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arXiv · 2403.05486

Confronting the Lippmann-Schwinger equation and the $N/D$ method for coupled-wave separable potentials

M. S. Sánchez·J. A. Oller·D. R. Entem
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Abstract

We study a family of separable potentials with and without added contact interactions by solving the associated Lippmann-Schwinger equation with two coupled partial waves. The matching of the resulting amplitude matrix with the effective-range expansion is studied in detail. When a counterterm is included in the potential we also carefully discuss its renormalization. Next, we use the matrix $N/D$ method and study whether the amplitude matrices from the potentials considered admit an $N/D$ representation in matrix form. As a novel result we show that it is typically not possible to find such matrix representation for the coupled partial-wave case. However, a separate $N/D$ representation for each coupled partial wave, a valid option known in the literature, is explicitly implemented and numerically solved in cases where the matrix $N/D$ method is unavailable.

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M. S. Sánchez, J. A. Oller, D. R. Entem. 2024-03-08. Confronting the Lippmann-Schwinger equation and the $N/D$ method for coupled-wave separable potentials. https://arxiv.org/abs/2403.05486

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