1. Nucleon and Roper on the Lattice Y. Chen Institute of High Energy Physics, CAS, China Collaborating with S.J. Dong, T. Draper, I. Horvath, F.X. Lee, K.F. Liu, N. Mathur, S. Tamhankar, and J.B. Zhang (Kentucky Lattice Group)

2. Introduction Roper resonance has been well established as a four-star state in Particle Data Table. A radial excited state of the nucleon? Same quantum number Parity reversal cannot be easily interpreted. Roper(1440) and (1535) A pentaquark candidate? (Jaffe-Wilczek, PRL91, 232003, 2003) Hybrid? Nonperturbative Method ------ Lattice QCD

3. Simulation Details lattice, quenched approximation Iwasaki gauge action ( improved) overlap fermion action (chiral symmetry, improved) The lattice spacing is set by The lowest quark mass gives 80 Configurations to do the statistics. Nucleon mass spectrum is simulated. (hep-lat/0306199) Nucleon and Roper wave functions are calculated.

4. Mass and spectral weights : hadron masses to be extracted : spectral weights  hadron matrix elements  wave functions

5. Nucleon Mass Spectrum Point-source point-sink correlation function are calculated and analyzed. Nucleon interpolation field operator Constrained curve fitting--------- “Sequential Empirical Bayes”(SEB) hep-lat/0405001(Kentucky Group) Roper mass and S11(1535) mass tends to cross over as quark mass decreases. Chiral symmetry may play a role for this crossover. Flavor-spin interaction takes place due to the Goldstone boson exchange (L.Y. Glozman and D.O. Riska, Phys. Rep. 268, 263(1996) )

6. Nucleon and Roper Wavefunctions Coulomb gauge fixed Wall-source point sink correlation functions are calculated and analyzed. The spectrum is similar to that of point source. The spectral weights of Roper are negative for both heavy and light quark masses. Wall-source means, qualitatively This hints that a radial node.

7. Spatially extended sink operator where, Nucleon two-point functions are calculated in Coulomb gauge. where and

9. Wavefunctions are fitted by the variational function form which are motivated from the non-relativistic potential model. The r.m.s radius of nucleon can be estimated as

11. Light Quark Region Point-source correlation function behaves bad at this quark mass. Therefore, Wall-source correlation function is used to extracte the wavefunctions There is an additional minus sign in the Roper wavefunction, due to the wall source effect. The Roper wavefunction has a radial node. The behavior of the roper wave function is a little bit puzzling.

12. Ghost State In quenched approximation, the Z-graph goes to the hairpin- graph which results in a ghost state. However, the spectral weight of the ghost is much smaller than that of the Roper, at this quark mass. It seems that the ghost can not account for the strange behavior of the Roper wave function completely.

13. Summary The simulation of nucleon spectrum turns out that the Roper mass and the mass of S11(1535) tend to cross over as quark mass goes down. Our result support the notion that Heavy quark Light quark SU(6) ----transition---  dynamics dominated color-spin by chiral symmetry The Roper wavefunction has definitely a radial node in medium quark region ( ). At lower quark mass, there is a hint the node also exists, but further work is needed. R.M.S radius of nucleon is about 0.7 fm, which seems insensitive to the quark mass, when quark mass is not too high.