IS THE MESON SPECTRUM LIMITED ? P. González

1. IS THE MESON SPECTRUM LIMITED ? P. González

2. References i) El Houssine Mezoir and P. González Phys. Rev. Lett. 101, 232001 (2008). ii)P. González Phys. Rev. D 80, 054010 (2009). iii)P. González and V. Mahieu Work in preparation.

3. MOTIVATIONS • One remaining problem in our understanding of QCD has to do with quark confinement in hadrons. We expect it to determine at great extent the highly excited (large sized) hadron spectrum • In recent years there has been important progress in the experimental knowledge of the spectrum of highly excited mesons in the light-quark (u, d) as well as in the heavy-quark (c, b) sectors. • C. Amsler et al. (PDG) Phys. Lett. B667, 1 (2008) • D. V. Bugg, Phys. Rep. 397, 257 (2004). • iii) What information about quark confinement can we infer from data?

4. The spectra of highly excited mesons could give us information about the consequences of The String Breaking Mechanism in QCD

5. INDEX • i) The highly excited light-quark meson spectrum. • Static approach for large-sized mesons. • iii) Static interaction from QCD. • iv) The Constituent Quark Model (CQM): • I = 1 light-quark unflavoured mesons. • Heavy quarkonia: charmonium and bottomonium. • v) Conclusions.

6. The light-quark meson spectrum

7. The light non-strange meson spectrum in the 1.9 - 2.4 GeV mass region seems to tend to a (L + n) degeneration pattern. • S. S. Afonin, Phys. Rev. C76, 015202 (2007). What is the physical origin of this pattern ?

8. Static approach for large sized mesons

9. 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)

10. Other meson sectors

11. The quenched static potential from latticeQCD Quenched Potential(valence quarks):Wilson loop Energy of the ground state G. S. Bali, Phys. Rep. 343,1 (2001)

12. The Constituent Quark Model (CQM) • Effective Potential : Static lattice QCD potential with effective values of the parameters • ii) Semirelativistic orSchrödinger equations. Cornell potential: Good description of heavy quarkonia up to 0.9 Gev excitation energy E. Eichten et al., Phys. Rev. D 21 (1980) 203

13. Screening effects For large-sized mesons the static quark and antiquark sources arescreened by light pairsthat pop out of the vacuum. Is it possible to parametrize this effect through an unquenchedeffective quark-antiquark static potential ?

14. Unquenched Potential (valence + sea quarks): The unquenched static potential from latticeQCD G. S. Bali et al. Phys. Rev. D 71, 114513 (2005)

15. Lattice QCD suggests a screened effective potential due to meson-meson thresholds giving rise to string breaking. The highly excited light-quark spectrum suggests a hydrogenlike degeneracy. Static potential ansatz:

16. This screened behavior can be compared with previous proposals: Lattice (K. D. Born et al., Phys. Rev. D 40, 1653 (1989)) QCD String Approach (A. M. Badalian, B. L. G. Bakker, Yu. A. Simonov, Phys. Rev. D 66, 034026 (2002))

17. Radial potential Spectrum of I = 1 light unflavoured mesons: Semirelativistic

18. When increasing the energy the spectrum is coulombic.

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

20. Charmonium

21. Bottomonium

22. 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.

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

24. Conclusions • i)Light Unflavoured mesons show a high excited coulombic spectrum that can be related to String Breaking in QCD. • The hadron spectrum is limited: no one meson (baryon) states exist beyond a limiting mass. • The charmonium s-state spectrum is nicely reproduced by assigning X(4260) to the 4s state. A 6s state at 4550 MeV. • A consistent description of the bottomonium spectrum within the same framework requires the existence of a 5s state with a mass about 10748 MeV. • At large distances Strong Interactions could behave in a similar manner to Electromagnetic and Gravitational ones.

25. THE END

27. 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 or quarks whose effect can be represented by an average instantaneous quark-antiquark interaction: the static potential. In the non-relativistic limit the Bethe-Salpeter equation becomes the Schrödinger equation.

28. Bethe-Salpeter Equation

29. Static approximation in the kernel Semirelativistic approach (Non-relativistic approximation in the kernel integral)

30. Fully non-relativistic approach Schrödinger Equation

31. Static Interaction from QCD Quenched: Schwinger-Dyson Equation J. M. Cornwall and J. Papavassiliou, Phys. Rev. D40 (1989) 3474 M:effective gluon mass

32. M =L

33. Unquenched Static Interaction from QCD + ? +

34. Mesons as quark model bound states Mesons made of quarks (antiquarks)uand/ord with I = 1: No annihilation, no components. Quantum numbers: I: Isospin. J: Total Angular Momentum. Parity G-parity For mesons made of quarks and their own antiquarks: Charge Conjugation