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: [hep-ph]
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)
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: A charmonium - molecule mixture ?
1) Choose the current: The X mass in QCD sum rules Assume that X is Sugiyama et al. PRD (2007)
2) Write the two-point correlation function: Write the hadronic side (phenomenological side):
Write the QCD side (OPE side): 4) Identify: 5) Apply Borel transform: 3) Perform the OPE:
6) Write the sum rule: Parameters : spectral density pole + continuum
7) Check the OPE convergence:
8) Check the pole dominance: 7) + 8) =Borel window
9) Compute the mass of X:
The X decay width : Calculate the couplings with QCDSR Maiani et al. PRD (2007)
Three-point correlation function: Currents: Assume that X is OPE side:
It is not a pure molecule of the type Sum rule: Phenomenological side: Divide the two sum rules:
It is not Assume that X is
Assume that X is :
Relation between the couplings : X can be the double mixture with
The X total decay width :
Conclusion
Back ups
Multiquark states Meson molecule Tetraquark QCD Sum Rules molecule tetraquark (no complete separation between tetraquarks and molecules)
X can be the double mixture with
XI HADRON PHYSICS March, , 2010, São Sebastião, Brazil
É difícil acreditar...
In QCD : No simple way to have KdV solitons ! There can be no preferred color ! Breaking waves !
Compute the Lagrangian, energy-momentum tensor and obtain the EOS : But we can estimate the Laplacian :