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arXiv · 1202.4607

Wave functions of composite hadron states and relationship to couplings of scattering amplitudes for general partial waves

F. Aceti·E. Oset
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Abstract

In this paper we present the connection between scattering amplitudes in momentum space and wave functions in coordinate space, generalizing previous work done for s-waves to any partial wave. The relationship to the wave function of the residues of the scattering amplitudes at the pole of bound states or resonances is investigated in detail. A sum rule obtained for the couplings provides a generalization to coupled channels, any partial wave and bound or resonance states, of Weinberg's compositeness condition, which was only valid for weakly bound states in one channel and s-wave. An example, requiring only experimental data, is shown for the $ρ$ meson indicating that it is not a composite particle of $ππ$ but something else.

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F. Aceti, E. Oset. 2012-05-29. Wave functions of composite hadron states and relationship to couplings of scattering amplitudes for general partial waves. https://doi.org/10.1103/physrevd.86.014012

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