How much is the compositeness of a bound state constrained by $a$ and $r_0$? The role of the interaction range

E.Oset; Jing Song; L.R.Dai

How much is the compositeness of a bound state constrained by a and r₀? The role of the interaction range

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arxiv 2201.04414 v2 pith:SWXD4KJF submitted 2022-01-12 hep-ph

How much is the compositeness of a bound state constrained by a and r₀? The role of the interaction range

Jing Song , L.R.Dai , E.Oset This is my paper

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keywords rangeinformationinteractionbindingcompositenessallowsexplicitlysmall

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We present an approach that allows one to obtain information on the compositeness of molecular states from combined information of the scattering length of the hadronic components, the effective range, and the binding energy. We consider explicitly the range of the interaction in the formalism and show it to be extremely important to improve on the formula of Weinberg obtained in the limit of very small binding and zero range interaction. The method allows obtaining good information also in cases where the binding is not small. We explicitly apply it to the case of the deuteron and the $D^{*}_{s0}(2317)$ and $D^{*}_{s1}(2460)$ states and determine simultaneously the value of the compositeness within a certain range, as well as get qualitative information on the range of the interaction.

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Compositeness of near-threshold eigenstates with Coulomb plus short-range interactions
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The compositeness of near-threshold eigenstates with Coulomb plus short-range forces is determined solely by the Coulomb scattering length, effective range, and Bohr radius, with the Coulomb interaction qualitatively ...