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Article overview
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Generalization of Weinberg's Compositeness Relations | | Yan Li
; Feng-Kun Guo
; Jin-Yi Pang
; Jia-Jun Wu
; | | Date: |
6 Oct 2021 | | 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. 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. | | Source: | arXiv, 2110.02766 | | Services: | Forum | Review | PDF | Favorites | |
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