Fock space expansion of sigma meson in leading-Nc

TL;DR

This paper investigates the Nc dependence of the sigma meson in QCD using a Fock space expansion and effective Hamiltonian, fitting to chiral perturbation theory results and estimating its internal structure.

Contribution

It introduces a Fock space truncation approach with an effective Hamiltonian to analyze the sigma meson and fits Nc-dependent coefficients to chiral perturbation theory data.

Findings

Successfully fits Nc dependence of sigma mass and width

Estimates the internal configuration mix of the sigma meson

Provides a preliminary good quality fit to data

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.