Wave functions for dynamically generated resonances; the two $Λ(1405)$ and $Λ(1670)$

Details Wave functions for dynamically generated resonances; the two $Λ(1405)$ and $Λ(1670)$ Wave functions for dynamically generated resonances; the two $Λ(1405)$ and $Λ(1670)$

2010-10-11

arxiv.org/abs/1010.2147v1

AIP Conf.Proc.1322:384-388,2010

Physics

High Energy Physics

High Energy Physics - Phenomenology

5pages, 1 figure. To appear in the proceedings of the International Workshop on Chiral Symmetry in Hadrons and Nuclei (Chiral1

Scientific paper

10.1063/1.3542011

In this work we develop a formalism to evaluate wave functions in momentum and coordinate space for the resonant states dynamically generated in a unitary coupled channel approach. The on shell approach for the scattering matrix, commonly used, is also obtained in Quantum Mechanics with a separable potential, which allows one to write wave functions in a trivial way. We develop useful relationships among the couplings of the dynamically generated resonances to the different channels and the wave functions at the origin. The formalism provides an intuitive picture of the resonances in the coupled channel approach, as bound states of one bound channel, which decays into open ones. It also provides an insight and practical rules for evaluating couplings of the resonances to external sources and how to deal with final state interaction in production processes. As an application of the formalism we evaluate the wave functions of the two $\Lambda(1405)$ states in the $\pi \Sigma$, $\bar{K} N$ and other coupled channels. It also offers a practical way to study three body systems when two of them cluster into a resonance.

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