A new method to study the number of colors in the final-state interactions of hadrons

Abstract

We match the $\pi \pi \to \pi \pi$ scattering amplitudes of Chiral Perturbation Theory with those from dispersion relations that respect analyticity and coupled channel unitarity, as well as accurately describing experiment. Their dependence on the number of colors ($N_C$) is obtained. By varying $N_C$ the trajectories of the poles and residues (the couplings to $\pi \pi$) of light mesons, the $\sigma$, $f_0(980)$, $\rho (770)$ and $f_2(1270)$ are investigated. Our results show that the method proposed is a reliable way to study the $N_C$ dependence in hadron-hadron scattering with final-state interactions.

7 pages, 3 figures, improved $N_C$ behaviour

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Cited by in corpus (10)

• A Review on Partial-wave Dynamics with Chiral Effective Field Theory and Dispersion Relation
• Semileptonic Decays of Charmed Mesons to Light Scalar Mesons
• ${\bar{B}}_s\to f_0(980)$ form factors and the width effect from light-cone sum rules
• Scalar-involved three-point Green functions and their phenomenology
• Dipion light-cone distribution amplitudes and $B\to \pi \pi$ form factors
• Test of semi-local duality in a large $N_C$ framework
• A study on the correlation between poles and cuts in $\pi \pi$ scattering
• Observation of $D^{+}\to f_0(500){\mu }^{+}{\nu }_{\mu }$ and study of $D^{+}\to {\pi }^{+}{\pi }^{-}{\ell }^{+}{\nu }_{\ell }$ decay dynamics
• Light-flavor resonance dynamics in the $U(3)$ chiral theory
• $N_C$ evolution of the light meson resonances