1. Study of nucleon resonances at EBAC@JLab Hiroyuki Kamano (Excited Baryon Analysis Center, Jefferson Lab) in collaboration with B. Julia-Diaz, T.-S. H. Lee, A. Matsuyama, S. Nakamura, T. Sato, N. Suzuki 7 th Japan-China Joint Nuclear Physics Symposium, Nov. 9-13 2009, Univ. of Tsukuba

2. Outline Excited Baryon Analysis Center (EBAC) at Jefferson Lab Dynamical origin of P11 nucleon resonances

3. Most of their properties were extracted from Are they all genuine quark/gluon excitations (with meson cloud) ? Is their origin dynamical ?  some could be understood as arising from meson-baryon dynamics Need consistent analysis including inelastic channels (  N,  N, KY,  N, …) PDG *s and N*’s origincore meson cloud mesonbaryon ? ? ? ? ? Arndt, Briscoe, Strakovsky, Workman PRC 74 045205 (2006)

4. Objectives and goals: Through the comprehensive analysis of world data of  N,  N, N(e,e’) reactions, Determine N* spectrum (masses, widths) Extract N* form factors, in particular the N-N* e.m. transition form factors Provide reaction mechanism information for interpreting the N* properties Excited Baryon Analysis Center (EBAC) at Jefferson Lab N* properties QCDQCDQCDQCD Lattice QCDHadron Models Dynamical Coupled-Channels Analysis @ EBAC Reaction Data http://ebac-theory.jlab.org/ Founded in January 2006 Theory support for Excited Baryon Program by CLAS@JLab (arXiv:0907.1901) Careful treatment of couplings between multi-reaction channels is necessary !! A. Matsuyama, T. Sato, T.-S.H. Lee Phys. Rep. 439 (2007) 193 “Dynamical coupled-channels model of meson production reactions”

5. Partial wave (LSJ) amplitude of a  b reaction: Reaction channels: Potential: coupled-channels effect Dynamical coupled-channels model @ EBAC For details see Matsuyama, Sato, Lee, Phys. Rep. 439,193 (2007) ground meson-baryon exchange ground meson-baryon exchange bare N* state

6. Current status of the EBAC-DCC analysis  N   N : model constructed up to W = 2 GeV. Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007)  N    N : cross sections calculated with the  N model; fit is ongoing. Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC79 025206 (2009)  N   N : model constructed up to W = 2 GeV Durand, Julia-Diaz, Lee, Saghai, Sato, PRC78 025204 (2008)   N   N : model constructed up to W = 1.6 GeV (& up to Q 2 = 1.5 GeV 2 ) (photoproduction) Julia-Diaz, Lee, Matsuyama, Sato, Smith, PRC77 045205 (2008) (electroproduction)Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki, PRC80 025207 (2009)  N    N : cross sections calculated with the  N &  N model; fit is ongoing. Kamano, Julia-Diaz, Lee, Matsuyama, Sato, arXiv:0909.1129 [nucl-th]   N   N : in progress  N  KY  N : in progress Hadronic part Electromagnetic part

7. Analysis of pi N  pi N & eta N reactions Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007) Durand, Julia-Diaz, Lee, Saghai, Sato, PRC78 025204 (2008) Differential cross sections and polarizations are also well reproduced !

8. Constructed pi N partial wave amplitudes Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007) Real part Imaginary part Isospin = 1/2 EBAC SAID06 W (MeV)

9. How can we extract N* information? PROPER definition of N* mass and width  Pole position of the amplitudes N*  MB,  N decay vertices  Residue of the pole N* pole position ( Im(E 0 ) < 0 ) N* pole position ( Im(E 0 ) < 0 ) N*  b decay vertex N*  b decay vertex Need analytic continuation of the amplitudes !!  Suzuki, Sato, Lee, PRC79 025205 (2009); arXiv:0910.1742

10. Dynamical origin of P11 nucleon resonances Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato arXiv:0909.1356 1.Two almost degenerate poles in the Roper resonance region. 2.All three poles below 2 GeV evolve from a same, single bare state. Im E (MeV) Re E (MeV) 100 Findings: 0 -100 -200 -300 140016001800 P11 N* resonances in the EBAC-DCC model P11 N* resonances in the EBAC-DCC model Eden, Taylor, Phys. Rev. 133 B1575 (1964) Multi-channels reactions can generate many resonance poles from a single bare state!! e.g.) Two poles for J  = 3/2 + resonance in He 5 Hale, Brown, Jarmie, PRL59 763 (1987)

11. Analytic structure of the scattering amplitudes × × physical sheet Re (E) Im (E) 0 0 Re (E) unphysical sheet E th (branch point) E + i  (“real world”) E th (branch point) Scattering amplitude is a double-valued function of E !! Scattering amplitude is a double-valued function of E !! e.g.) single-channel meson-baryon scattering N-channels  Need 2 N Riemann sheets 2-channel case (4 sheets): (channel 1, channel 2) = (p, p), (u, p),(p, u), (u, u) p = physical sheet u = unphysical sheet 2-channel case (4 sheets): (channel 1, channel 2) = (p, p), (u, p),(p, u), (u, u) p = physical sheet u = unphysical sheet

12. Re E (MeV) Im E (MeV)  threshold C:1820–248i B:1364–105i  N threshold  N threshold A:1357–76i Bare state Dynamical evolution of P11 resonances Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato arXiv:0909.1356 (  N,  N,  ) = (u, u, u) (  N,  N,  ) = (p, u, － ) (  N,  N,  ) = (p, u, p)(  N,  N,  ) = (p, u, u) Trajectory of N* propagator Trajectory of N* propagator (  N,  N) = (u,p) for three P11 poles self-energy:

13. Summary Continuous effort for exploring the N* states in Excited Baryon Analysis Center (EBAC) at Jefferson Lab. Scattering amplitudes are successfully constructed by dynamical coupled-channels analysis of meson production reactions. Dynamical origin of the P11 nucleon resonances:  Two resonance poles are found in the Roper energy region.  (Two) Roper and N*(1710) originate from a same, single bare state. Treatment of multi-reaction channels is key to understanding the N* spectrum !!

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15. Real part Imaginary part Constructed pi N partial wave amplitudes Isospin = 3/2 Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007) EBAC SAID06

16. All extracted N*s originate from bare N* states. (At present no molecular-type resonances are found.) Comparison with PDG values Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato arXiv:0909.1356 PDG values are close to ours! 1540 –191i 1642 –41i L 2I 2J

17. EBAC-DCCArndt06Doring09HoelerCutkosky R,φ S11(1535) 154044, -4216,-1631,-3--120+/-40,15+/-45 S11(1650) 164218, -9314,-6955,-4439,-2760+/-10,-75+/-25 S31(1620) 156321, -13415,-9212,-10819,-9515+/-2,-110+/-20 P11(1440) 135737, -11038,-9848,-6440,--52+/-5,-100+/-35 P11 136464, -9986,-46 P33 (1232) 121152, -4652,-4747,-3750,-4853+/-2,-47+/-1 D33(1700) 160412, -5918,-4016,-3810,--13+/-3,-20+/-25 D13(1520) 152138, 738,-532,-1832,-835+/-2,-12+/-5 D15(1675) 165431, -2427,-2123,-2231+/-5,-30+/-19 F15(1680) 167440, -1142,-444,-1734+/-2,-25+/-5 F35(1905) 17385, -7915,-3025,--25+/-8,-50+/-20 F35 19288, 25 F37(1950) 186841, -3353,-3147,-3250+/-7,-33+/-8 Residue of resonance poles in pi N amplitude

18. EBAC-DCCAhrens04/02Arndt04/02Dugger07Blanpied01 P33(1211)A3/2-269 + 12i-258 +/- 3-243 +/- 1-266.9+/-1.6+/-7.8 A1/2-132 + 38i-137 +/- 5-129 +/- 1-135+/-1.3+/-3.7 D13(1521)A3/2 125 + 25i147 +/- 10165 +/- 5143 +/- 2 A1/2 -42 + 8i-38 +/- 3-20 +/- 7-28 +/- 2 P11(1357)A1/2 -12 + 21i -63 +/- 5-51 +/- 2 (1364)A1/2-14 + 22i S11(1540)A1/2 -8 + 43i60 +/- 1591 +/- 2 (1642)A1/229 – 17i69 +/- 522 +/- 7 D15(1654)A3/244 – 9i10 +/- 721 +/- 1 A1/258 – 0.5i15 +/-1018 +/- 2 F15(1674)A3/2-95 - 3i145 +/- 5134 +/- 2 A1/2-67 + 11i-10 +/- 4-17 +/- 1 S31(1563)A1/2137 – 70i 35 +/- 2050 +/- 2 D33(1604)A3/2 -45+9i 97 +/- 20105 +/- 3 A1/2 -1 -17i90 +/- 25125 +/- 3 Helicity amplitudes of N-N* e.m. transition (Q 2 = 0)

19. “Nearest” Riemann sheet to the “physical axis” -100 -200 -300 -400 1200140016001800 0 Im E (MeV) Re E (MeV) (p, p, p, p, p, p)(u, p, p, p, p, p)(u, u, p, p, p, p)(u, u, u, p, p, p)(u, u, u, u, p, p) (u, u, u, u, u, p) (u, u, u, u, u, u) (u, u, p, u, p, p)  N (ch.1)  N (ch.2)  N (ch.4)  (ch.3)  N (ch.5)  N (ch.6) Physical axis = “real world”  N  N  N,  N  N)