1. R.D. Matheus, F. S. N., M. Nielsen and C.M. Zanetti IF – USP BRAZIL based on: X(3872) as a charmonium-molecule mixture: mass and decay width arXiv:0907.2683 [hep-ph]

2. Introduction 2003: discovery of X(3872) by BELLE Probably not a pure quarkonium ! the decay violates isospin ! If it is a Is the X a new charmonium state ? Mass does not agree with quark models! Barnes, Godfrey, Swanson, (2005) Eichten, Lane, Quigg, (2006)

3. Probably not a pure molecule ! Observed decay width is too small ! Is the X a D - D* molecule ? Observed production rate is too large ! Observed radiative decay rate is too large ! Swanson, PLB (2004) Tornqvist, (1994) Braaten, Kusunoki, PRD (2004) BaBar, arXiv:0907.4575 A charmonium - molecule mixture ?

4. 1) Choose the current: The X mass in QCD sum rules Assume that X is Sugiyama et al. PRD (2007)

5. 2) Write the two-point correlation function: Write the hadronic side (phenomenological side):

6. Write the QCD side (OPE side): 4) Identify: 5) Apply Borel transform: 3) Perform the OPE:

7. 6) Write the sum rule: Parameters : spectral density pole + continuum

8. 7) Check the OPE convergence:

9. 8) Check the pole dominance: 7) + 8) =Borel window

10. 9) Compute the mass of X:

11. The X decay width : Calculate the couplings with QCDSR Maiani et al. PRD (2007)

12. Three-point correlation function: Currents: Assume that X is OPE side:

13. It is not a pure molecule of the type Sum rule: Phenomenological side: Divide the two sum rules:

14. It is not Assume that X is

15. Assume that X is :

16. Relation between the couplings : X can be the double mixture with

17. The X total decay width :

18. Conclusion

19. Back ups

21. Multiquark states Meson molecule Tetraquark QCD Sum Rules molecule tetraquark (no complete separation between tetraquarks and molecules)

22. X can be the double mixture with

25. XI HADRON PHYSICS March, 22 - 27, 2010, São Sebastião, Brazil

27. É difícil acreditar...

28. In QCD : No simple way to have KdV solitons ! There can be no preferred color ! Breaking waves !

29. Compute the Lagrangian, energy-momentum tensor and obtain the EOS : But we can estimate the Laplacian :