1. Charmonium spectroscopy above thresholds
11th International Workshop on Meson Production, Properties and Interaction
KRAKÓW, POLAND June 2010
A. Valcarce
University of Salamanca (Spain)
T. Fernández-Caramés (U. Salamanca), J. Vijande (U. Valencia)
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Charmonium spectroscopy ...

2. Motivation: New charmonium (open charm) mesonsDD
3872
cc mass spectrum
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.
X (3872), X (3940),Y (3940), Z (3940), Y(4140),...
Charmonium
Open charm
DsJ*(2317), DsJ(2460), D0*(2308),DsJ(2632), DsJ*(2700), ...
R.L. Jaffe, Phys. Rev. D15, 267 (1977) =0
ccnn
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Charmonium spectroscopy ...

3. Could these new mesons be deeply bound four quark states?
X(3872)
X,Y,Z(3940)
Y(4260)
Z+(4430)
DD|S(0++)
DD*|S(1++)
DsDs|S(0++)
DD1|S
D*D1|S
Could these new mesons be deeply bound four quark states?
If not, could they be meson-meson molecular states?
Charmonium
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Charmonium spectroscopy ...

4. Charmonium spectroscopy ...
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 n –
ccnn
cncn D —
J/ w +
cncn
ccnn
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Charmonium spectroscopy ...

5. Solving the Schrödinger equation: HH or VM1 2 3 1 2 3 4
1,2  c
3,4  n
ccnn 1 2 3 1 2 3 4
1,2  c
3,4  n
cncn
C-parity is a good symmetry.
Pauli principle must be imposed.
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Charmonium spectroscopy ...

6. Interacting potentials
Parameters determined on meson spectroscopy
BCN
Confinement: Linear potential
One-gluon exchange: Standard Fermi-Breit potential
Confinement: Linear screened potential
One-gluon exchange: Standard Fermi-Breit potential
Scale dependent as
Boson exchanges: Chiral symmetry breaking
Not active for heavy quarks
CQC
Parameters determined on the NN interaction and meson/baryon spectroscopy
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Charmonium spectroscopy ...

7. cncn. CQC model 4q Energy Theoretical threshold
3800
3900
4000
4100
4200
4300
4400
4500
4600
4q Energy
Theoretical threshold ) V e M (
J. Vijande et al., Phys. Rev. D79, (2009) E + 1 + 2 + - 1 - 2 - + 1 + 2 + - 1 - 2 - ( 2 8 ) ( 2 4 ) ( 3 ) ( 2 1 ) ( 2 1 ) ( 2 1 ) ( 2 8 ) ( 2 4 ) ( 3 ) ( 2 1 ) ( 2 1 ) ( 2 1 ) I = I = 1
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Charmonium spectroscopy ...

8. No deeply bound (compact) states in the ccnn sector.
cncn (I=0). BCN model
4q Energy
Theoretical threshold
No deeply bound (compact) states in the ccnn sector.
J. Vijande et al., Phys. Rev. D76, (2007)
What about molecular states?
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Charmonium spectroscopy ...

9. Molecular vs. compact states
← Molecular state
(ΔE 0, ΔR finite ~1–2, a domi-
nant single physical channel)
← Unbound state
(ΔE >0, ΔR → ∞, a single
physical channel)
← Compact state
(ΔE <0, ΔR <1, several diffe-
rent physical channels)
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Charmonium spectroscopy ...

10. Charmonium spectroscopy ...x z y 1 2 3 4
1,2  c
3,4  n
ccnn
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Charmonium spectroscopy ...

11. Solving the Lippmann-Schwinger equation for the two meson system
(II)
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Charmonium spectroscopy ...

12. Charmonium spectroscopy ...
Coupled channels
[(cn)(nc)]
JPC (I)
(S,L)
[(c c) (nn)] DD
0+ + (0)
(0,0)
c - 
DD*
1+ (+) (0)
(1,0),(1,2)
J/ - 
1+ (–) (1)
J/ - 
D*D*
(0,0),(2,2)
1+ – (0)
c - 
1– – (0)
(0,1),(2,3)
J/ -
1– + (0)
(1,1),(1,3)
2+ + (0)
(2,0),(2,2)
2– – (0)
(1,1),(2,1),(1,3),(2,3)
0– + (1)
1+ – (1)
J/ - 
2+ + (1)
(I)
(II)
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Charmonium spectroscopy ...

13. where for practical purposes we have used the convention
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Charmonium spectroscopy ...

14. Interacting potentials
Parameters determined on meson spectroscopy
BCN
Confinement: Linear potential
One-gluon exchange: Standard Fermi-Breit potential
Confinement: Linear screened potential
One-gluon exchange: Standard Fermi-Breit potential
Scale dependent as
Boson exchanges: Chiral symmetry breaking
Not active for heavy quarks
CQC
Parameters determined on the NN interaction and meson/baryon spectroscopy
25 February, 2019
Charmonium spectroscopy ...

15. Heavy baryons Non-strange two- Strange two- baryon systems
A. Valcarce et al., Eur. Phy. J. A37, 217 (2008)
Heavy
baryons
Non-strange two-
baryon systems
A. Valcarce et al., Rep. Prog. Phys. 68, 965 (2005)
H. Garcilazo et al., Phys. Rev. C76, (2007)
Strange two-
baryon systems
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Charmonium spectroscopy ...

16. No charge partners of the X(3872) [diquark-antidiquark]
DD*
DD* – J/ 
JPC(I)=1++(0)
T. Fernández-Caramés et al., Phys. Rev. Lett. 103, (2009)
X(3872)
No charge partners of the X(3872) [diquark-antidiquark]
JP=1+ and I=1, coupled to J/   Repulsive
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Charmonium spectroscopy ...

17. Charmonium spectroscopy ...
D D – c 
D* D* – J/  
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Charmonium spectroscopy ...

18. ! ! System JPC(I) DD 0++(0) DD* 1++(0) D*D* 2++(0) 2++(1)
Attractive channels for the two D(Ds)-meson systems !
R.Mizuk et al., Phys. Rev. D78, (2008)
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, (2009). D*D* JPC(I)=0++ (0)[2++(0)]. Effective lagrangians.
[Y(3940) J/ ]> 1 MeV.
Y(4140)  T. Branz et al. PRD 80, (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, (2009). D*D* D*sD*s JPC(I)=0++ (0), 2++(0). Dynamically generated resonances.
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Charmonium spectroscopy ...

19. Charmonium spectroscopy ...
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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Charmonium spectroscopy ...