MeV X(3872) is a very shallow bound state of D 0 D* 0 -bar: D 0 D* 0 -bar Molecule

8. Problem of X(3872) as D 0 D* 0 -bar Molecule 1. D 0 D *0 -bar is 50% isovector and 50% isoscalar: Too big the isovector component 2. Why are there no charged X(3872)? D + D *0 -bar, D 0 D *- molecules 3. The production rate of such molecular- like state may be too small.

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

10. 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* - +.....

11. 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

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

13. Interaction between D 0 and D* 0bar, D + and D* - cc u-bar c-bar D0D0 D* 0 -bar cc d-bar c-bar D+D+ D* - u u d-bar d d Like the σ -meson exchange No isospin symmetry breaking

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

15. Diagram c c-bar core D* 0 -bar D0D0 D+D+ D* - +..... c c-bar core

16. Coupling between C C-bar core, D0 D*0-bar and D+ D*- 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

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

18. 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)

19. 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 3.871 GeV with coupling strength g = 0.0185 GeV 3/2 Lambda = 0.3 GeV, Calculated bound state energy is 3.871 GeV with coupling strength g = 0.0094 GeV 3/ 2

20. Numerical results: Wavefunction Lambda = 0.5 GeV Lambda = 0.3 GeV Large isospin symmetry breaking Cutoff dependence is small

21. Why so large isospin symmetry breaking? m D0 + m D*0 = (3871.81 ± 0.36) MeV m D+ + m D*- = (3879.89 ± 0.37) MeV m X = 3871.5 MeV Binding Energy Neutral D case: 0.81 MeV Charged D case: 8.89 MeV Large difference

22. Numerical results: Wavefunction Lambda = 0.5 GeV D 0 D *0 -bar D + D *- r [fm] r psi(r) [GeV 1/2 ]

23. Numerical results: Energy spectrum Lambda = 0.3 GeV GeVX(3872) bound state CC-bar state

24. Numerical results: Energy spectrum Lambda = 0.5 GeV GeVX(3872) bound state CC-bar state disappears

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 & 1.0 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 g / g (lambda=0)

27. Numerical results: X(3872) components Λ =0.5 GeV g / g (lambda=0)

28. Numerical results: X(3872) components Λ =1.0 GeV g / g (lambda=0)

29. Numerical results: X(3872) components Λ =1.0 GeV g / g (lambda=0)

30. Discussion Bound state of hadrons Kinetic energy v.s. Potential energy Bound state of two hadrons Deuteron Heavier Hadron -> Smaller kinetic term About 1 GeV mass (proton, neutron) -> bound state exists

31. Discussion Charm quark hadrons -> mass is bigger than 1 GeV Possibility of forming the bound states Bottom quark hadrons -> more probable Possibility of the exotic hadrons

32. Discussion -X(3872)- Quarkonium-hadronic molecule hybrid structure ー＞ new style of hadrons Properties of X(3872) can be explained by the charmonium-hadronic molecule structure, naturally Quark model result of the charmonium is meaningful as the core state.

33. Discussion -X(3872)- Large Isospin symmetry breaking can be explained by the present picture No observation of isospin multiplet is clearly explained, since the intermediate isoscalar cc bar state causes the attractive force between D and D*

34. Discussion -X(3872)- Production rate compact cc bar component Radiative decay Charmonium state is 2 3 P 1 Easy to transit to ψ (2S) than J/ ψ (need the calculation to confirm it)

35. Summary Charmonium-hadronic molecule hybrid structure can explain the observed properties of the X(3872) naturally.

36. Backup

37. Numerical results: Wavefunction Lambda = 0.5 GeV D 0 D *0 -bar D + D *- r [fm] psi(r) [GeV 3/2 ]

38. Numerical results: Wavefunction Lambda = 0.3 GeV D 0 D *0 -bar D + D *- r [fm] r psi(r) [GeV 1/2 ]

39. Numerical results: Wavefunction Lambda = 0.3 GeV D 0 D *0 -bar D + D *- r [fm] psi(r) [GeV 3/2 ]

40. Numerical results: cc-bar core in complex energy plane Λ =0.5 GeV