1. 1 Keitaro Nagata and Atsushi Hosaka Research Center for Nuclear Physics, Osaka Univ. Quark-Diquark approach for the nucleon and Roper resonance Workshop on Hadron Structure at J-PARC, Nov. 30- Dec. 2 '05

2. 2 The Role of diquarks for the exotics, R.L.Jaffe, F. Wilczek, PRL91,232003 for the non-exotics, R.L.Jaffe, Phys. Rept.409,1 1.Motivation Quark-Diquark picture for the nucleon (K.N and A.H, hep-ph/0506193) generates the state which are neglected in "uncorrelated" quark model. the correlation between quarks, diquark correlation

3. 3 Wave-function of N In SU(6) QM of uncorrelated quarks with (0s) 3 config. In general, two components (nucleon operator) are independent e.g. lattice QCD, QCD Sum Rule (Ioffe, Z.Phys C18, 67 (83) ) ⇒ two state with quantum number of N ?

4. 4 Two nucleon states Mass difference ～

5. 5 ● Chiral q-D model : NJL + diquark ● Effective meson-baryon Lagrangian Path-integral hadronization of a chiral q-D model ★ Structure change of hadrons and interactions of them in a finite density system can be calculated. The effect of chiral restoration to the nucleon 2. Model meson ~ qq-bar baryon ~ qD chiral symmetry

6. 6 DSDS DSDS DADA DADA DADA DSDS q

7. 7 B1B1 q DSDS B1B1 B2B2 q DADA B2B2 B1B1 B 1,2 G 3. Masses of two states

8. 8 MNMN M Roper q-D A q-D S m q =0.39,  GeV] (3D cutoff) G S, G A are fixed so that a S,A =m q + M S,A － 50 MeV. M S =0.65, M A =1.05 [GeV]

9. 9 The correlation between quarks violates the degeneracy of these two states, which gives two N=0 states. The excitation energy comes from the spin-spin int. between quarks. No correlations between quarks in the construction of the S-F w.f. The excitation energy comes from the single particle excitation 2 h . (N=2) N 2 1 0

10. 10 ● Correlation between quarks allow the state forbidden in uncorrelated QM appear as a physical state. ● In order to check whether the state is Roper or not, → magnetic moment, radius and axial coupling of N → transition N' → N by  or  ● The properties of N and N' in a finite density system 4. Summary

11. 11 ● Radial excitation ? In QM, breathing mode and lattice QCD, it is radialy excited. G.E.Brown, et.al, NPA397, 447(83), T. Burch, et.al, PRD70, 054502(04). ● Magnetic moments ? In NQM, N and N' have the same value of magnetic moments. ● Octet and decuplet e.g.  (1660),  (1670) ? For octet, probably it is possible, but for decuplet.... ● Level ordering of N' and N*(1535) ? ● Helicity amplitude? Problems about Roper

12. 12 Wave-function