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EBAC-DCC analysis of world data on p N, g N, and N(e,e’) reactions

EBAC-DCC analysis of world data on p N, g N, and N(e,e’) reactions. Hiroyuki Kamano Osaka City University (Excited Baryon Analysis Center, Jefferson Lab). ( Presented by T.-S. H. Lee). NSTAR2011. Outline. Strategy for N* study at EBAC

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EBAC-DCC analysis of world data on p N, g N, and N(e,e’) reactions

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  1. EBAC-DCC analysis of world data on pN, gN, and N(e,e’) reactions Hiroyuki Kamano Osaka City University (Excited Baryon Analysis Center, Jefferson Lab) ( Presented by T.-S. H. Lee) NSTAR2011

  2. Outline • Strategy for N* study at EBAC • EBAC-DCC analysis of pN and gN reactions (2006 - 2009) • EBAC-DCC analysis of pN and gN reactions (2010 - ) • Summary • Highlights of the fits to data • Extracted N* spectrum (poles) • N-N* transition form factors (residues)

  3. Strategy for N* study at EBAC

  4. Excited Baryon Analysis Center (EBAC) of Jefferson Lab http://ebac-theory.jlab.org/ Founded in January 2006 Reaction Data • Objectives : • Perform a comprehensive analysis • of world dataof pN, gN, N(e,e’) reactions, • Determine N* spectrum (pole positions) • Extract N-N* form factors (residues) • Identify reaction mechanisms forinterpreting the properties and dynamical origins of N* Dynamical Coupled-Channels Analysis @ EBAC N* properties Hadron Models Lattice QCD QCD

  5. Dynamical coupled-channels model of EBAC N* spectrum, structure, … Meson production data Reaction mechanisms Dynamical coupled-channels model of meson production reactions A. Matsuyama, T. Sato, T.-S.H. Lee Phys. Rep. 439 (2007) 193 • a • a Singular!

  6. Dynamical coupled-channels model of EBAC For details see Matsuyama, Sato, Lee, Phys. Rep. 439,193 (2007) • Partial wave (LSJ) amplitude of a  b reaction: • Reaction channels: • Transition potentials: coupled-channels effect Meson-exchange potentials (Derived from Lagrangians) bare N* states

  7. Dynamical coupled-channels model of EBAC Physical N*s will be a “mixture” of the two pictures: meson cloud core baryon meson For details see Matsuyama, Sato, Lee, Phys. Rep. 439,193 (2007) • Partial wave (LSJ) amplitude of a  b reaction: • Reaction channels: • Transition potentials: coupled-channels effect exchange potentials of ground state mesons and baryons bare N* states

  8. Stage 1 Perform comprehensive analysis of meson production reactions Develop analytic continuation of amplitudes to complex energy plane  Suzuki, Sato, Lee PRC79 025205; PRC82 045206 Stage 2 Extract resonance informationfrom the determined partial-wave amplitudes • N* spectrum (poles); N*  gN, MB transition form factors (residues) Stage 3 Interpret the extracted resonance information in terms of hadron structure calculations . • Quark models, Dyson-Schwinger approaches, LQCD,… Strategy for N* study at EBAC

  9. EBAC-DCC analysis of pN and gN reactions: 2006-2009

  10. EBAC-DCC analysis (2006-2009) pN, hN, ppN (pD,rN,sN) coupled- channels calculations were performed. Hadronic part • p N  pN : Used forconstructing a hadronic model up to W = 2 GeV. Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007) • p N  h N : Used for constructing a hadronic model up to W = 2 GeV Durand, Julia-Diaz, Lee, Saghai, Sato, PRC78 025204 (2008) • p N  pp N : First full dynamical coupled-channels calculation up toW = 2 GeV. Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC79 025206 (2009) • g(*) N  p N : Used for constructing a E.M. model up to W = 1.6 GeV and Q2 = 1.5 GeV2 (photoproduction) Julia-Diaz, Lee, Matsuyama, Sato, Smith, PRC77 045205 (2008) (electroproduction)Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki, PRC80 025207 (2009) • g N  pp N : First full dynamical coupled-channels calculation up to W = 1.5 GeV. Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC80 065203 (2009) Electromagnetic part

  11. pi N amplitudes (2006-2009) Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007) Isospin 1/2 Imaginary T

  12. Single pion photoproduction (Q2 = 0) Julia-Diaz, Lee, Matsuyama, Sato, Smith, PRC77 045205 (2008) • Fit up to W = 1.6 GeV. • Only is varied.

  13. Single pion electroproduction (Q2 > 0) Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki, PRC80 025207 (2009) Fit to the structure function data (~ 20000) from CLAS p (e,e’ p0) p W < 1.6 GeV Q2 < 1.5 (GeV/c)2 is determined at each Q2.

  14. Single pion electroproduction (Q2 > 0) Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki, PRC80 025207 (2009) Five-fold differential cross sections at Q2 = 0.4 (GeV/c)2 p (e,e’ p0) p p (e,e’ p+) n

  15. 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. Full result C.C. effect off

  16. Parameters used in the calculation are from pN  pN & gN  pN analyses. Double pion photoproduction Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC80 065203 (2009) • Good description near threshold • Reasonable shape of invariant mass distributions • Above 1.5 GeV, the total cross sections of p00 and p+- overestimate the data.

  17. Consistent with the resonance theory based on Gamow vectors G. Gamow (1928), R. E. Peierls (1959), … A brief introduction of Gamowvectors: de la Madrid et al, quant-ph/0201091 (complex) energy eigenvalues = pole values transition matrix elements = (residue)1/2 of the poles Extraction of N* information • Definitions of • N* masses(spectrum)  Pole positions of the amplitudes • N*  MB, gN decay vertices  Residues1/2 of the pole N*  b decay vertex N* pole position ( Im(E0) < 0 )

  18. N* poles from EBAC-DCC analysis Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, PRL104 042302 (2010) L2I 2J Two resonance poles in the Roper resonance region !!

  19. pole A: pD unphys. sheet pole B: pD phys. sheet Dynamical coupled-channels effect on N* poles and form factors Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, PRL104 065203 (2010) Suzuki, Sato, Lee, PRC82 045206 (2010) Pole positions and dynamical origin of P11 resonances

  20. Crucial role of non-trivial multi-channel reaction mechanisms for interpreting the structure and dynamical origin of nucleon resonances ! Dynamical coupled-channels effect on N* poles and form factors Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, PRL104 065203 (2010) Suzuki, Sato, Lee, PRC82 045206 (2010) Nucleon - 1st D13 e.m. transition form factors Real part Imaginary part

  21. EBAC-DCC analysis of pN and gN reactions: 2010 -

  22. EBAC-DCC analysis: 2010 ~ Fully combinedanalysis of gN , N  N , hN , KY reactions !! 2010 ~ 7 channels (pN,hN,pD,rN,sN,KL,KS) < 2.1 GeV < 2 GeV < 2 GeV < 2GeV < 2.1 GeV < 2.1 GeV 2006 ~ 2009 5 channels (pN,hN,pD,rN,sN) < 2 GeV < 1.6 GeV < 2 GeV ― ― ― • # of coupled channels • N  N • gN  N • N hN • gN hN • pN KY • gN KL

  23. Pion-nucleon elastic scattering Angular distribution Target polarization 1234 MeV 1449 MeV 1678 MeV 1900 MeV Current model (full combined analysis, PRELIMINARY) Previous model (fitted to pN  pN dataonly) [PRC76 065201 (2007)]

  24. Angular distribution Photon asymmetry 1154 MeV 1232 MeV 1334 MeV 1313 MeV 1154 MeV 1232 MeV 1313 MeV 1137 MeV 1232 MeV 1334 MeV 1137 MeV 1232 MeV 1462 MeV 1416 MeV 1527 MeV 1519 MeV 1617 MeV 1617 MeV 1416 MeV 1462 MeV 1519 MeV 1527 MeV 1617 MeV 1617 MeV 1729 MeV 1690 MeV 1834 MeV 1798 MeV 1958 MeV 1690 MeV 1899 MeV 1729 MeV 1834 MeV 1958 MeV 1798 MeV 1899 MeV Single pion photoproduction Current model (full combined analysis Previous model (fitted to gN  pN data up to 1.6 GeV) [PRC77 045205 (2008)]

  25. 1535 MeV 1549 MeV 1674 MeV 1657 MeV 1811 MeV 1787 MeV 1930 MeV 1896 MeV Eta production reactions Photon asymmetry • Analyzed data up to W = 2 GeV. • p- p  h n data are selected following Durand et al. PRC78 025204.

  26. pi N  KY reactions Angular distribution 1732 MeV 1757 MeV 1792 MeV 1732 MeV 1792 MeV 1757 MeV 1845 MeV 1879 MeV 1879 MeV 1845 MeV 1879 MeV 1879 MeV 1985 MeV 1966 MeV 1966 MeV 1985 MeV 1966 MeV 1966 MeV 2031 MeV 2059 MeV 2059 MeV 2031 MeV 2059 MeV 2059 MeV Recoil polarization

  27. gamma p  K+ Lambda Measure ALL 16 observables !! (ds + 15 polarization asymmetries) “(Over-) complete experiment” is ongoing at CLAS@JLab ! Expected to be a crucial source for establishing N* spectrum !! Formulae for calculating polarization observables Sandorfi, Hoblit, Kamano, Lee JPG 38, 053001 (2011) (Topical Review) 1781 MeV 1883 MeV 2041 MeV

  28. Summary

  29. Summary and outlook • Extraction of N* from EBAC-DCC analysis 2006-2009: • The Roper resonance is associated with two resonance poles. • The two Roper poles and N*(1710) pole are generated from a single bare state. • N-N* e.m. transition form factors are complex. Multi-channel reaction mechanisms plays a crucial role for interpreting the N* spectrum and form factors !!

  30. Summary and outlook Previous model: Q2 < 1.5 GeV2 • Extraction of N* from EBAC-DCC analysis 2006-2009: • Fully combined analysis of pN, gN  pN, hN, KYreactions is underway. • The Roper resonance is associated with two resonance poles. • The two Roper poles and N*(1710) pole are generated from a single bare state. • N-N* e.m. transition form factors are complex. • Re-examine resonance poles • Analyze CLAS ep  epN data with Q2 < ~ 4 GeV2;  Extract N-N* electromagnetic transition form factors at high Q2 • Include pN, gN  ppN, … reactions to the combined analysis.

  31. Summary and outlook Projected progress Spring of 2012 Complete the combined analysis to reach DOE milestone HP3: “Complete the combined analysis of available single pion, eta, kaon photo-production data for nucleon resonances and incorporate analysis of two-pion final states into the coupled-channels analysis of resonances”

  32. EBAC Collaborations • J. Durand • B. Julia-Diaz • Kamano (Jlab) • T.-S. H. Lee (1/4 EFT) • A. Matsuyama • S. Nakamura (JLab) • B. Saghai • Sato • C. Smith • N. Suzuki

  33. Summary and outlook Works need to be accomplished Summer of 2013 Complete the extraction of N-N* form factors to reach DOE milestone HP7: End of 2013 Make the EBAC-DCC code available for future analysis of “complete experiments” and N* experiments with 12 GeV upgrade “Measure the electromagnetic excitations of low-lying baryon states (< 2GeV) and their transition form factors over the range Q2 = 0.1 – 7 GeV2 and measure the electro- and photo-production of final states with one and two pseudoscalar mesons”

  34. back up

  35. Summary and outlook Nakamura, arXiv:1102.5753 Kamano, Nakamura, Lee, Sato, in preparation New direction • Application of the DCC approach to meson physics: (3-body unitarity effect are fully taken into account) p g X B, D, J/Y... Exotic hybrids? p f0, r, .. p Heavy meson decays GlueX

  36. Summary and outlook Dalitz plot of a1(1260)  ppp decay from our model Isobar model Unitary model (with full 3-body unitarity) Nakamura, arXiv:1102.5753 Kamano, Nakamura, Lee, Sato, in preparation New direction • Application of the DCC approach to meson physics: (3-body unitarity effect are fully taken into account)

  37. Coupled-channels effect in various reactions Pion photoproductions Full c.c. effect of ppN(pD,rN,sN) & hN off Pion electroproductions Full c.c. effect of ppN(pD,rN,sN) & hN off Double pion productions Full c.c effect off

  38. Dynamical coupled-channels model of EBAC For details see Matsuyama, Sato, Lee, Phys. Rep. 439,193 (2007)

  39. 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. s (mb) W (GeV) Full result Full result Phase space

  40. The resulting amplitudes are now completely unitary in channel space !! Improvements of the DCC model Processes with 3-body ppN unitarity cut

  41. self-energy: (hN, rN, pD) = (p, u, u) (hN, rN, pD) = (p, u, p) (hN, rN, pD) = (u, u, u) (hN, rN, pD) = (p, u, －) Dynamical origin of P11 resonances Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, PRL104 042302 (2010) Pole trajectory of N* propagator Bare state hN threshold pD threshold A:1357–76i Im E (MeV) rN threshold B:1364–105i C:1820–248i (pN,sN) = (u,p) for three P11 poles Re E (MeV)

  42. Residues of resonance poles in pi N amplitude

  43. Helicity amplitudes of N-N* e.m. transition (Q2 = 0)

  44. Q2 dependence of the form factors: 1/3 Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki, PRC80 025207 (2009) Suzuki, Sato, Lee, arXiv:0910.1742 N-D transition GM form factor GM / (3GD) real part other analyses imaginary part

  45. Q2 dependence of the form factors: 2/3 Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki, PRC80 025207 (2009) Suzuki, Sato, Lee, arXiv:0910.1742 N-D13 e.m. transition amplitude A3/2 A1/2 real part CLAS imaginary part

  46. real imaginary Q2 dependence of the form factors: 3/3 Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki, PRC80 025207 (2009) Suzuki, Sato, Lee, arXiv:0910.1742 N-P11 e.m. transition amplitude CLAS Collaboration PRC78, 045209 (2008) A1/2 real imaginary

  47. pi N amplitudes (2006-2009) Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007) Isospin 1/2 Real T

  48. Parameters used in the calculation are from pN  pN & gN  pN analyses. Double pion photoproduction Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC80 065203 (2009) • Good description near threshold • Reasonable shape of invariant mass distributions • Above 1.5 GeV, the total cross sections of p00 and p+- overestimate the data.

  49. pi N amplitudes (2006-2009) Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007) Isospin 1/2 Imaginary T

  50. pi N amplitudes (2006-2009) Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007) Isospin 3/2 Real T

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