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D D production and their interactions

D D production and their interactions. 刘言锐 Tokyo Institute of Technology. April 18, 2010 Nanchang University. Collaborators. Content. Introduction D D interactions and their production: e^+ e^- → D D Information from B B production Discussion and conclusion. Quark model & QCD.

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D D production and their interactions

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  1. DD production and their interactions 刘言锐 Tokyo Institute of Technology April 18, 2010 Nanchang University

  2. Collaborators

  3. Content • Introduction • DD interactions and their production: e^+ e^- → DD • Information from BB production • Discussion and conclusion

  4. Quark model & QCD • Quark model: • Successful, spectra • Phenomenology model: constitute quarks • Exceptions: Exotic states (qqqq, qqqqq, ...) • u: ~350 MeV c: ~1.5 GeV t: • d: ~350 MeV s: ~500 MeV b: ~4.5 GeV • QCD: • Underlying theory of the strong interaction • Fields: current quarks, gluons • u: 1.5~3.3 MeV, c: 1.27 GeV, t: 171.2 GeV • d: 3.5~6.0 MeV, s: 104 MeV, b: 4.2 GeV • States in QCD: • qq,qqq,qqqq,qqqqq,qqg,qqqg, gg,... • (meson,baryon,multiquark,hybrid,glueball)

  5. Exotic XYZ states(contain cc quarks): challenging quark model Borrow from S.Godfrey, arXiv: 0910.3409

  6. Understanding XYZ Interpretations: 1. Non cc mesons: tetraquark, molecule, hybrid， ... 2. cc+high Fock states/couple channel 3. Cusp, threshold effects, dynamical generated states，... Molecular picture: X(3872): D^0D^{0*} (3871.2 MeV) + ρJ/ψ(3872.42 MeV) + D^+D^-*(3875 MeV) + ωJ/ψ(3879.54 MeV) Y(3940): Ds^+Ds^- Y(4260): DD_0^* ... Possible heavy quark meson-meson bound states: DD*? DD? D*D*? Ds^+Ds^-? ...

  7. DD interactions • D meson: • 1. M=1869.62 MeV • 2. cu,cd • 3. J^P=0^- • DD pair: • 1. The simplest hidden charm system • 2. J^{PC}=0^{+ +}, 1^{- -}, 2^{+ +}, etc. • 3. No S-D mixing, no contact interaction • 4. Bound state: not excluded yet • Purpose I: • Bound state problem, partial wave scattering

  8. Anomalous lineshape in e^+ e^- →Hadrons • BES data: PRL 101, 102004 (2008)

  9. Similar lineshape in e^+ e^- →DD • Purpose II: • DD rescattering effect ? BES data: PLB 668, 263 (2008)

  10. DD interactions:

  11. DD interactions: one-meson-exchange model • m: exchanged meson mass, Λ: cutoff • (βg_V)=5.22, δ: phase shift

  12. DD interactions: binding energy • Finite Λ: 0.8, 1.0, 1.2, 1.5, 2.0 GeV

  13. DD interactions:S wave δ & σ • m_sigma=600 MeV • Binding solution sensitive to Λ • σ(E=0)=4π(scattering length)^2

  14. DD interactions:P wave δ & σ • No binding solution • Bump

  15. DD interactions: scattering length & volume S-wave scattering length (unit: fm) P-wave scattering volume (unit: fm^3)

  16. DD interactions:total cross section • σ_{tot}=σ_{L=0}+σ_{L=1} • No bump • Line shape is similar to that of σ_{L=0}

  17. Rescattering effect:schematic diagram • P wave DD

  18. Rescattering effect:separable potential • V_int: V_σ+V_ρ+V_ω • β, B: reproduce the calculated P wave phase shifts and cross sections • λ: expressed by a_1 (scattering volume), β, and B • Multiple scattering • ================================================ • σ_{prod}=σ_1 + σ_2 • σ_1: part without rescattering • σ_2: rescattering part

  19. Rescattering effect: production parameters • g_{ψDD}: from Br(ψ→ D D) • f_ψ: from Γ_{ee} • φ: relative phase • F_0: fitting parameter • M.Z. Yang, Mod. Phys. Lett. A 23, 3113 (2008).

  20. DD production: reproduced phase shift • m_σ=600 MeV, Λ=0.8 GeV m_σ=400 MeV, Λ=2.0 GeV

  21. DD production:obtained cross section • m_σ=600 MeV, Λ=0.8 GeV m_σ=400 MeV, Λ=2.0 GeV • No anomalous line shape • BES data: PLB 668, 263 (2008)

  22. DD production:an extreme case • phase shift production cross section • Anomalous line shape appears • BUT: a_1= 2 fm^3 too large, not realistic

  23. Information from BB production: • P wave bound state/resonance relys on Λ • If no P wave bound state/resonance → upper limit of Λ

  24. Information from BB production: P wave phase shifts • m_σ=600 MeV, Λ=2.0 GeV m_σ=400 MeV, Λ=2.0 GeV • (sharp resonance) (shallow bound state)

  25. Information from BB production: cross section • m_σ=600 MeV, Λ=2.0 GeV m_σ=400 MeV, Λ=2.0 GeV • (sharp resonance) (shallow bound state) • Anomalous line shape

  26. Information from BB production: BaBar data • PRL102, 012001 (2009) • Line shape → Λ<2.0 GeV • Further calculation → Λ<1.7 GeV

  27. Discussion • 1. Bound state problem, scattering problem, production • problem with FSI, sensitive to Λ • 2. Rescattering may affect the line shape of the • production cross section • 3. Difficult to understand the BES measurements • with this mechanism. • 4. With Λ_{DD}～Λ_{BB} < 1.7 GeV, • binding energy:<10 MeV (DD),< 100 MeV (BB) • 5. Approach may be applied to other systems: • D^*D^*, DD^*, ... • 6. Future measurement/lattice simulation for the S • and P wave phase shifts, scattering length and • scattering volume may provide more information.

  28. Conclusion 1. The existence of DD bound state is still not excluded 2. Difficult to understand BES anomalous line shapes with the rescattering mechanism 3. A way of extracting information from P wave production 谢谢！

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