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Dynamical coupled-channels model of $K^- p$ reactions (I): Determination of partial-wave amplitudes

We develop a dynamical coupled-channels model of K^- p reactions, aiming at extracting the parameters associated with hyperon resonances and providing the elementary antikaon-nucleon scattering amplitudes that can be used for investigating various phenomena in the strangeness sector such as the production of hypernuclei from kaon-nucleus reactions. The model consists of (a) meson-baryon (MB) potentials v_{M'B',MB} derived from the phenomenological SU(3) Lagrangian, and (b) vertex interactions Gamma_{MB,Y*} for describing the decays of the bare excited hyperon states (Y*) into MB states. The model is defined in a channel space spanned by the two-body barK N, pi Sigma, pi Lambda, eta Lambda, and K Xi states and also the three-body pi pi Lambda and pi barK N states that have the resonant pi Sigma* and barK* N components, respectively. The resulting coupled-channels scattering equations satisfy the multichannel unitarity conditions and account for the dynamical effects arising from the off-shell rescattering processes. The model parameters are determined by fitting the available data of the unpolarized and polarized observables of the K^- p --> barK N, pi Sigma, pi Lambda, eta Lambda, K Xi reactions in the energy region from the threshold to invariant mass W=2.1 GeV. Two models with equally good chi^2 fits to the data have been constructed. The partial-wave amplitudes obtained from the constructed models are compared with the results from a recent partial-wave analysis by the Kent State University group. We discuss the differences between these three analysis results. Our results at energies near the threshold suggest that the higher partial waves should be treated on the same footing as the S wave if one wants to understand the nature of Lambda(1405)1/2^- using the data below the barK N threshold, as will be provided by the J-PARC E31 experiment.