The $a_0(980)$, $a_0(1450)$ and $K_0^*(1430)$ Scalar Decay Constants and the Isovector Scalar Spectrum

TL;DR

This paper uses finite energy sum rules to analyze the scalar decay constants of the $a_0(980)$ and $a_0(1450)$, providing insights into their quark structure and challenging molecular interpretations.

Contribution

It introduces a novel application of finite energy sum rules to determine scalar decay constants, clarifying the nature of the $a_0$ states and their relation to other scalar mesons.

Findings

Decay constants of $a_0(980)$ and $a_0(1450)$ are comparable.

Results disfavor $a_0(980)$ as a $Kar{K}$ molecule.

Implications for the quark structure of scalar mesons.

Abstract

The isovector scalar correlator is studied using a class of finite energy sum rules shown recently to be very well satisfied in the vector isovector channel. The values of the $a_0$ scalar decay constants extracted in this analysis, which describe the couplings of the $a_0(980)$ and $a_0(1450)$ to the isovector scalar current, are shown to be comparable, strongly disfavoring any scenario in which the $a_0(980)$ is interpreted as a loosely bound $K\bar{K}$ molecule and the $a_0(1450)$ is assigned to the same flavor multiplet as the $K_0^*(1430)$. The $a_0$ decay constants are also compared to the analogous decay constant describing the coupling of the $K_0^*(1430)$ to the divergence of the strange vector current (which may be obtained from experimental $K_{e3}$ and $K\pi$ phase shift data), and implications of the relative magnitudes for the interpretation of the nature of the $a_0$ states discussed.