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Extraction of resonance parameters from meson production reactions

Extraction of resonance parameters from meson production reactions. T. Sato (Osaka U.) Collaborators: N. Suzuki (Osaka) T.-S. H. Lee(ANL) and B. Julia-Diaz(Barcelona), H. Kamano(Jlab), A. Matsuyama(Shizuoka). [ Suzuki, Sato, Lee PRC 79 (2009) 025205]. motivation

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Extraction of resonance parameters from meson production reactions

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  1. Extraction of resonance parameters from meson production reactions T. Sato (Osaka U.) Collaborators: N. Suzuki(Osaka) T.-S. H. Lee(ANL) and B. Julia-Diaz(Barcelona), H. Kamano(Jlab), A. Matsuyama(Shizuoka) [Suzuki, Sato, Lee PRC 79 (2009) 025205]

  2. motivation • dynamical model of meson production reaction • extraction of resonance parameters, (analytic continuation of • scattering amplitudes) • P33 and P11 from current EBAC model • summary

  3. Excited baryon  resonance in πN, γ *N reactions Structure of resonance : mass, form factor, branching ratio

  4. Dynamical Coupled-Channels Analysis @ EBAC Reaction Data Mass, Width, Electromagnetic N-N* form factors Hadron Models Lattice QCD QCD

  5. Resonance • Resonances: poles of the scattering amplitudes • characterize resonances Pole position mass, widthResidueForm factors Form Factor

  6. Extraction of Resonance Parameters Dynamical model BW Breit-Wigner, SP speed-plot, AC Analytic continuation

  7. Dynamical Model of meson production reaction Coupled channels model with ππN three-body unitarity • G0(W): MB Green function • N* Green function: mass • N* vertex : form factor

  8. Im W Resonance Pole on unphysical sheet Physical Sheet Bound state Scattering Re W Resonance Un-physical sheet • Need to examine T(W) for complex W, un-physical sheet • Multi-sheets for coupled channel • Ex: 2ch pp uu up pu (Kato 65,..) Resonance

  9. Analytic continuation of T(W) T(W) : obtained by solving Lippman-Schwinger Equation p-plane W-plane Im p Im W = Re p Re W Example: T for un-physical sheet above threshold • Choose appropriate path for phys/un-phys sheets (Pearce-Gibson ‘89) • V(p’,p) must be analytic in the region of path deformation

  10. Green functions with unstable particle Example: for un-phys and W-plane p-plane (Pearce Afnan ‘84)

  11. Toy model • N* couple with only πΔ • S-wave, non-rela : ‘analytic’ solution

  12. Results from EBAC model (preliminary) Contour plot of |T(W)| P33 Im W Re W

  13. Pole trajectory P11 1 2 3 Multi-poles associated with single resonance in coupled channel preliminary

  14. Summary • Pole of T matrix gives resonance information • Mass and width from pole position, form factors from residue • A method to extract resonance parameters using analytic continuation of the scattering amplitude is developed. • Applied for πN scattering amplitude of EBAC current model • P33, P11 resonance poles are extracted • Extracting resonance form factor is in progress.

  15. Resonance Mass Resonance Form Factor (complexnumber)

  16. PDG 08: BW and Pole Example P11 Re(M_pole) ~ m_pi + m_Delta, < m_eta + m_N

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