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

TL;DR

This paper compares the pole position and Breit-Wigner mass definitions of meson resonances in the large Nc limit, showing their differences are suppressed by 1/Nc^2 and providing specific predictions for the f0(600) resonance.

Contribution

It demonstrates that the Breit-Wigner mass differs from the pole position by terms of order 1/Nc^2 and applies this to predict the scalar mass of the f0(600) resonance.

Findings

Breit-Wigner mass differs from pole position by O(Nc^{-2})

Predicted Breit-Wigner scalar mass for f0(600) is about 700 MeV

True pole position of f0(600) is around 800 MeV

Abstract

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.