Fock space expansion of sigma meson in leading-N(c)

Abstract

We examine the leading-N(c) 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 (c) 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 N(c) 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 (q) over bar like (subdominant) and exotic-like (marginal) configurations in the sigma.