1. Charm2010 4TH International Workshop on Charm Physics
Unquenched Quark Model Description of Charmonium
P. González Universitat de València and IFIC (SPAIN)

2. 15 new charmonium states from PDG 00
Motivation
15 new charmonium states from PDG 00
K. Nakamura et al. (PDG)
JPG 37, (2010)

3. Why a Quark Model description ?
Lattice-QCD: Charmonium
C. Ehmann, G. Bali, PoS LAT 2007: 094 (2007)

4. T. Burch et al., PRD 81, (2010)

5. Effectively Unquenched Quark Models may describe with precision the High Excited Meson Spectrum.

6. INDEX
Hadrons: QCD bound states.
Quark Model Static Approach.
Static Potential.
Static Spectrum.
Highly excited light-quark mesons: results.
Heavy Quarkonia: testable predictions.
Summary.

7. 1. Hadrons: QCD bound states
MESONS
Bethe-Salpeter Equation

8. 2. Quark Model Static Approach
Bethe-Salpeter Equation
Static approximation in the kernel

9. Schrödinger Equation Fully non-relativistic approach
Non Relativistic Quark Models (NRQM)

10. Spinless Salpeter equation
(Neglecting spin and the coupling of the large-large and small-small components)
SemiRelativistic Quark Models (SRQM)
: Mass of the meson
: Static potential
The Static Approximation means that the time scale for the relative movement of the constituent quark and antiquark is much larger than the associated with gluons whose effect can be represented by an average instantaneous quark-antiquark interaction: the Static Potential.

11. 3. Static Potential One Gluon Exchange (OGE) Interaction from QCD
Running coupling :

12. Schwinger-Dyson Equation
Running Coupling
Schwinger-Dyson Equation
J. Papavassiliou and J. M. Cornwall, Phys. Rev. D44, 1285 (1991) +

13. Quenched Static OGE Potential from QCD
Coulombic
Linear
Richardson Potential

14. Static potential from Lattice - QCD
The Static Potential is defined as the energy of the ground state of two interacting static sources in terms of their separation distance r.

15. Quenched Potential (valence quarks)
G. S. Bali, Phys. Rep. 343, 1 (2001)
Cornell potential:
Good description of heavy quarkonia below the threshold for OZI allowed decay to open heavy flavor mesons.
E. Eichten et al., Phys. Rev. D 21, 203 (1980)

16. Mixing Effects
For large-sized mesons the static quark and antiquark sources are screened by light pairs that pop out of the vacuum: mixing with two meson-like components and string breaking.
G. S. Bali et al., Phys. Rev. D 71, (2005)

17. Unquenched Static OGE Potential from QCD
Coulombic
Coulombic ?

18. Is there any phenomenological indication of a coulombic long-distance potential?

19. Light-quark meson spectrum
The light non-strange meson spectrum in the GeV mass region seems to tend to a (L + n) degeneracy pattern.
S. S. Afonin, Phys. Rev. C76, (2007).

20. Unquenched Static Potential
The highly excited light-quark spectrum suggests a hydrogenlike degeneracy.
Static Potential ansatz:
P. G., Phys. Rev. D 80, (2009)

21. This unquenched behavior can be compared with previous proposals:
NRQM (Y.-B. Ding, K. –T. Chao, D. –H. Qin, Phys. Rev. D 51, 5064 (1995))
QCD String Approach (SRQM)) (A. M. Badalian, B. L. G. Bakker, Yu. A. Simonov, Phys. Rev. D 66, (2002))

22. 4. Static Spectrum

23. Light-quark mesons
The constituent quark mass can be inferred from Spontaneous Chiral Symmetry Breaking (SCSB) in QCD
P.O.Bowman et al., Nucl. Phys. B 128, 23 (2004)

24. Other meson sectors

25. 5. Highly Excited Light-Quark Mesons : results.
Spectrum of I = 1 light unflavoured mesons: Semirelativistic
P.G., V. Mathieu

26. When increasing the energy the spectrum is coulombic.

27. The I = 1 light quark meson spectrum is finite.
The light unflavoured meson spectrum is finite.
The light quark baryon spectrum is finite.

28. Charmonium

29. X(4260)
F. J. Llanes-Estrada, Phys. Rev. D 72, (2005)

30. Bottomonium

31. Experimentally:
B. Aubert et al. (BaBar), Phys. Rev. Lett. 102, (2009).

32. Conclusions
The Unquenched OGE static potential from QCD points out to a coulombic long-distance behavior, also supported by high excited light-quark meson data.
This asymptotic behavior can be implemented in a Cornell potential by means of an unquenching factor. The resulting potential may provide a precise description of high excited mesons.
The hadron spectrum may be limited: no one meson (baryon) states exist beyond a limiting mass.
The charmonium s-state spectrum is well reproduced by assigning X(4260) to the 4s state. A 6s state at 4537 MeV.
A consistent description of the bottomonium requires the existence of a 5s state with a mass about MeV.

33. THE END

34. Bottomonium

36. A 5s state with mass about 1750 MeV is predicted
This resonance would make the mass pattern in the charmonium and bottomonium spectra to be similar.

37. ¡(10735)
E. van Beveren, G. Rupp, arXiv hep-ph

38. 1. Meson Spectrum Mesons (176) K. Nakamura et al. (PDG)
(112)
K. Nakamura et al. (PDG)
JPG 37, (2010)
E. Klempt, A. Zaitsev
Phys. Rep. 454, 1 (2007)

39. Observation from of more than 30 new meson resonances with
masses 1.9 – 2.4 GeV in the CBC +
PS172 data analyses
V. Anisovich, V. V. Anisovich, A. V.
Sarantsev, PRD62, (2000).
D. V. Bugg: Phys. Rep. 397, 257 (2004).

40. Unquenched static potential from Lattice - QCD
Unquenched Potential (valence + sea quarks):
Unquenched static potential from Lattice - QCD
G. S. Bali et al.
Phys. Rev. D 71, (2005)
Is there any phenomenological indication about g(r)?

41. A. Bazavov et al. (MILC)
Rev Mod. Phys. 82, 1349 (2010)

42. Quantum Chromo Dynamics
1. QCD : Bound States
Quantum Chromo Dynamics
Running Parameters:

43. (SDE)
A.C.Aguilar, A.Mihara, A.A.Natale,
PRD 65, (2002)
(SCSB)
P.O.Bowman et al.,
NPB 128, 23 (2004)