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Couplings in coupled channels versus wave functions: application to the X(3872) resonance
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Couplings in coupled channels versus wave functions: application to the X(3872) resonance
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We perform an analytical study of the scattering matrix and bound states in problems with many physical coupled channels. We establish the relationship of the couplings of the states to the different channels, obtained from the residues of the scattering matrix at the poles, with the wave functions for the different channels. The couplings basically reflect the value of the wave functions around the origin in coordinate space. In the concrete case of the X(3872) resonance, understood as a bound state of $\ddn$ and $\ddc$ (and $c.c.$), with the $\ddn$ loosely bound, we find that the couplings to the two channels are essentially equal leading to a state of good isospin I=0 character. This is in spite of having a probability for finding the $\ddn$ state much larger than for $\ddc$ since the loosely bound channel extends further in space. The analytical results, obtained with exact solutions of the Schr\"odinger equation for the wave functions, can be useful in general to interpret results found numerically in the study of problems with unitary coupled channels methods.
Forward citations
Cited by 7 Pith papers
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Predicted Exotic Doubly Heavy-Strange Pentaquarks
Predictions of two states in u d-bar s cc, three in u d-bar s cb, and four in u d-bar s bb sectors plus virtual states, obtained via unitary coupled channels with off-diagonal binding dominance.
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$KX(3872)$ interaction and correlation function
A unitarized fixed-center approximation predicts a narrow KX(3872) bound state 50 MeV below threshold and a characteristic femtoscopic correlation function.
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Searching for the pseudoscalar partner of $G(3900)$ via radiative $Y(4230)$ decays
Calculates B(Y(4230) → γ G0(3900)) = 3.8×10^{-5}–3.3×10^{-4} assuming P-wave molecular interpretations for both states and a triangle mechanism.
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Probing the hadronic molecular nature of the $\Omega(2012)$, $\Omega(2380)$, and $\Omega_c(3120)$ via femtoscopy correlation functions
Correlation function calculations with coupled-channel potentials produce low-momentum enhancements that the authors interpret as signatures of the molecular structure of Ω(2012), Ω(2380), and Ωc(3120).
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Probing the hadronic molecular nature of the $\Omega(2012)$, $\Omega(2380)$, and $\Omega_c(3120)$ via femtoscopy correlation functions
Numerical correlation functions computed from effective potentials exhibit enhancements that indicate the hadronic molecular nature of the Ω(2012), Ω(2380), and Ωc(3120) resonances.
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Correlation function and bound state from the $K D_{s0}^*(2317)$ interaction
The K D_s0*(2317) system develops a narrow resonance 40 MeV below threshold under the fixed-center molecular assumption, producing a characteristic correlation function for strong attraction.
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Radiative decays of $X(3872)$ within $D{\bar D}^*$ molecular framework
Using nonrelativistic effective field theory, the X(3872) is treated as a D*D molecule to predict radiative decay widths to D D gamma, finding a strong neutral-over-charged hierarchy and quantifying D D rescattering effects.
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