1. Sixth International Conference on Quarks and Nuclear Physics
Exotic gifts of nature
Paris, April 18th, 2012
Exotic gifts of nature

2.
Paris, April 18th, 2012
Exotic gifts of nature

3. Starting point of a new era: 2003
X(3872)
<2.3 MeV
Ds0*(2317), JP=0+, <3.8 MeV
Ds1(2460), JP=1+,  < 3.5 MeV
Paris, April 18th, 2012
Exotic gifts of nature

4. Charmonium DD cc mass spectrum Molecular cc + molecular Hibrid
cc + Higher order Fock components DD
3872
cc mass spectrum
X (3872), X (3940),Y (3940), Z (3940), Y(4260 ),...
More complicated
Simple color Fermi-Breit quark-antiquark scheme
Si l a existencia de estos estado moleculares uno debe necesariamente estudiar lo que ocurre con los exoticos.
Paris, April 18th, 2012
Exotic gifts of nature

5. EXOTIC states will appear!
R.L. Jaffe, Phys. Rev. D15, 267 (1977)
= 0)
0+,1+,2+ (ℓi=0)
0+,1+,2+ (L=1)
Positive parity
0–,1– (ℓi0)
0–,1– (L=0)
Negative parity
qqqq (~ 4mq)
qq (~ 2mq)
L L MeV
qq MeV
Si l a existencia de estos estado moleculares uno debe necesariamente estudiar lo que ocurre con los exoticos.
EXOTIC states will appear!
Paris, April 18th, 2012
Exotic gifts of nature

6. The gift from nature to hadronic physicists!!
They cannot camouflage themselves among charmonium states
Paris, April 18th, 2012
Exotic gifts of nature

7. Solving the Schrödinger equation for QQnn1 2 3 1 2 3 4
1,2  c
3,4  n
ccnn
Expansion of the trial wave function in terms of HH functions
Generalize formalism of spherical harmonics (r, W)
Difficult to construct functions with proper symmetry
Solve Schrödinger equation with these base states.
CQC model for the interaction
Hyperspherical Harmonics Method
J.V., et al., Phys. Rev. D79, (2009)
The simplest system with a nontrivial color structure.
Being formed by identical quarks Pauli principle has to be imposed.
Paris, April 18th, 2012
Exotic gifts of nature

8. J.V., A.V., N. Barnea, Phys. Rev. D79, 074010 (2009)
cncn.
3800
3900
4000
4100
4200
4300
4400
4500
4600
4q Energy
M1M2 threshold ) V e M (
J.V., A.V., N. Barnea, Phys. Rev. D79, (2009) E
Decir que estos resultados se han hecho con modelos y los resultados son “independientes” de modelo. + 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
Paris, April 18th, 2012
Exotic gifts of nature

9. J.Vijande, A.V., Phys. Rev. C80, 035204 (2009)1 2 3 1 2 3 4
1,2  c
3,4  n
ccnn
Physical channels
J.Vijande, A.V., Phys. Rev. C80, (2009)
Paris, April 18th, 2012
Exotic gifts of nature 9

10. x z y 1 2 3 4 1,2  c 3,4  n ccnn Bound. Unbound.
Paris, April 18th, 2012
Exotic gifts of nature

11. Solving the Lippmann-Schwinger equation for the two meson systemII
Solving the Lippmann-Schwinger equation for the two meson system
Same interacting potential
as before
Y ahora todo esto se puede rehacer con grados de libertad hadronicos.
Paris, April 18th, 2012
Exotic gifts of nature

12. All positive parity channels up to JP=2+ have been analyzed.
Only one channel, (I) JP = (0) 1+, is attractive enough to be bound.
(I) JP = (0) 1+ D*
DD* ¬® D c n N NN ¬®
Paris, April 18th, 2012
Exotic gifts of nature

13. T. F. Caramés et al., Phys. Lett. B. 699, 291 (2011)
(I) JP = (0) 1+
(I)
(II)
Meson-meson states
Four-quark states
PDD*
PD*D*
PDD
Formalisms based on meson-meson and four-quark configurations are fully compatible if they incorporate all the relevants basis vectors (channels)!
Paris, April 18th, 2012
Exotic gifts of nature

14. Candidates for observation (QQnn).
Decay modes.
Electromagnetic:
E4q > M(D)+M(D)
Weak:
E4q < M(D)+M(D)
Charm Sector: ccnn
1: (I) JP= (0) 1+: ΔE≈ [ – 80, – 10] MeV → E ≈ 3800 – 3865 MeV
Bottom Sector: bbnn
1: (I) JP= (0) 1+: ΔE≈ [ -220, – 140] MeV → E ≈ – MeV
Decaying weak.
2: (I) JP= (0) 0+: ΔE≈ [ -150, – 50] MeV → E ≈ – MeV
Decaying electromagnetical.
3: (I) JP= (1) 3-: ΔE≈ [ -140, – 120] MeV → E ≈ – MeV
4: (I) JP= (0) 1-: ΔE≈ [ -10, 0] MeV → E ≈ – MeV
Paris, April 18th, 2012
Exotic gifts of nature

15. Paris, April 18th , 2012
Exotic gifts of nature

16. Summary
There is an increasing interest in hadron spectroscopy due to the advent of a large number of experimental data in several cases of difficult explanation.
These data provide with the best laboratory for studying QCD in the so-called strong limit. We have the methods, so we can learn about the dynamics.
Explicit exotic states with flavor components not reachable by standard quark-antiquark or three quark components are the best states to test our understanding of hadron spectroscopy
Experimentalists: Exotic charmed four-quark systems may exist if our understanding of the dynamics does not hide some information. I hope you can answer this question to help in the advance of hadron spectroscopy.
Theorists: All theoretical models agree on the existence of these kind of exotics. It is imperative to provide testable predictions in order to discriminate between models/approaches.
Paris, April 18th, 2012
Exotic gifts of nature

17. Paris, April 18th, 2012
Exotic gifts of nature

18. 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
Exotic gifts of nature

19. Charm mesons and charmonium
Light mesons
Strange meson
Charm mesons and charmonium
JV et al, J. Phys. G. 31, 481
Bottom mesons and bottomonium
Quarkonia properties at high temperatures
JV et al, Eur. Phys, Jour. A40, 89
Munich, June 16th, 2010
Exotic gifts of nature

20. Light baryons Heavy baryons Doubly Heavy baryons Strange baryons
JV et al., Phys. Rev. C72,
A. Valcarce et al., Eur. Phy. J. A37, 217
Doubly Heavy
baryons
Strange baryons
JV et al., Phys. Rev. D70,
Exotic gifts of nature

21. Ligth scalars cccc states Dsj Bsj Exotic gifts of nature
N. Barnea et al., Phys. Rev. D73,
JV et al., Phys. Rev. D72,
Dsj
Bsj
JV et al., Phys. Rev. D73,
JV et al., Phys. Rev. D77,
Exotic gifts of nature

22. Non-strange two- baryon systems Strange two- baryon systems S=-2 two-
A. Valcarce et al., Rep. Prog. Phys. 68, 965 (2005)
H. Garcilazo et al., Phys. Rev. C76, (2007)
Strange two-
baryon systems
Predictions
A. Valcarce et al., Unpublished
S=-2 two-
baryon systems
Exotic gifts of nature

23. Exotic gifts of nature

24. P. Gonzalez et al.
qqq+MB
Pure qqq
Exotic gifts of nature

25. Exotic gifts of nature

26. Molecular states: Probability of physical channels vs. binding energyx z y 1 2 3 4
1,2  c
3,4  n
ccnn
We multiply the interaction between the light quarks by a fudge factor. This modifies the 4q energy but not the threshold
Exotic gifts of nature

27. J. Vijande et al., Phys. Rev. D79, 074010 (2009)
cncn (I=0).
Theorerical Thresholds
No deeply bound (compact) states in the ccnn sector.
J. Vijande et al., Phys. Rev. D79, (2009)
Exotic gifts of nature

28. + One compact state in the ccnn sector Which is the difference?
No compact states in the ccnn sector
One compact state in the ccnn sector
Which is the difference? c n –
ccnn
cncn D —
J/ w +
Exotic gifts of nature

29. Solving the Lippmann-Schwinger equation for the two meson system
(II)
Exotic gifts of nature

30. 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
Exotic gifts of nature