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]

Introduction

2003: discovery of X(3872) by BELLE

MeV3.2

Probably not a pure quarkonium !

the decay violates isospin !

ccIf 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:0907.4575

A charmonium - molecule mixture ?

1) Choose the current:

The X mass in QCD sum rules

cc 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:OPEphen

5) Apply Borel transform: 22 MQ

)()2(sin)()2(sin)26(

)()(cos)26(

)( )4,4(2)4,2()2,2(2

2

2

qquu

quu

q

3) Perform the OPE:

6) Write the sum rule:

Parameters :

spectral density

pole + continuum

GeVs 4.40

7) Check the OPE convergence:

8) Check the pole dominance:

22 3.3 GeVM

7) + 8) = Borel window

9) Compute the mass of X:

The X decay width :

Calculate the couplings with QCDSR

,V

3,2F

VXpgL VX 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:

cc

0

It is not cc

Assume that X is

molccuu

)(sin)(cos

)26(

DDDDDDDDccX **00*00* ||||

Assume that X is :

y

Relation between the couplings :

X can be the double mixture with

The X total decay width :

Conclusion

Back ups

Multiquark states

qqcc

Meson molecule

Tetraquark

QCD Sum Rulesmolecule

tetraquark

(no complete separation between tetraquarks and molecules)

DDDDDDDDccX **00*00* ||||

X can be the double mixture with

XI HADRON PHYSICSMarch, 22 - 27, 2010, São Sebastião, Brazil

É difícil acreditar...

In QCD :

No simple way to have KdV solitons !

There can be no preferred color !

Breaking waves !

BV

V

m

gV 2

202

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

But we can estimate the Laplacian :