Non-ordinary light meson couplings and the $1/N_c$ expansion

Abstract

We study the large $N_c$ behavior of couplings among light meson states with different compositions in terms of quarks and gluons. We shortly review the most common compositions of mesons, which are of interest for the understanding of low-lying meson resonances, namely, the ordinary quark-antiquark states as well as the non-ordinary, glueball, tetraquark, etc. We dedicate special attention to Jaffe's generalization of the tetraquark with $N_c-1$ $q\bar{q}$ pairs, that is the only type of state we have identified, whose width does not necessarily vanish with $N_c$, while it does decouple exponentially with $N_c$ from the $\pi \pi$ channel, so that is weakly coupled to the meson-meson system.

arXiv comment37 pages and 12 figures

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• Large-$N_c$ naturalness in coupled-channel meson-meson scattering
• Tetraquarks in large-$N_c$ QCD
• Study the molecular nature of $\sigma$, $f_0(980)$, and $a_0(980)$ states
• Chiral and $U(1{)}_A$ restoration for the scalar/pseudoscalar meson nonets
• Interpretation of $Y_b(10750)$ as a tetraquark and its production mechanism
• Glueballs as the Ithaca of meson spectroscopy
• Tetraquark and two-meson states at large $N_{\mathrm{c}}$
• Light- and strange-quark mass dependence of the $\rho (770)$ meson revisited
• Feynman-Hellmann theorem for resonances and the quest for QCD exotica
• Analysis on the composite nature of the light scalar mesons $f_0(980)$ and $a_0(980)$
• A new method to study the number of colors in the final-state interactions of hadrons
• How tetraquarks can generate a second chiral phase transition
• Tetraquarks, Pentaquarks and Dibaryons in the large $N$ QCD
• Can the $\psi (4040)$ explain the peak associated with $Y(4008)$?
• OPE and quark-hadron duality for two-point functions of tetraquark currents in $1/N_c$ expansion
• Using QCD Counting rules to Identify the Production of Gluonium
• Observation of $D^{+}\to f_0(500){\mu }^{+}{\nu }_{\mu }$ and study of $D^{+}\to {\pi }^{+}{\pi }^{-}{\ell }^{+}{\nu }_{\ell }$ decay dynamics
• The Relativistic Cornell-type Mechanism of Exotic Scalar Resonances
• The $1/N_c$ expansion in hadron effective field theory
• Dynamical origin of neutrino masses and dark matter from a new confining sector
• $N_C$ evolution of the light meson resonances
• Precision dispersive approaches versus unitarized Chiral Perturbation Theory for the lightest scalar resonances $\sigma /f_0(500)$ and $\kappa /K_0^{\ast }(700)$