Fock space expansion of sigma meson in leading-Nc

Abstract

We examine the leading-Nc behavior of the masses and transition matrix elements of some low-lying, few-particle configurations in QCD. A truncation of the Fock space produces an effective, symmetric Hamiltonian that we diagonalize. The lowest eigenvalue is identified as the sigma meson if the Hamiltonian is chosen to represent the scalar sector. As an application, the coefficients of the Nc powers are then fit to two-loop Unitarized SU(2) Chiral Perturbation Theory results for the sigma mass and width as a function of the number of colors, and we show that those results can be accommodated using the QCD Nc dependence previously derived for matrix elements, without the need for unnatural parameters or fine tunings. Finally, we show a very preliminary good quality fit, estimating the proportion of tetraquark/molecule-like (dominant), q-anti-q-like (subdominant) and exotic-like (marginal) configurations in the sigma.

4 pages, 4 figures, Proceedings of QCD10, the 15th High-Energy Physics International Conference on Quantum Chromodynamics

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• Nature of the f_0(600) from its N_c dependence at two loops in unitarized Chiral Perturbation Theory
• The nature of $\sigma$, $\kappa$, $a_0(980)$ and $f_0(980)$
• Experimental status of the $\pi \pi$ isoscalar S wave at low energy: $f_0(600)$ pole and scattering length
• The Inverse Amplitude Method and Adler Zeros
• Properties of the rho and sigma Mesons from Unitary Chiral Dynamics
• Gluonium nature of the sigma/f_0(600) from its coupling to KK
• Precise dispersive data analysis of the f0(600) pole

Cited by in corpus (6)

• Chiral dynamics in form factors, spectral-function sum rules, meson-meson scattering and semilocal duality
• Conformal anomaly and the vector coupling in dense matter
• Chiral dynamics in U(3) unitary chiral perturbation theory
• Non-ordinary light meson couplings and the $1/N_c$ expansion
• Glueballs as the Ithaca of meson spectroscopy
• Enhanced non-quark-antiquark and non-glueball Nc behavior of light scalar mesons