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									       X(3872) as a
charmonium-molecule mixture:
   mass and decay width

         R.D. Matheus, F. S. N. ,
         M. Nielsen and C.M. Zanetti



                   IF – USP
                    BRAZIL



  based on: arXiv:0907.2683 [hep-ph]
                    Introduction
                                                2.3 MeV
2003: discovery of X(3872) by BELLE




Is the X a new charmonium state ?


Mass does not agree with quark models!   Barnes, Godfrey, Swanson, (2005)
                                           Eichten, Lane, Quigg, (2006)


If it is a   cc
the decay violates isospin !


Probably not a pure quarkonium !
Is the X a D - D* molecule ?                      Tornqvist, (1994)
                                                  Braaten, Kusunoki,
                                                    PRD (2004)


Observed decay width is too small !

Observed production rate is too large !

Observed radiative decay rate is too large !


                                 
    BaBar, arXiv:0907.4575                     Swanson, PLB (2004)


Probably not a pure molecule !

       A charmonium - molecule mixture ?
     The X mass in QCD sum rules

  Assume that X is       cc   

1) Choose the current:

                                   Sugiyama et al.
                                    PRD (2007)
2) Write the two-point correlation function:




   Write the hadronic side (phenomenological side):
            Write the QCD side (OPE side):

               u u 2                            uu 
    ( q)           cos2 ( )  (2, 2) (q)         sin (2 )  (2, 4) (q)  sin 2 (2 )  (4, 4) (q)
              (6 2 ) 2                            (6 2 )




        3) Perform the OPE:




        4) Identify:            OPE
                               phen
                                     



        5) Apply Borel transform:                    Q2  M 2
6) Write the sum rule:

                         Parameters :


                         




                            spectral density

                             pole + continuum



                              s0  4.4 GeV
7) Check the OPE convergence:
8) Check the pole dominance:




                                   M 2  3.3 GeV 2




7) + 8) =                      Borel window
9) Compute the mass of X:
    The X decay width :

                                       V   ,

                                       F  2  , 3



     L  g XV     p X   V   Maiani et al.
                                        PRD (2007)




Calculate the couplings with QCDSR
Assume that X is

Three-point correlation function:




Currents:



OPE side:
  Phenomenological side:




  Sum rule:




  Divide the two sum rules:




It is not a pure molecule of the type
Assume that X is               cc     
             uu 
              cos ( )  c c   sin ( )  mol
                                                
             (6 2 )


                                                    0




It is not          cc    
Assume that X is :

| X   | c c   | D*0 D 0  D *0 D 0   | D* D   D * D  




                           y
      Relation between the couplings :




X can be the double mixture with
The X total decay width :
Conclusion
Back ups
             Multiquark states                cc qq


Meson molecule




Tetraquark




                                                 molecule
QCD Sum Rules
                                                 tetraquark

(no complete separation between tetraquarks and molecules)
  X can be the double mixture with

| X   | c c   | D*0 D 0  D *0 D 0   | D* D   D * D  
            XI HADRON PHYSICS
March, 22 - 27, 2010, São Sebastião, Brazil
É difícil acreditar...
     In QCD :




                                                          There can be no
                                                          preferred color !




No simple way to have KdV solitons !   Breaking waves !
But we can estimate the Laplacian :


                                  gV 2
                        2 V0     2
                                      B
                                  mV




Compute the Lagrangian, energy-momentum tensor and obtain the EOS :

								
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