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.)

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

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

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) meson baryon Fixed with SU(3) symmetry (S-wave) Lippmann-Schwinger equation: S-wave projection

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

Cutoff factors Introduced to regularize loop integral

Data-fitting WT E-indep. E-dep. 810 1100 550 Large error bars Obtained from a simple model analysis of  Not “observable” !! Magnitude is arbitrary. Few data points

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

Pole Trajectory × Varying pS-pS coupling constant × × × × WT E-dep. E-indep. × -50 -100 -150 × -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)

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!!