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

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 $\mathcal{O}(N_C^0)$ and exploiting unitarity, we show that the BW determination of the resonance mass differs from the pole position by $\mathcal{O}(N_C^{-2})$ 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.

7 pages. No figures. (elsevier preprint)

References in corpus (16)

• ππscattering
• Mass and width of the lowest resonance in QCD
• The inverse amplitude method in Chiral Perturbation Theory
• On the nature of light scalar mesons from their large $N_c$ behavior
• Nature of the f_0(600) from its N_c dependence at two loops in unitarized Chiral Perturbation Theory
• Bethe-Salpeter Approach for Unitarized Chiral Perturbation Theory
• The $S_{11}-N$(1535) and $-N$(1650) Resonances in Meson-Baryon Unitarized Coupled Channel Chiral Perturbation Theory
• Experimental status of the $\pi \pi$ isoscalar S wave at low energy: $f_0(600)$ pole and scattering length
• Large-N_c Baryons
• The Inverse Amplitude Method in $\pi \pi$ Scattering in Chiral Perturbation Theory to Two Loops
• Ordinary and Extraordinary Hadrons
• Finding the sigma pole by analytic extrapolation of $\pi \pi$ scattering data
• Error estimates for pi-pi scattering threshold parameters in Chiral Perturbation Theory to two loops
• The Inverse Amplitude Method and Chiral Perturbation Theory to two Loops
• On different lagrangian formalisms for vector resonances within chiral perturbation theory
• Model dependent analyses on the $N_c$ dependence of the $\sigma$ pole trajectory

Cited by in corpus (12)

• From controversy to precision on the sigma meson: a review on the status of the non-ordinary $f_0(500)$ resonance
• Systematics of radial and angular-momentum Regge trajectories of light non-strange q\bar{q}-states
• Large-Nc Properties of the rho and f0(600) Mesons from Unitary Resonance Chiral Dynamics
• Low-lying even parity meson resonances and spin-flavor symmetry
• Large-$N_c$ naturalness in coupled-channel meson-meson scattering
• Padé Approximants and Resonance Poles
• Scalar-isoscalar states in the large-Nc Regge approach
• Low-lying even parity meson resonances and spin-flavor symmetry revisited
• Enhanced non-quark-antiquark and non-glueball Nc behavior of light scalar mesons
• A new method to study the number of colors in the final-state interactions of hadrons
• Test of semi-local duality in a large $N_C$ framework
• $N_C$ evolution of the light meson resonances