# Possible signatures for tetraquarks from the decays of $a_0(980)$, $a_0(1450)$

## TL;DR

This paper investigates the decay patterns of $a_0(980)$ and $a_0(1450)$ under a tetraquark mixing scheme, finding that their decay ratios support their interpretation as tetraquark states.

## Contribution

It introduces a mixing scheme for tetraquarks and demonstrates that decay ratios of $a_0(980)$ and $a_0(1450)$ align with tetraquark signatures, supported by experimental data.

## Key findings

- Decay ratios match experimental data reasonably well.
- Couplings are enhanced for $a_0(980)$ and suppressed for $a_0(1450)$.
- Support for tetraquark interpretation of these states.

## Abstract

Based on the recent proposal for the tetraquarks with the mixing scheme, we investigate fall-apart decays of $a_0(980), a_0(1450)$ into two lowest-lying mesons. This mixing scheme suggests that $a_0(980)$ and $a_0(1450)$ are the tetraquarks with the mixtures of two spin configurations of diquark and antidiquark. Due to the relative sign differences in the mixtures, the couplings of fall-apart decays into two mesons are strongly enhanced for $a_0(980)$ but suppressed for $a_0(1450)$. We report that this expectation is supported by their experimental decays. In particular, the ratios of the associated partial decay widths, which depend on some kinematical factors and the couplings, are found to be around $\Gamma [a_0(980)\rightarrow \pi \eta]/\Gamma [a_0(1450)\rightarrow \pi \eta] = 2.51-2.54$, $\Gamma [a_0(980)\rightarrow K\bar{K}]/\Gamma [a_0(1450)\rightarrow K\bar{K}] = 0.52-0.89$, which seems to agree with the experimental ratios reasonably well. This agreement can be interpreted as the tetraquark signatures for $a_0(980), a_0(1450)$.