Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalization of Weinberg's Compositeness Relations   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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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: math
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The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org