Tetraquark nature of the $a_0(980)$ meson in hadronic $D$ decays

TL;DR

This paper investigates the internal structure of the $a_0(980)$ meson in $D$ decays, providing evidence that supports its tetraquark nature over the traditional $qar q$ model based on decay amplitude analyses.

Contribution

The study introduces additional topological amplitudes in decay models, demonstrating that the tetraquark hypothesis better explains experimental data on $a_0(980)$ production in $D$ decays.

Findings

$a_0(980)$ decay constants are inconsistent with $qar q$ model predictions.

Tetraquark model introduces new decay amplitudes $ar{T}$ and $ ilde T$ that fit experimental data.

Measurements of $D$ and $D_s^+$ decays support the tetraquark structure of $a_0(980)$.

Abstract

The internal structure of the light scalar meson $a_0(980)$ is explored in the three-body $D$ decays of $D\to a_0(980)P\to P_1P_2P$ through the intermediate state $a_0(980)$, where $P$ denotes a pseudoscalar meson. The quasi-two-body $D\to a_0(980)^+P$ decays are governed by the external $W$-emission diagram in which $a_0(980)^+$ is emitted. The predicted branching fractions in the $q\bar q$ model of $a_0(980)$ are too small by one to two orders of magnitude compared to experiment as the amplitude is suppressed by the smallness of the $a_0(980)^+$ decay constant, while those for $D^+\to a_0(980)^0 P$ and $D^0\to a_0(980)^{-}P$ are usually too large. These discrepancies can be resolved provided that $a_0(980)$ is a tetraquark state. In this case, there exist two additional $T$-like topological amplitudes, denoted by $\overline{T}$ and $\tilde T$ which readily account for the discrepancies. An important implication of the tetraquark model is that the $D_s^+\to a_0(980)^+\pi^0+a_0(980)^0\pi^+$ decay is not a purely $W$-annihilation process as in the diquark model of $a_0(980)$; it receives dominant contributions from $\overline{T}$ newly noticed in this work. Therefore, measurements of $(D,D_s^+)\to a_0(980)P$ decays lend strong support to the tetraquark picture of $a_0(980)$.