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Structure of the exotic heavy mesons

Structure of the exotic heavy mesons. arXiv:1206.4877. 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 . Contents.

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Structure of the exotic heavy mesons

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  1. Structure of the exotic heavy mesons arXiv:1206.4877 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

  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 • Zb1 and Zb2 • Consistency between X(3872) and Zb

  3. X(3872): experimental status • First observation: 2003, Belle, KEKB Mass: (3871.57 ± 0.25) MeV (PDG 2011)0.16 MeV below D0 D*0-bar thresold 3871.73MeV PDG2012 (3871.68 ± 0.17) MeVCharged 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 pbar 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: JPC = 1++ , 2-+ ?

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

  5. X(3872) : How exotic X(3872) is? • Not CCbarEstimated energy of 2 3P1 c c-bar state by the potential model is 3950 MeV, which is about 80 MeV higher than the observed mass of X(3872). • Large isospin symmetry breakingIf X(3872) is c c-bar state, it is isoscalar.X(3872) → ρ0 J/ψ → π+ π- J/ψ : isovectorThis 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. Not 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.

  8. CharmoniumD0 D*0-bar, D+ D*- molecule hybrid • 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

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

  10. 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

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

  12. 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

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

  14. 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 3.87157 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? • mD0 + mD*0 = 3871.73 MeV • mD+ + mD*- = 3879.79 ± 0.37 MeV • mX = 3871.57 MeV • Binding EnergyNeutral D case: 0.16 MeVCharged D case: 8.22 MeV Large difference

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

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

  19. Lambda = 0.5 GeV, B.E. = 3.03 MeV

  20. 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)

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

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

  23. Interaction between D and D* D0 D+ cc-bar core cc-bar core D*0-bar D*- . . . . . +

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

  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 • 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, mX= 3.87157 GeV

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

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

  29. Summary of X(3872) • Charmonium- hadronic molecule haybridΛ=0.5 GeV, B.E. = 3.03 MeV, g/g0 = 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 ccbar cannot couple to the charged state • cc-bar core state: decay width is large -> not observed

  30. Zb • M(Zb1) = 10607.2 ± 2.0 MeV/c2Γ1 = 18.4 ± 2.4 MeVBB*bar threshold: 10604 MeV/c2BB*bar molecule • M(Zb2) = 10652.2 ± 1.5 MeV/c2Γ2 = 11.5 ± 2.2 MeVB*B*bar threshold: 10650 MeV/c2B*B*bar molecule • IG (JP) = 1+ (1+)

  31. Interaction between B and B*is similar to that between D and D* because of the heavy quark symmetryIn the case of X (3872), about 60% of the attraction is coming from coupling to ccbar core state and rest (40%) is interaction between D and D* -> JUST FOR Zb 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

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