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 :