1,302 research outputs found
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 and exploiting unitarity, we show
that the BW determination of the resonance mass differs from the pole position
by 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
), 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
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