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Details of EBAC-DCC model

Details of EBAC-DCC model. Hiroyuki Kamano. Informal EBAC meeting, May 24-26, 2010 (revised version of the talk at 2009 EBAC meeting). e.g.) D13  Total J = 3/2 , Isospin = 1/2 , Parity =. MB ( LS ). EBAC-DCC model: hadronic part.

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Details of EBAC-DCC model

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  1. Details of EBAC-DCC model Hiroyuki Kamano Informal EBAC meeting, May 24-26, 2010 (revised version of the talk at 2009 EBAC meeting)

  2. e.g.) D13  Total J = 3/2 , Isospin = 1/2 , Parity = MB( LS ) EBAC-DCC model: hadronic part For details see Matsuyama, Sato, Lee, Phys. Rep. 439,193 (2007) • Partial wave (LSJ)amplitude of a  b reaction: • Reaction channels: • Potential: 2-body v potential (no ppN cut) 2-body Z potential (with ppN cut) bare N* state

  3. Meson-baryon Green’s functions Stable channels = (p, N), (h, N), (K,L), (K,S) : Unstable channels = (p, D), (r, N), (s, N) : (D, r, s) self-energy in the presence of spectator particle

  4. Branch point of unstable Green functions (MeV) Meson-baryon Green’s function Unstable channels = (p, D), (r, N), (s, N) :

  5. Original Model 2 • Branch points now have more realistic values. • sN Green function has two branch points. Meson-baryon Green’s function Unstable channels = (p, D), (r, N), (s, N) : Model 2: Betz-Lee PRC23 375 (1981) Simple s-wave (separable) pp model

  6. 2-body “v” potentials (non-strange channels) 5 diagrams s-ch N u-ch N u-ch D t-ch r t-ch s 3 diagrams s-ch N u-ch N t-ch p 2 diagrams s-ch N u-ch N 2 diagrams s-ch N t-ch r 2 diagrams s-ch N u-ch N 2 diagrams s-ch N u-ch N 1 diagram s-ch N 1 diagram s-ch N 2 diagrams s-ch N u-ch N 2 diagrams s-ch N u-ch N 4 diagrams s-ch N u-ch N t-ch p t-ch w 2 diagrams s-ch N u-ch N 2 diagrams s-ch N u-ch N 4 diagrams s-ch N u-ch N u-ch D t-ch r 2 diagrams s-ch N u-ch N Total 36 diagrams

  7. 2-body “v” potentials (channels with strange hadrons) 3 diagrams s-ch N u-ch S t-ch K* 4 diagrams s-ch N u-ch X t-ch w t-ch f 5 diagrams s-ch N u-ch X t-ch r t-ch w t-ch f Total 18 diagrams 3 diagrams s-ch N u-ch S u-ch L t-ch K* 3 diagrams s-ch N u-ch X t-ch r At present, KY couples to non-strange channels through pN channel only.

  8. 2-body “v” potentials All potentials are described in Matsuyama, Sato, Lee, Phys. Rep. 439 193 (2007)

  9. Partial wave decomposition Used for the coupled-channels equation Plane wave matrix element in helicity representation

  10. Unitary transformation (UT) method See e.g., Ann. Phys. 322, 736 (2007) nucl-th/0102037 for details of UT method e.g.) p N  p N “v” potential (s-channel nucleon) UT method • Independent of total scattering energy s1/2!! • Potentials agree with usual Feynman diagram at on-shell. The off-shell behavior is uniquely defined within UT method.

  11. Rules forattaching cutoff factors • Attach cutoff factors to each vertex (currently dipole form is used) • For s- and u-channel potential, use 3-momentum of external meson • For t-channel potential, use 3-momentum of exchanged meson • For contact potential, use product of two cutoff factors

  12. 2-body “Z” potentials Feshbach projection:

  13. 2-body “Z” potentials

  14. Numerical treatment of Z potentials Z(E)(k,k’;E)potentials have logarithmic singularity. ZpD,pD as a function of k at k’=0.3 GeV, E=1.88 GeV pN  pN, hN, KY Contour-rotation method e.g., Larson et al, PRC9 699 (1974) pN  ppN Spline method e.g., Matsuyama, PLB152 42 (1985); Matsuyama Lee, PRC34 1900 (1986)

  15. Use same cutoff  9 Bare N*  MB vertex function × # of parameters for a bare N* state # of bare N* state S11 2, S31 1 P11 2, P13 1, P31 1, P33 2 D13 1, D15 1, D33 1, D35 0 F15 1, F17 0, F35 1, F37 1  total 16 bare N* state (as of today) e.g.) D13 state ( I = 1/2, J = 3/2, Parity = minus) 18  17

  16. EBAC-DCC model: electromagnetic part For details see Matsuyama, Sato, Lee, Phys. Rep. 439,193 (2007) • Meson-exchange amplitude: • Dressed N* propagating amplitude: = hadronic process

  17. gamma N  MB potentials 2 diagrams s-ch N u-ch N 4 diagrams s-ch N u-ch N t-ch r contact 6 diagrams s-ch N u-ch L u-ch S t-ch K t-ch K* contact 5 diagrams s-ch N u-ch N u-ch D t-ch p contact 2 diagrams s-ch N u-ch N 7 diagrams s-ch N u-ch N u-ch D t-ch p t-ch r t-ch s contact 6 diagrams s-ch N u-ch L u-ch S t-ch K t-ch K* contact Total 32 diagrams

  18. gamma N  MB potentials All potentials are described in Matsuyama, Sato, Lee, Phys. Rep. 439 193 (2007)

  19. gamma N  MB potentials helicity-JLSmixed representation (angular projection of gN part is not needed for our purpose)

  20. gamma N  N* bare vertex function where Bare N* helicity amplitude: for transverse photon for longitudinal photon

  21. Parameterizations of bare helicity amplitudes Introduce appropriate threshold behavior + dipole form factor

  22. Plan for EBAC-DCC analysis in 2010 EBAC second generation model Full combined analysis (global fit) of: • N  N (W < 2 GeV) • N  N (W < 2 GeV) • N  N (W < 1.6 GeV  2 GeV) • N  N (W < 2 GeV) • N  KY (W < 2 GeV) • pN  ppN (W < 2 GeV) • gN  ppN (W < 1.5 GeV  2 GeV) ~ End of 2010 2010 ~ 2011

  23. pi- p  K0 Lambda Preliminary EBAC-DCC Julia-Diaz, Saghai, Lee, Tabakin PRC73 055204

  24. gamma p  K Lambda Preliminary

  25. gamma p  K Lambda Preliminary

  26. Coupling effect of KY channels on piN PWA Preliminary S11 Re S11 Im P11 Re P11 Im P13 Im P13 Re D13 Re D13 Im D15 Re D15 Im F15 Re F15 Im Add KY channels 5ch calc. SAID-EDS F17 Re F17 Im

  27. Coupling effect of piN, pipiN, etaN channels on KY observables Meson-exchange amplitudes Amplitude with Dressed N*

  28. Coupling effect of piN, pipiN, etaN channels on KY observables Preliminary Current EBAC-DCC result Couplings to pN, hN, ppN channels off (At least) about 20% reduction except backward angles is observed.

  29. Back up

  30. pi N  pi N PWAs Preliminary S11 Re S11 Im P11 Re P11 Im P13 Im P13 Re D13 Re D13 Im D15 Re D15 Im F15 Re F15 Im Add KY channels 5ch calc. SAID-EDS F17 Re F17 Im

  31. gamma p  K Lambda Preliminary Kamano, Nakamura, Lee, Sato in preparation Effect of ppN channels on gp  KL Current EBAC-DCC result Couplings to ppN (pD,rN,sN) channels are turned off

  32. pi N  pi N @ W=1232 MeV EBAC Juelich V Re(T) Output is T, not Im(T)

  33. pi N  pi N @ W=1600 MeV EBAC Juelich V Re(T) Im(T)

  34. pi N  pi D @ W=1232 MeV V Re(T) Im(T)

  35. pi N  pi D @ W=1600 MeV V Re(T) Im(T)

  36. EBAC-DCC model: hadronic part For details see Matsuyama, Sato, Lee, Phys. Rep. 439,193 (2007) • Meson-exchange amplitude: • DressedN* amplitude:

  37. Parameters Hadronic part: 29 + 247 (15 bare N*) = 271 (roughly 20 parameters for each partial wave) nonresonant potential N* parameters Electromagnetic part: 2 + 39 (15 bare N*) = 41 grp & gwp couplings N* bare helicity amps. (roughly 3 parameters for each partial wave)

  38. 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 % !!

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