Mixing mechanism for the $J^{P}=0^{+}$ mesons

TL;DR

This paper proposes a new mixing mechanism based on tetraquark models to explain the small mass difference between certain scalar mesons, addressing limitations of previous mechanisms.

Contribution

It introduces a color-spin structure-based mixing model for scalar mesons, offering a potential explanation for observed mass differences in nonet structures.

Findings

The mixing mechanism can account for the small mass difference between $a_0(1450)$ and $K_0^*(1430)$.

Limitations of other mixing mechanisms are discussed and contrasted.

The model provides insights into the tetraquark structure of scalar mesons.

Abstract

There are three scalar nonets in the Particle Data Group (PDG), one of which includes [$a_0(980), K_0^*(700)$], another includes [$a_0(1450), K_0^*(1430)$], and the third includes [$a_0(1710), K_0^*(1950)$]. Motivated by Ref.[1], we examine an alternative mixing mechanism that could potentially explain the small mass difference between the $a_0 (1450)$ and $K_0^* (1430)$. According to the tetraquark mixing model, two types, distinguished by their color-spin structures, are necessary to describe the tetraquark structure of the two nonets containing [$a_0(980), K_0^*(700)$] and [$a_0(1450), K_0^*(1430)$]. Considering the color-spin structures, we argue that the mixing mechanism generating $a_0(1450)$ and $K_0^* (1430)$ on the one hand, and $a_0(1710)$ and $K_0^* (1950)$ on the other hand might be relevant for resolving the small mass difference. We also discuss the limitations of other mixing mechanisms that generate the two nonets involving [$a_0(980),K_0^*(700)$] and [$a_0(1450)$, $K_0^* (1430)$] or [$a_0(980),K_0^*(700)$] and [$a_0(1710)$, $K_0^* (1950)$]