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Analytic Extraction of Meson Resonance Parameters from Production Reactions

This study focuses on extracting resonances in meson production reactions, such as P33 and P11, using analytic continuation of scattering amplitudes. Collaborators apply dynamical models to uncover key parameters like mass, form factor, and branching ratio. The research delves into dynamical-coupled channels, resonance structure, and hadron models to characterize resonances. The method involves identifying pole positions for mass and width determination and residue for form factor extraction. The development allows for detailed analysis of resonances in πN and γ*N reactions.

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Analytic Extraction of Meson Resonance Parameters from 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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