1. Exotic charmed four-quark mesons: molecules versus compact states
A. Valcarce
University of Salamanca (Spain)
J. Vijande (U. Valencia)
Beijing, October 23rd, 2010
Exotic charmed four-quark states

2. Motivation: New open-charm and charmonium mesons
2800
DsJ mesons
Ds1
(2458)
DsJ*
(2317)
2600
D*K
2400
Open-charm mesons )
D0K V e M ( E
2200
2000
1800
Ok! – 1 – + 1 + 2 +
J.V., A.V. et al, Phys. Rev. D73, (2006)
Beijing, October 23rd, 2010
Exotic charmed four-quark states

3. Exotic charmed four-quark statesDD
3872
cc mass spectrum
X (3872), X (3940),Y (3940), Z (3940), Y(4140),...
More complicated (See J. Vijande talk on Thursday)
Charmonium
Simple color Fermi-Breit quark-antiquark scheme
R.L. Jaffe, Phys. Rev. D15, 267 (1977) =0
ccnn
Beijing, October 23rd, 2010
Exotic charmed four-quark states

4. Further evidences: light baryons
The effect of the admixture of hidden flavor components in the baryon sector has also been studied. With a 30% of 5q components a larger decay width of the Roper resonance has been obtained. 10% of 5q components improves the agreement of the quark model predictions for the octet and decuplet baryon magnetic moments. The admixture is for positive parity states and it is postulated. D. Riska et al., Nucl. Phys. A791, (2007)
From the spectroscopic point of view one would expect the effect of 5q components being much more important for low energy negative parity states (5q S wave)
S. Takeuchi et al., Phys. Rev. C76, (2007)
L(1405) [1/2–], QM 1500 MeV (L(1520) [3/2–])
=  |3q [(0s)20p]> +  |5q[(0s)5]>
=0; QCM Sp–NK–Lud  No resonance found
,   0  A resonance is found
OGE
T.-S.H. Lee et al., Phys. Rev. C 61, (2000)
E. Oset et al., Phys. Rev. Lett. 95, (2005)
Beijing, October 23rd, 2010
Exotic charmed four-quark states

5. Solving the Schrödinger equation: VM and HH
0.363
3861.4
0.367
3860.6
RMS E
L=0 S=1 I=0 ccnn – 1 2 3 1 2 3 4
1,2  c
3,4  n
ccnn
Hyperspherical Harmonics Method
J.V., A.V. et al., Phys. Rev. D79, (2009)
Variational Method
J. V., A.V., Symmetry 1, 155 (2009)
Pauli principle must be imposed.
Beijing, October 23rd, 2010
Exotic charmed four-quark states

6. 1 2 3 1 2 3 4 1,2  c 3,4  n ccnn Physical channels
J.Vijande, A.V., Phys. Rev. C80, (2009)
Beijing, October 23rd, 2010
Exotic charmed four-quark states 6

7. cncn. CQC model 4q Energy M1M2 threshold
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 + 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
Beijing, October 23rd, 2010
Exotic charmed four-quark states

8. Exotic charmed four-quark states
Bound
Unbound x z y 1 2 3 4
1,2  c
3,4  n
ccnn
Beijing, October 23rd, 2010
Exotic charmed four-quark states

9. 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
Beijing, October 23rd, 2010
Exotic charmed four-quark states

10. Exotic charmed four-quark states
No compact states in the ccnn sector (J. Vijande)
One compact state in the ccnn sector (JP=1+)
Which is the difference? c n –
ccnn
cncn D —
J/ w +
II. Is that all? NO!
Beijing, October 23rd, 2010
Exotic charmed four-quark states

11. Beyond the naive quark model
Diquark hypothesis: The idea is to restrict the Hilbert Space selecting those components that may favor the binding of the system. A diquark is an S-wave bound state of two quarks, antisymmetric in color (3), isospin (0) and spin (0).
I. For some quantum numbers this implies discarding a priori more than
90% of the basis vectors.
II. Numerically, these vectors account for less than 3% of the total
probability.
Application to four-quark states can be found in several papers by Maiani, F. Piccinini, and A.D. Polosa and also by D. Ebert, R.N. Faustov, and V.O. Galkin.
Many-body interactions: Three- or four-body interactions not factorizable into a sum of two-body terms could be playing a role.
Beijing, October 23rd, 2010
Exotic charmed four-quark states

12. Many-body forces in nuclear physics
AV18
(2B) 2H 3H
4He
CDBonn/TM
(3B) 2H 3H
4He
Beijing, October 23rd, 2010
Exotic charmed four-quark states

13. Many-body forces in the hadron spectra( ) a y x L V r
MIN MB ij j i B 46 . 5 2 3 4 21 1 8 16 23 14 24 13 34 12 + = ø ö ç è æ - å
< l a a x x x a
Beijing, October 23rd, 2010
Exotic charmed four-quark states

14. Beyond two-body interactions
J. V., A.V., J.M. Richard, Phys. Rev. D76, (2007)
Beijing, October 23rd, 2010
Exotic charmed four-quark states

15. Candidates for observation (QQnn).
Decay modes.
Electromagnetic:
E4q > M(D)+M(D)
Weak:
E4q < M(D)+M(D)
Charm Sector: ccnn
1: JP=1+: CQC: ΔE= –76,ΔR= Compact. Weak decay
I=0 BCN: ΔE= –7,ΔR~1 – 2. Molecular. γ decay
Bottom Sector: bbnn
1: JP=1+: CQC: ΔE= –214,ΔR= Compact. Weak decay
I=0 BCN: ΔE= –144,ΔR= Compact. Weak decay
2: JP=0+: CQC: ΔE= –149,ΔR= Compact. γ decay
I=0 BCN: ΔE= –52,ΔR= Compact. γ decay
3: JP=3 – : CQC: ΔE= –140,ΔR= Compact. γ decay
I= BCN: ΔE= –119,ΔR= Compact. γ decay
4: JP=1 – : CQC: ΔE= –11,ΔR ~1 – 2. Molecular. Weak decay
I=0
Beijing, October 23rd, 2010
Exotic charmed four-quark states

16. Exotic charmed four-quark states
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.
Hidden flavor components (unquenching the quark model) offer a possible explanation of the new experimental data and old problems in the meson and baryon spectra.
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: We have seen many different approaches to the new charmonium states, it would be great to have predictions for the exotic charmed meson states to be tested in the near future.
Beijing, October 23rd, 2010
Exotic charmed four-quark states