Couplings in coupled channels versus wave functions: application to the X(3872) resonance

Abstract

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 Schrödinger 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.

14 pages, 4 figures

References in corpus (14)

• Charmonium
• Is X(3872) {\sl Really} a Molecular State?
• Is X(3872) a molecule?
• Reconciling the X(3872) with the near-threshold enhancement in the D^0\bar{D}^{*0} final state
• Axial Resonances in the Open and Hidden Charm Sectors
• Estimate for the X(3872) to gamma J/psi decay width
• Isospin breaking effects in the X(3872) resonance
• Line Shapes of the X(3872)
• X(3872) as a hadronic molecule and its decays to charmonium states and pions
• QCD Sum Rules for the X(3872) as a mixed molecule-charmoniun state
• X(3872) as a molecular DD* state in a potential model
• Is Z^+(4430) a loosely bound molecular state?
• The Effects of Charged Charm Mesons on the Line Shapes of the X(3872)
• Photon induced Lambda(1520) production and the role of the K^* exchange

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