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

15 new charmonium states from PDG 00 Motivation 15 new charmonium states from PDG 00 K. Nakamura et al. (PDG) JPG 37, 075021 (2010)

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

T. Burch et al., PRD 81, 034508 (2010)

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

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

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

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

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

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.

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

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

Quenched Static OGE Potential from QCD Coulombic Linear Richardson Potential

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.

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)

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, 114513 (2005)

Unquenched Static OGE Potential from QCD Coulombic Coulombic ?

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

Light-quark meson spectrum The light non-strange meson spectrum in the 1.9 - 2.4 GeV mass region seems to tend to a (L + n) degeneracy pattern. S. S. Afonin, Phys. Rev. C76, 015202 (2007).

Unquenched Static Potential The highly excited light-quark spectrum suggests a hydrogenlike degeneracy. Static Potential ansatz: P. G., Phys. Rev. D 80, 054010 (2009)

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, 034026 (2002))

4. Static Spectrum

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)

Other meson sectors

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

When increasing the energy the spectrum is coulombic.

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

Charmonium

X(4260) F. J. Llanes-Estrada, Phys. Rev. D 72, 031503 (2005)

Bottomonium

Experimentally: B. Aubert et al. (BaBar), Phys. Rev. Lett. 102, 012001 (2009).

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 10740 MeV.

THE END

Bottomonium

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.

¡(10735) E. van Beveren, G. Rupp, arXiv.0910.0967 hep-ph

1. Meson Spectrum Mesons (176) K. Nakamura et al. (PDG) (112) K. Nakamura et al. (PDG) JPG 37, 075021 (2010) E. Klempt, A. Zaitsev Phys. Rep. 454, 1 (2007)

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, 051502 (2000). D. V. Bugg: Phys. Rep. 397, 257 (2004).

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, 114513 (2005) Is there any phenomenological indication about g(r)?

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

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

(SDE) A.C.Aguilar, A.Mihara, A.A.Natale, PRD 65, 054011 (2002) (SCSB) P.O.Bowman et al., NPB 128, 23 (2004)