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The charmonium -molecule hybrid structure of the X (3872)

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

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The charmonium -molecule hybrid structure of the X (3872)

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  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 D0 D*0-bar molecule • Coupling between C C-bar core state, D0 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. International Journal of Theoretical Physics International Journal of Theoretical Physics About X(3872) • First observation: 2003, Belle, KEKBcited more than 500 times • B- → K-π+π- J/ψ decaySharp peak of the invariant mass distribution of π+π- J/ψ • Mass: (3871.5 ± 0.19) MeV about 0.3 MeV below D0 D*0-bar thresold • Width: less than 3.0 MeV • Quantum Number: JPC = 1++ ? • Other decay mode:X(3872) → γ J/ψ、γψ(2S)X(3872) → π+π- π0 J/ψ

  4. B+ → K+ + J/ψ + ππ(π) 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 • Estimated energy of 2 3P1 cc-bar state by the potential model is 3950 MeV, which is about 80 MeV higher than the observed mass of X(3872). • If X(3872) is cc-bar state, it is isoscalar.X(3872) → ρ0 J/ψ → π+π- J/ψ : isovectorThis 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. Kerlinerand H. J. Lipkin, arXiv:1008.0203.K. Terasaki, Prog. Theor. Phys. 122:1205,2010.

  7. X(3872) as D0 D*0-bar Molecule • mD0 + mD*0 = (3871.81 ± 0.36) MeV • mX(3872) = (3871.50 ± 0.19) MeVX(3872) is a very shallow bound state of D0 D*0-bar: D0 D*0-bar Molecule

  8. Problem of X(3872) as D0 D*0-bar Molecule • D0 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, D0 D*- molecules • The production rate of such molecular-like state may be too small.

  9. Coupling between C C-bar core and D0 D*0-bar, D+ D*- • Structure of X(3872): cc-bar core state (charmonium) is coupling to D0 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 D0 D*0-bar, D+ D*- D0 D+ cc-bar core D*0-bar D*- . . . . . +

  11. Coupling between C C-bar core, D0 D*0-bar and D+ D*- • cc-bar core state: • D0 D*0-bar state : • D+ D*- state : in the center of mass frameq is the conjugate momentum of the relative coordinate

  12. Coupling between C C-bar core, D0 D*0-bar and D+ D*- • Charge conjugation + state is assumed • Interaction: Isospin symmetric

  13. Interaction between D0 and D*0bar, D+ and D*- D0 c c u-bar u-bar u u c-bar c-bar D*0-bar Like the σ-meson exchange No isospin symmetry breaking D+ c c d-bar d-bar d d c-bar c-bar D*-

  14. Interaction between D0 and D*0bar, D+ and D*- • Interaction:

  15. Diagram D0 D+ cc-bar core cc-bar core D*0-bar D*- . . . . . +

  16. Coupling between C C-bar core, D0 D*0-bar and D+ D*- • X(3872) is a mixed state: • Isospin base:Isospin symmetric case: c2 = c3 No isovector component

  17. Coupling between C C-bar core, D0 D*0-bar and D+ D*- • Schroedinger Equation

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

  19. Numerical results: Mass • Mass of the cc-bar core: 3.95 GeVfrom S. Godfrey, N. Isgur, Phys. Rev. D 32 (1985) 189. • Cutoff: 0.3GeV and 0.5 GeVLambda = 0.5 GeV, Calculated bound state energy is 3.871 GeV with coupling strength g = 0.0185 GeV3/2Lambda = 0.3 GeV, Calculated bound state energy is 3.871 GeV with coupling strength g = 0.0094 GeV3/2

  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? • mD0 + mD*0 = (3871.81 ± 0.36) MeV • mD+ + mD*- = (3879.89 ± 0.37) MeV • mX = 3871.5 MeV • Binding EnergyNeutral D case: 0.81 MeVCharged D case: 8.89 MeV Large difference

  22. Numerical results: Wavefunction • Lambda = 0.5 GeV rpsi(r) [GeV1/2] D+ D*- D0 D*0-bar r [fm]

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

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

  25. Numerical results: • Mass of the cc-bar core: 3.95 GeVfrom S. Godfrey, N. Isgur, Phys. Rev. D 32 (1985) 189. • Cutoff: 0.5 GeV & 1.0 GeV • Determination of the interaction strengthsFirst, we set λ=0, then gis fixed so as to reproduce mass of X(3872) to be3.8715 GeVThen, we change the value of gfrom 0.9g, 0.8g, 0.7g, … and determine the value of λ so as to reproduce mass of X(3872) to be3.8715 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 hadronsKinetic energy v.s. Potential energy • Bound state of two hadronsDeuteron • Heavier Hadron -> Smaller kinetic termAbout 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 ismeaningful as the core state.

  33. Discussion -X(3872)- • Large Isospinsymmetry breaking can be explained by the present picture • No observation of isospinmultiplet is clearly explained, since the intermediate isoscalarccbar state causes the attractive force between D and D*

  34. Discussion -X(3872)- • Production ratecompact ccbar component • Radiative decayCharmonium state is 2 3P1Easy to transit to ψ(2S) thanJ/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 psi(r) [GeV3/2] D+ D*- D0 D*0-bar r [fm]

  38. Numerical results: Wavefunction • Lambda = 0.3 GeV rpsi(r) [GeV1/2] D+ D*- D0 D*0-bar r [fm]

  39. Numerical results: Wavefunction • Lambda = 0.3 GeV psi(r) [GeV3/2] D+ D*- D0 D*0-bar r [fm]

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

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