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On the analytic structure of the KN - pS scattering amplitudes

On the analytic structure of the KN - pS scattering amplitudes. Hiroyuki Kamano (Excited Baryon Analysis Center, Jefferson Lab) in collaboration with Yoichi Ikeda, Toru Sato (Osaka Univ.). K -. p. p. Connection with meson-baryon dynamics and L (1405). Motivation.

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On the analytic structure of the KN - pS scattering amplitudes

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  1. On the analytic structure of the KN - pS scattering amplitudes Hiroyuki Kamano (Excited Baryon Analysis Center, Jefferson Lab) in collaboration with Yoichi Ikeda, Toru Sato (Osaka Univ.)

  2. K- p p Connection with meson-baryon dynamicsand L(1405) Motivation To explore few-body systems like K-pp, need reliable information on two-body amplitudes: • NN  NN, YN  YN • KN  KN, KN  pS, … Are there 3-body resonance states in ? e.g.) FINUDA collaboration PRL94 212303 (2005) ( Few-body systems could access L(1405) )

  3. We DO NOT have enough data to construct a reliable model giving quantitative evaluations/predictions of amplitudes and resonance pole positions ! Models of KN-pS reactions and L(1405) • Quasi-bound state of KN system • CDD pole coupling with mesons • a • Large error bars • Total cross sections (only?) Extracting scattering amplitudes Data ( Input ) Amplitudes ( Output ) Model • Data points • Precision • Total cross section Angular distribution Polarization … Examine using Lippmann-Schwinger approach with Weinberg-Tomozawa term (potential) • Symmetries • Dynamics • Approximations

  4. meson baryon (S-wave) Lippmann-Schwinger equation: Weinberg-Tomozawa Potential Original: Weinberg, PRL17 616 (1966) Tomozawa Nuov. Cim. 46A 707(1966) Chiral Lagrangian: e.g., Bernard, Kaiser, Meissner IJMP E4 193 (1995) Fixed with SU(3) symmetry S-wave projection

  5. Energy-dependent potential (E-dep.) Energy-independent potential (E-indep.) Approximations in WT potential Weinberg-Tomozawa potential (WT) e.g., Oset, Ramos NPA635 99 (1998) Ikeda, Sato PRC76 035203 (2007)

  6. Cutoff factors Introduced to regularize loop integral

  7. Data-fitting Large error bars • Obtained from a simple model analysis of Not “observable” !! • Magnitude is arbitrary. Few data points

  8. Pole positions Analytic structure on KN-physical (1st-Riemann), pS-unphysical (2nd-Riemann) sheet WT E-dep. E-indep.

  9. × × × Pole Trajectory WT Varying pS-pS coupling constant E-indep. E-dep. × 0 -50 -100 -150 × 0 -50 -100 -150 × × Im[E] (MeV) Im[E] (MeV) 1250 1300 1350 1400 1450 1250 1300 1350 1400 1450 Re[E] (MeV) Re[E] (MeV)

  10. Summary • Examined the analytic structure of the KN-pS amplitudes obtained from solving Lippmann-Schwinger equations using WT potential and its two different approximations • Within the available data, approximations can make a drastic change in the analytic structure of the amplitudes. • Also, within the current situation, ONLY the pole around 1420 –i15 MeV looks “model independent”. • Need much more data to constrain models and make them reliable for quantitative evaluations/predictions. • J-PARC will be a capable facility to provide such data!!

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