Meson Resonances at large NC : Complex Poles vs Breit-Wigner Masses
نویسندگان
چکیده
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(N C) and exploiting unitarity, we show that the BW determination of the resonance mass differs from the pole position by O(N C ) terms, which can be extracted from ππ scattering data. For the case of the f0(600) pole, the BW scalar mass is predicted to occur at ∼ 700 MeV while the true value is located at ∼ 800 MeV.
منابع مشابه
Unitarity and Interfering Resonances in Ππ Scattering and in Pion Production
Additivity of Breit-Wigner phases has been proposed to describe interfering resonances in partial waves in ππ scattering. This assumption leads to an expression for partial wave amplitudes that involves products of Breit-Wigner amplitudes. We show that this expression is equivalent to a coherent sum of Breit-Wigner amplitudes with specific complex coefficients which depend on the resonance para...
متن کاملPole versus Breit-Wigner resonance description of the orbitally excited baryons
We consider the masses used in recent studies involving the nonstrange sector of the l = 1 baryons. The use of T -matrix and K-matrix poles versus the conventional Breit-Wigner masses is discussed within the context of a large-Nc fitting scheme. While the mass and charge of a particle are typically the easiest quantities to determine experimentally, the proper way to define and extract the mass...
متن کاملMeson resonances from unitarized meson scattering at one loop in Chiral Perturbation Theory
We show the results for the scattering poles associated to the ρ, f 0 , a 0 , K * , σ and κ resonances in meson-meson scattering. Our amplitudes are obtained from the complete one-loop meson-meson scattering amplitudes from Chiral Perturbation Theory. Once unitarized with the Inverse Amplitude Method, they describe remarkably well the data simultaneously in the low energy and resonance regions ...
متن کاملThe Multichannel Quark Model
We discuss the non–relativistic multichannel quark model and describe the techniques developed to solve the resulting equations. We then investigate some simple solutions to demonstrate how the model unifies meson–meson scattering with meson spectroscopy, thereby greatly extending the domain of applicability of the näıve quark model. In the limits of narrow resonance widths and no quark exchang...
متن کاملModified Breit-Wigner formula for mesonic resonances describing OZI decays of confined qq̄ states and the light scalar mesons
A general expression resembling Breit-Wigner formulae is derived for the description of resonances which appear in meson-meson scattering. Starting point is a unitarised meson model, but reduced to a simpler form and freed from the specific assumption about the confining force. The parameters of the resulting “Resonance-Spectrum Expansion” are directly related to the confinement spectrum and th...
متن کامل