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arXiv · 2110.02766

Generalization of Weinberg's Compositeness Relations

Yan Li·Feng-Kun Guo·Jin-Yi Pang·Jia-Jun Wu
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Abstract

We generalize the time-honored Weinberg's compositeness relations by including the range corrections through considering a general form factor. In Weinberg's derivation, he considered the effective range expansion up to $\mathcal{O}(p^2)$ and made two additional approximations: neglecting the non-pole term in the Low equation; approximating the form factor by a constant. We lift the second approximation, and work out an analytic expression for the form factor. For a positive effective range, the form factor is of a single-pole form. An integral representation of the compositeness is obtained and is expected to have a smaller uncertainty than that derived from Weinberg's relations. We also establish an exact relation between the wave function of a bound state and the phase of the scattering amplitude neglecting the non-pole term. The deuteron is analyzed as an example, and the formalism can be applied to other cases where range corrections are important.

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Yan Li, Feng-Kun Guo, Jin-Yi Pang, Jia-Jun Wu. 2021-10-06. Generalization of Weinberg's Compositeness Relations. https://doi.org/10.1103/physrevd.105.l071502

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