Effective range expansion for narrow near-threshold resonances

Abstract

We discuss some general features of the effective range expansion, the content of its parameters with respect to the nature of the pertinent near-threshold states and the necessary modifications in the presence of coupled channels, isospin violations and unstable constituents. As illustrative examples, we analyse the properties of the ${\chi }_{c1}(3872)$ and $T_{cc}^{+}$ states supporting the claim that these exotic states have a predominantly molecular nature.

15 pages, 1 figure

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• Multiquark Resonances
• Study of the doubly charmed tetraquark $T_{cc}^{+}$
• Pion Interactions in the X(3872)
• Analytic properties of the scattering amplitude and resonances parameters in a meson exchange model
• $T_{cc}^{+}$ coupled channel analysis and predictions
• Interplay of quark and meson degrees of freedom in a near-threshold resonance
• Insights into the inner structures of the fully charmed tetraquark state $X(6900)$
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• Nature of the doubly-charmed tetraquark $T_{cc}^{+}$ in a constituent quark model
• One Born$-$Oppenheimer Effective Theory to rule them all: hybrids, tetraquarks, pentaquarks, doubly heavy baryons and quarkonium
• Heavy Flavour Physics and CP Violation at LHCb: a Ten-Year Review
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• Spectrum of the molecular tetraquarks: Unraveling the $T_{cs0}(2900)$ and $T_{c\bar{s}0}^a(2900)$
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• Radiative decays of the spin-$2$ partner of $X(3872)$
• The interplay between compact and molecular structures in tetraquarks
• The nature of ${\chi }_{c1}\left(3872\right)$ and $T_{cc}^{+}\left(3875\right)$
• hidden charm decays of $X(4014)$ in a $D^{\ast }{\bar{D}}^{\ast }$ molecule scenario
• Substructure of Multiquark Hadrons (Snowmass 2021 White Paper)
• Compositeness of hadrons, nuclei, and atomic systems
• Two-pion exchange for coupled-channel scattering of two heavy mesons
• How does the $X(3872)$ show up in $e^{+}{e}^{-}$ collisions: dip versus peak
• Spectroscopic Properties of Double-Strangeness Molecular Tetraquarks
• Molecular states in $D_s^{(\ast )+}{\Xi }_c^{{(}^{\prime },\ast )}$ systems
• A short review on the compositeness of the $X(3872)$
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• ${\chi }_{c1}(2p)$: an overshadowed charmoniumlike resonance
• Electromagnetic characteristics as probes into the inner structures of the predicted ${\Xi }_c^{{(}^{\prime },\ast )}{D}_s^{(\ast )}$ molecular states
• Hadronic molecules and multiquark states
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