1. PATTERNS IN THE NONSTRANGE BARYON SPECTRUM P. González, J. Vijande, A. Valcarce, H. Garcilazo

2. INDEX i) The baryon spectrum: SU(3) and SU(6) x O(3). ii) The Quantum Number Assignment Problem. iii) Screened Potential Model for Nonstrange Baryons. iv) SU(4) x O(3) : Spectral predictions up to 3 GeV. v) Conclusions.

4. What is the physical content of the baryon spectrum? The richness of the baryon spectrum tells us about the existence, properties and dynamics of the intrabaryon constituents. The Eightfold Way: SU(3) The pattern of multiplets makes clear the existence of quarks with “triplet” quantum numbers and the regularities in the spectrum. From the spectral regularities one can make predictions and obtain information on the dynamics (SU(3) breaking terms). How can we extract this physical content? The knowledge of spectral patterns is of great help.

5. SU(3 ) : Quarks (3 x 3 x 3 = 10 + 8 + 8 + 1) Baryons I prediction by Gell- Mann Strange quark mass splitting?

6. Quarks with Spin : SU(6) i SU(3) x SU(2) Quarks with Spin in a Potential : SU(6) x O(3)

7. SU(6) Breaking : Strange quark mass + Hyperfine (OGE) splitting

8. The Baryon Quantum Number Assignment Problem

9. The Baryon Quantum Number Assignment, determined by QCD, requires in practice the use of dynamical models (NRQM,…). Regarding the identification of resonances the experimental situation for nonstrange baryons is (though not very precise) more complete. From a simple NRQM calculation we shall show that SU(4) x O(3) is a convenient classification scheme for non-strange baryons in order to identify regularities and make predictions.

11. NRQM for Baryons Lattice QCD : Q-Q static potential (G. Bali, Phys. Rep. 343 (2001) 1) Quenched approximation (valence quarks) The Bhaduri Model

12. The Missing State Problem E > 1.9 GeV: many more predicted states than observed resonances. The observed resonances seem to correspond to predicted states with a significant coupling to pion-nucleon channels (S. Capstick, W. Roberts PRD47, 1994 (1993)).

13. Lattice QCD : Q-Q static potential Unquenched (valence + sea quarks) (DeTar et al. PRD 59 (1999) 031501).

14. String breaking The saturation of the potential is a consequence of the opening of decay channels. The decay effect can be effectively taken into account through a saturation distance in the potential providing a solution to the quantum number assignment.

15. Screened Potential Model

18. (N,  Ground States : SU(4) x O(3)

19. For J > 5/2 :

22. Dynamical Nucleon Parity Series For J > 5/2 :

24. (N,  First Nonradial Excited States Our dynamical model (absence of spin-orbit and tensor forces) suggests the following rule satisfied by data at the level of the 3% The first nonradial excitation of N,  (J) and the ground state of N,  (J+1) respectively are almost degenerate. For radial as well as for higher excitations the results are much more dependent on the details of the potential.

26. For J > 5/2 the pattern suggests the following dynamical regularities Spectral Pattern Rules

27. Conclusions i)The use of a NRQM containing a minimal screened dynamics provides an unambiguous assignment of quantum numbers to nonstrange baryon resonances, i. e. a spectral pattern. ii) The ground and first non-radial excited states of N’s and  ’s  are classified according to SU(4) x O(3) multiplets with hyperfine splittings inside them. iii) The spectral pattern makes clear energy step regularities, N-  degeneracies and N parity doublets. iv)Ground and first non-radial excited states for N’s and  ’s, in the experimentally quite uncertain energy region between 2 and 3 GeV, are predicted.

28. THE END

32. (N,  Ground States : SU(4) x O(3)

34. For J > 5/2 the pattern suggests the following dynamical regularities