arXiv 2403.054862024-03-08nucl-thhep-ph

针对耦合波可分离势的Lippmann-Schwinger方程与$N/D$方法的对比研究

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

M. S. Sánchez, J. A. Oller, D. R. Entem

备注：: 45 pages, 3 figures

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AI总结：

本研究针对含耦合分波的可分离势，对比求解Lippmann-Schwinger方程与矩阵$N/D$方法，发现耦合分波下通常不存在矩阵形式的$N/D$表示，并实现了分波独立$N/D$表示的数值求解。

摘要：

我们通过求解含两个耦合分波的相关Lippmann-Schwinger方程，研究了一类包含和不包含附加接触相互作用的可分离势。我们详细探究了所得振幅矩阵与有效力程展开的匹配问题。当势中包含抵消项时，我们还细致讨论了其重整化问题。随后，我们使用矩阵$N/D$方法，研究所考虑势的振幅矩阵是否允许矩阵形式的$N/D$表示。作为一项新结果，我们表明在耦合分波情形下通常无法找到此类矩阵表示。不过，针对每个耦合分波分别进行$N/D$表示是文献中已知的可行方案，我们在矩阵$N/D$方法不适用的情形下明确实现了该方案并进行了数值求解。

英文摘要：

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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