1. The 5-th International Conference on Quarks and Nuclear Physics
Meson-meson molecules and compact four-quark states
The 5-th International Conference on Quarks and Nuclear Physics
Beijing , September 21－26, 2009
A. Valcarce
University of Salamanca (Spain)
J. Vijande, N. Barnea, J.-M. Richard.
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2. Motivation: New open-charm and charmonium mesons
Heavy meson spectroscopy is the best example of the color Fermi-Breit structure of the heavy hadron spectra
The formerly comfortable world of heavy meson spectroscopy is being severely tested by new experiments
3872 DD
cc mass spectrum
Charmonium
X (3872), X (3940),Y (3940), Z (3940),
Y(4260),Y(4385), X(4664), Z (4430)+,...
Open charm
DsJ*(2317), DsJ(2460), D0*(2308),
DsJ(2632), DsJ*(2700), DsJ(2860), ...
meson-meson molecules, compact four-quark states
ccnn
cncn
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3. Solving the Schrödinger equation: (I) HH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.
Radial part is expanded into HH functions, hyperangular part, (up to a Kmax value) and a sum of Laguerre functions, hyperradial part.
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4. Solving the Schrödinger equation: (II) VM
The radial part is expanded in terms of generalized gaussians:
where a,b,c,d,e, and f are variational parameters
Each generalized gaussian contains an infinite number of relative angular momentum l1, l2, and l3, but it has L=0 and positive parity (can be generalized, not trivial) – –
L=0 S=1 I=0 ccnn HH VM E
RMS
3860.6
0.367
3861.4
0.363
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5. Bound states: Meson-meson molecules vs. Compact four-quark states
Figures of merit.
Physical channel: A vector of the Hilbert space whose quantum numbers allow to identify it with two physical mesons.
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6. Meson-meson molecules ...1 2 3 1 2 3 4
1,2  c
3,4  n
ccnn
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7. The four-quark zoo: what can we expect?
Unbound state (threshold ): An state with ΔE >0, ΔR → ∞, and whose wave-function comes determined in terms of a single physical channel.
Meson-meson molecule: An state with ΔE <0, ΔR finite ~1–2, and described dominantly in terms of a single physical channel.
Compact four-quark state: An state with ΔE <0, ΔR <1, and whose wave function contains several different physical channels.
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8. 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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9. Meson-meson molecules ...
cncn (I=0). CQC Model
4q Energy
Theoretical threshold
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10. Meson-meson molecules ...
cncn (I=0). BCN Model
4q Energy
Theoretical threshold
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11. cncn (I=0). BCN Model Experimental threshold Theorerical Thresholds 5!
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12. Meson-meson molecules ...
cncn. CQC Model
4q Energy
Theoretical threshold
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13. Thresholds
Uncoupled two-meson threshold: Impose L, S, J, I, P, C (when defined) conservation, and the spin-statistic theorem (when identical particles are considered).
Coupled two-meson threshold: Impose J, I, P, C (when defined) conservation, and the spin-statistic theorem (when identical particles are considered).
Uncoupled threshold ≥ Coupled threshold
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14. Meson-meson molecules ...
cncn. CQC Model
4q Energy
Uncoupled threshold
Coupled threshold
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15. Meson-meson molecules ...x z y 1 2 3 4
1,2  c
3,4  n
ccnn
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16. Meson-meson molecules ...x z y 1 2 3 4
1,2  c
3,4  n
ccnn
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17. Probability of physical channels vs. Binding energy
We multiply the interaction between the light quarks by a fudge factor. This modifies the 4q energy but not the threshold
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18. Behaviour of the radius
← Compact state
(1+ CQC)
← Molecular state
(1+ BCN)
← Unbound state
(0+ CQC)
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19. Meson-meson molecules ...
No compact states in the ccnn sector.
One bound state in the ccnn sector (and four/three bound states in the bbnn sector).
which is the difference?
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20. Meson-meson molecules ...– D —
J/ w + c n –
ccnn
cncn c n – D +
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21. Meson-meson molecules ...
No compact states in the ccnn sector.
One bound state in the ccnn sector (and four/three bound states in the bbnn sector).
which is the difference?
is that all?
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22. 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.
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23. Many-body forces in nuclear physics
AV18
(2B) 2H 3H
4He
CDBonn/TM
(3B) 2H 3H
4He
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24. 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
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25. Meson-meson molecules ...
Summary
There is an increasing interest in heavy 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 the predictions of QCD in what has been called the strong limit. There are enough data to learn about the glue holding quarks together inside the hadrons.
Hidden flavor components, unquenching the quark model, seem to be necessary to tame the bewildering landscape of hadrons, but an amazing folklore is borning around.
Compact four-quark states with non-exotic quantum numbers are hard to justify while “many-body (medium)” effects do not enter the game.
Meson-meson molecules seem to be present in the meson spectra.
Four-quark exotic systems should exist if our understanding of the dynamics does not hide some information. I hope experimentalists can answer this question to help in the advance of hadron spectroscopy.
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26. Beyond two-body interactions
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27. Subject for another talk
X(3872)
X,Y,Z(3940)
Y(4260)
Z+(4430)
DD|S(0++)
DD*|S(1++)
DSDS|S(0++)
DD1|S(1--)
D*D1|S(1--)
Subject for another talk
Charmonium
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28. 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
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