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Study of Excited Nucleon States at EBAC: Status and Plans

Study of Excited Nucleon States at EBAC: Status and Plans. Hiroyuki Kamano (Excited Baryon Analysis Center, Jefferson Lab) in collaboration with B. Julia-Diaz, T.-S. H. Lee, A. Matsuyama, T. Sato, N. Suzuki. NSTAR 2009, April 19-22, 2009. PDG *s and N*’s origin.

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Study of Excited Nucleon States at EBAC: Status and Plans

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  1. Study of Excited Nucleon States at EBAC: Status and Plans Hiroyuki Kamano (Excited Baryon Analysis Center, Jefferson Lab) in collaboration with B. Julia-Diaz, T.-S. H. Lee, A. Matsuyama, T. Sato, N. Suzuki NSTAR 2009, April 19-22, 2009

  2. PDG *s and N*’s origin Most of their properties are 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 ? ? meson cloud ? core ? baryon ? Arndt, Briscoe, Strakovsky, Workman PRC 74 045205 (2006) meson Need consistent analysis of pN and ppN channels

  3. Data will change N* structure study Recent high precision data of meson photo- and electro-production reactionsopen a great opportunity of making quantitative study of the N* structure. ELSA, JLab, MAMI, … e.g.) single pion electroproduction g* N N Corresponds to beam resolution N* N-N* e.m. transition form factors

  4. Reaction Data Dynamical Coupled-Channels Analysis @ EBAC N* properties Hadron Models Lattice QCD QCD Approaches to extracting N* properties

  5. Dynamical coupled-channels model @ EBAC N* spectrum, structure, … Meson production data Reaction mechanism Dynamical coupled-channels model of meson production reactions A. Matsuyama, T. Sato, T.-S.H. Lee Phys. Rep. 439 (2007) 193 Maintain coupled-channels unitarity of • a • a Singular! Can treat 3-body unitary cut

  6. Dynamical coupled-channels model @ EBAC For details see Matsuyama, Sato, Lee, Phys. Rep. 439,193 (2007) • Partial wave (LSJ) amplitude of a  b reaction: • Reaction channels: • Potential: coupled-channels effect Impose minimal number of bare N* state: at present 16 of 18(= # of 3* and 4* N*s below 2 GeV) meson exchange bare N* state

  7. Extraction of N* poles and N*  MB decay form factors Extract N*  hN, KY, wN Application Fit hadronic part of parameters Refit hadronic part of parameters Pass hadronic parameters Pass hadronic parameters Extraction of N-N* ele.-mag. transition form factors Application Extract N*  hN, KY, wN Strategy for N* study @ EBAC Feedback Application Develop a method to connect our f.f.s with hadron structure calculations Feedback Refit electro-magnetic part of parameters Fit electro-magnetic part of parameters Application

  8. Current status of the analysis @ EBAC Hadronic part • p N  pN : fitted to the SAID PWA up to W = 2 GeV. Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007) • p N  pp N : cross sections calculated with the pN model; fit is not finished. Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC79 025206 (2009) • p N  h N : fitted to the data up to W = 2 GeV Durand, Julia-Diaz, Lee, Saghai, Sato, PRC78 025204 (2008) • g(*) N  p N : fitted to the data up to W = 1.6 GeV (and up to Q2 = 1.5 GeV2) (photoproduction) Julia-Diaz, Lee, Matsuyama, Sato, Smith, PRC77 045205 (2008) (electroproduction)Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki, arXiv:0904.1918 • g(*) N  pp N : in progress • g(*) N  h N : in progress • g N  K L : in progress Electromagnetic part Explained in detail by Bruno Julia-Diaz (PS7, Apr. 22 11:15-11:40)

  9. Re(T) with I = 1/2 Pion-nucleon elastic scattering Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007) • coupled-channels is considered. • Fitted tothe SAID pN partial wave amplitudes up to 2GeV. • MINUIT library is employed for the numerical minimization. Unitarity is satisfied in ~ 1 % !!

  10. Pion-nucleon elastic scattering Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007) Angular distribution Target polarization EBAC SAID06

  11. pi N  pi pi N reaction Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC79 025206 (2009) Parameters used in the calculation are from pN  pN analysis. Need combined analysis of p N and pp N !

  12. pi N  pi pi N reaction Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC79 025206 (2009) Invariant mass distributions Full result Phase space Data handled with the help of R. Arndt

  13. How can we extract N* information? • PROPER definition of • N* mass and width  Pole position of the amplitudes • N*  MB, gN decay vertices  Residueat the pole Need analytic continuation of the amplitudes !! N*  b decay vertex Explained in detail by Toru Sato (Apr. 20 14:00-14:30) N* pole position ( Im(E0) < 0 )

  14. Comparison with PDG values 1540 –191i 1642 –41i PRELIMINARY Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, in preparation All extracted N*s originate from bare N* states. (At present it is found no pole associated with meson exchanges.) PDG values are close to ours!

  15. Future works N* Study • Extracting N*  MB, gN decay form factors from the EBAC model • Searching for new N* states via the analysis of g N  K Y, w N • Developing a method linking our form factors to Hadron models and Lattice QCD calculations • Refinement of the model parameters with the combined analysis of p N, g(*) N  p N, p p N • Full treatment of the direct ppN 3-body unitarity cut. Model Upgrade

  16. back up

  17. Meson-baryon potentials (Driving terms of LS eq.) All potentials are described in Matsuyama, Sato, Lee, Phys. Rep. 439 193 (2007)

  18. Attach appropriate Green functions ( ) and vertex functions ( ) to p N(on-shell) → MB (off-shell) amplitude ( ) Dynamical coupled-channels model for double pion production reactions All ingredientsalready prepared in 2-body calculation !!

  19. Not included in No new parameter introduced Dynamical coupled-channels model for double pion production reactions + 2 → 3 effective potential … + + =

  20. Approximate treatment of direct term = + part of V23 part of

  21. Dynamical coupled-channels modelfor double pion production reactions To obtain g N → p p N amplitude, just make replacement below: where

  22. Results full c.c. effect off res. only nonres. only

  23. Contribution of V23 PRC result PRC result + V23

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