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 O(NC0) and exploiting unitarity, we show that the BW determination of the resonance mass differs from the pole position by O(NC−2) terms, which can be extracted from ππ scattering data. For the case of the σ (f0(600)) pole, the BW scalar mass is predicted to occur at ∼700 MeV while the true value is located at ∼800 MeV.