Transcript Document

Charmonium spectroscopy above thresholds
11th International Workshop on Meson
Production, Properties and Interaction
KRAKÓW, POLAND 10 - 15 June 2010
A. Valcarce
University of Salamanca (Spain)
T. Fernández-Caramés (U. Salamanca), J. Vijande (U. Valencia)
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Charmonium spectroscopy ...
1
Motivation: New charmonium (open charm) mesons
Below the DD threshold charmonium spectroscopy is a
good example of the simple color Fermi-Breit structure
of the heavy hadron spectra. Above this threshold new
experimental data indicate a more complicated situation.
Charmonium
3872
X (3872), X (3940),Y (3940), Z (3940), Y(4140),...
DD
Open charm
cc mass spectrum
Meson ( B 
=00)

qq
,
DsJ*(2317), DsJ(2460), D0*(2308),DsJ(2632), DsJ*(2700), ...
qqqq
R.L. Jaffe, Phys. Rev. D15, 267 (1977)
ccnn
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Charmonium spectroscopy ...
2
4600
4400
Z+(4430)
D*D1|S
4200
Y(4260)
DD1|S
E (MeV)
4000
3800
X,Y,Z(3940)
DsDs|S(0++)
DD*|S(1++)
X(3872)
DD|S(0++)
3600
3400
3200
3000
Charmonium
2800
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0+
1--
J++
Charmonium spectroscopy ...
1+
3
MULTIQUARK states , although stationary in a potential or bag, do not in general correspond to stable
hadrons or even resonances. Far from it, most, perharps even all, fall apart into valence mesons and
baryons without leaving more than a ripple on the meson-meson or meson-baryon scattering amplitude. If
the multiquark state is unsually light or sequestered from the scattering channel, it may be prominent. If
not, it is just a silly way of enumerating the states of the continuum.
c
+
–
c
cncn
–
n
+
ccnn
–
n
D
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n
–c
–n
–
c
n
––
cncn
—
D
D
c
c
w
J/
c
–n
n
+
c
c
–n
c
D
––
ccnn
Charmonium spectroscopy ...
–n
–n
4
Solving the Schrödinger equation: HH or VM
  Color Isospin  Spin  R 
ccnn
1
1
3
1
2
3
2
1,2  c

4
3,4  n
Color  312 334 , 612 634

Pauli principle must be imposed.
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JM
cncn
3
3
1
2
2
1,2  c
4
3,4  n
Color   112134 , 812834

C-parity is a good symmetry.
Charmonium spectroscopy ...
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Interacting potentials
-Confinement: Linear potential
BCN
-One-gluon exchange: Standard Fermi-Breit potential
Parameters determined on meson spectroscopy
-Confinement: Linear screened potential
CQC
-One-gluon exchange: Standard Fermi-Breit potential
Scale dependent as
- Boson exchanges: Chiral symmetry breaking
Not active for heavy quarks
Parameters determined on the NN interaction and meson/baryon spectroscopy
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Charmonium spectroscopy ...
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cncn. CQC model
4q Energy
Theoretical threshold
4500
4400
4300
E (MeV)
J. Vijande et al., Phys. Rev. D79, 074010 (2009)
4600
4200
4100
4000
3900
3800
0+
(28)
1+
(24)
2+
(30)
0
(21)
1
(21)
2
(21)
0+
(28)
1+
(24)
I=0
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2+
(30)
0
(21)
1
(21)
2
(21)
I=1
Charmonium spectroscopy ...
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cncn (I=0). BCN model
4q Energy
Theoretical threshold
4300
4200
4100
4000
3900
E (MeV)
J. Vijande et al., Phys. Rev. D76, 094022 (2007)
4400
3800
3700
3600
3500
3400
3300
3200
3100
0++
(24)
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0+ 
(22)
1++
(20)
1+ 
(22)
2++
(26)
2 +
(28)
1+
(19)
1
(19)
Charmonium spectroscopy ...
0+
(17)
0
(17)
2 +
(21)
2
(21)
8
Molecular vs. compact states
← Unbound state
1.8
(ΔE >0, ΔR → ∞, a single
physical channel)
1.6
 E  E4q  E(M1, M 2 )
1.4
R
R 
1.2
RMS4 q
RMSM1  RMSM 2
← Molecular state
(ΔE 0, ΔR finite ~1–2, a dominant single physical channel)
1
← Compact state
0.8
(ΔE <0, ΔR <1, several different physical channels)
0.6
0
4
8
12
16
20
24
K
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1
ccnn
3
y
x
z
2
1,2  c
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4
3,4  n
Charmonium spectroscopy ...
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Solving the Lippmann-Schwinger equation for the two meson system
(I)
(II)
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Coupled channels
[(cn)(nc)]
JPC (I)
(S,L)
[(c c) (nn)]
DD
0+ + (0)
(0,0)
c - 
1+ (+) (0)
(1,0),(1,2)
J/ - w
1+ (–) (1)
(1,0),(1,2)
J/ - 
0+ + (0)
(0,0),(2,2)
c - 
1+ – (0)
(1,0),(1,2)
c - w
1– – (0)
(0,1),(2,3)
J/ -
1– + (0)
(1,1),(1,3)
c - 
2+ + (0)
(2,0),(2,2)
J/ - w
2– – (0)
(1,1),(2,1),(1,3),(2,3)
c - w
0– + (1)
(0,0),(2,2)
J/ - 
1+ – (1)
(1,0),(1,2)
J/ - 
2+ + (1)
(2,0),(2,2)
J/ - 
DD*
(I)
D*D*
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Charmonium spectroscopy ...
(II)
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1
 DD*  DD* 
D+ =
2
1
 DD* +DD* 
D =
2
 C  D+  = + D+
 C  D  =  D
where for practical purposes we have used the convention
C  D = D
C  D*  =  D*
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Interacting potentials
-Confinement: Linear potential
BCN
-One-gluon exchange: Standard Fermi-Breit potential
Parameters determined on meson spectroscopy
-Confinement: Linear screened potential
CQC
-One-gluon exchange: Standard Fermi-Breit potential
Scale dependent as
- Boson exchanges: Chiral symmetry breaking
Not active for heavy quarks
Parameters determined on the NN interaction and meson/baryon spectroscopy
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Strange twobaryon systems
Charmonium spectroscopy ...
A. Valcarce et al., Eur. Phy. J. A37, 217 (2008)
H. Garcilazo et al., Phys. Rev. C76, 034001 (2007)
A. Valcarce et al., Rep. Prog. Phys. 68, 965 (2005)
Non-strange twobaryon systems
Heavy
baryons
15
T. Fernández-Caramés et al., Phys. Rev. Lett. 103, 222001 (2009)
JPC(I)=1++(0)
DD*
DD* – J/ w
X(3872)
No charge
JP=1+ partners
and I=1, of
coupled
the X(3872)
to J/ [diquark-antidiquark
 Repulsive ]
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D D – c 
D* D* – J/  
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Attractive channels for the
two D(Ds)-meson systems
R.Mizuk et al., Phys. Rev. D78, 072004 (2008)
System
DD
JPC(I)
0++(0)
DD*
1++(0)
D*D *
0++(0)
D*D *
2++(0)
D*D *
2++(1)
!
!
PRL67, 556 (1991) N.A. Törnqvist. PV and VV two-meson systems are the most natural candidates to be
bound, in spite of the different working framework.
Y(3940)  T. Branz et al. PRD 80, 054019 (2009). D*D* JPC(I)=0++ (0)[2++(0)]. Effective lagrangians.
[Y(3940) J/ w]> 1 MeV.
Y(4140)  T. Branz et al. PRD 80, 054019 (2009). D*sD*s JPC(I)=0++ (0)[2++(0)]. Effective lagrangians.
[Y(4140) J/ ]> 1 MeV.
R.M. Albuquerque et al. PLB 678, 186 (2009). D*sD*s JPC(I)=0++ (0). QCD sum rules.
G.-J. Ding. EPJC 64, 297 (2009). D*sD*s JPC(I)=0++ (0). One-boson exchange model.
Y(3940), Z(3940), X(4160)  R. Molina et al. PRD 80, 114013 (2009). D*D* D*sD*s JPC(I)=0++ (0),
2++(0). Dynamically generated resonances.
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Summary
• Hidden flavor components (unquenching the quark model) offer a possible
explanation of the new experimental data in heavy meson spectroscopy.
• Deeply-bound (compact) four-quark states with non-exotic quantum numbers
are hard to justify [while “many-body (medium)” effects do not enter the
game].
• Slightly bound (meson-meson molecules) four-quark states seem to be
present in the heavy meson spectra.
• PV: 1++ (0) are the candidate quantum numbers to lodge meson-meson
molecules for systems made of non-identical mesons [X(3872)].
• PP: 0++ (0) would the only candidate to lodge a broad meson-meson molecule
for systems made of identical pseudoscalar mesons.
• VV: 0++ (0) and 2++ (0,1) should show meson-meson molecules for systems
made of identical vector mesons [Y(3940),Y(4140)].
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