# Testing the tetraquark mixing framework from QCD sum rules for $a_0(980)$

## TL;DR

This paper supports the tetraquark mixing framework for the $a_0(980)$ meson using QCD sum rules, showing the importance of spin-1 diquark configurations in its mass generation and the significance of mixed tetraquark states.

## Contribution

It provides the first QCD sum rule analysis incorporating both tetraquark types for the $a_0(980)$, confirming the dominance of the spin-1 diquark configuration in its structure.

## Key findings

- Spin-1 diquark configuration is essential for $a_0(980)$ mass.
- Mixed tetraquark correlation functions have large strength.
- Spin-0 diquark alone fails to predict the $a_0(980)$ mass.

## Abstract

According to a recent proposal of the tetraquark mixing framework, the two light-meson nonets in the $J^{P}=0^{+}$ channel, namely the light nonet composed of $a_0 (980)$, $K_0^* (800)$, $f_0 (500)$, $f_0(980)$, and the heavy nonet of $a_0 (1450)$, $K_0^* (1430)$, $f_0 (1370)$, $f_0 (1500)$, can be expressed by linear combinations of the two tetraquark types, one type containing the spin-0 diquark and the other with the spin-1 diquark. Among various consequences of this mixing model, one surprising result is that the second tetraquark with the spin-1 diquark configuration is more important for the light nonet. In this work, we report that this result can be supported by the QCD sum rule calculation. In particular, we construct a QCD sum rule for the isovector resonance $a_0(980)$ using an interpolating field composed of both tetraquark types and then perform the operator product expansion up to dimension 10 operators. Our sum rule analysis shows that the spin-1 diquark configuration is crucial in generating the $a_0(980)$ mass. Also, the mixed correlation function constructed from the two tetraquark types is found to have large strength which seems consistent with what the tetraquark mixing framework is advocating. On the other hand, the correlation function from the interpolating field with the spin-0 diquark configuration alone fails to predict the $a_0(980)$ mass mostly by the huge negative contribution from dimension 8 operators.