The origin of light $0^{+}$ scalar resonances

TL;DR

This paper models the light scalar mesons below 2 GeV as unitarized quark states dressed by hadron loops, explaining their spectrum, decays, and behavior in the large N_c limit.

Contribution

It introduces a unitarized quark model with chiral constraints and SU(3) breaking to describe light scalar resonances as poles in the complex plane, distinguishing dynamically generated states from quark-antiquark seeds.

Findings

Light scalars below 2 GeV are described as poles in a unitarized quark model.

Dynamically generated states like sigma, kappa, and f0(980) move away from the real axis with increasing N_c.

Other states tend toward quark-antiquark seeds as N_c increases.

Abstract

We demonstrate how most of the light $J^{P}=0^{+}$ spectrum below $2.0\,\mathrm{GeV}$ and their decays can be consistently described by the unitarized quark model incorporating the chiral constraints of Adler zeros and taking SU(3) breaking effects into account. These resonances appear as poles in the complex $s$ plane in a unified picture as $q\bar{q}$ states strongly dressed by hadron loops. Through the large $N_c$ analysis, these resonances are found to naturally separate into two kinds: $\sigma, \kappa, f_0(980), a_0(980)$ are dynamically generated and run away from the real axis as $N_c$ increases, while the others move towards the $q\bar q $ seeds. In this picture, the line shape of $a_0(980)$ is produced by a broad pole below the $K\bar{K}$ threshold, and exhibits characteristics similar to the $\sigma$ and $\kappa$.