Meson Resonances at large Nc: Complex Poles vs Breit-Wigner Masses

The rigorous quantum mechanical definition of a resonance requires determining the pole position in the second Riemann sheet of the analytically continued partial wave scattering amplitude in the complex Mandelstam s-variable plane. For meson resonances we investigate the alternative Breit-Wigner (BW) definition within the large Nc expansion. By assuming that the pole position is ${\cal O} (N_C^{0})$ and exploiting unitarity, we show that the BW determination of the resonance mass differs from the pole position by ${\cal O} (N_C^{-2})$ terms, which can be extracted from pi-pi scattering data. For the case of the f0(600) pole, the BW scalar mass is predicted to occur at about 700 MeV while the true value is located at about 800 MeV.Comment: 7 pages. No figures. (elsevier preprint

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

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.Comment: 14 pages, 4 figure