Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scalar resonances in the final state interactions of the decays $D^{0}
  \rightarrow \pi^{0}\pi^{0}\pi^{0}, \pi^{0}\pi^{0}\eta,\pi^{0}\eta\eta$   We investigate the scalar resonances in the processes of $D^{0} \rightarrow
\pi^{0}\pi^{0}\pi^{0}, \pi^{0}\pi^{0}\eta, \pi^{0}\eta\eta$ decays based on the
chiral unitary approach for the final state interaction. We start from singly
Cabibbo-suppressed production diagrams which provide a primary quark pair to
hadronize two pseudoscalar mesons in $D^{0}$ decays. The resonances
$f_{0}(500)$, $f_{0}(980)$ and $a_{0}(980)$ are dynamically produced from the
final state interactions of the meson pairs. In our results, the experimental
data for the $\pi^{0}\eta$ invariant mass spectrum of the $D^{0} \rightarrow
\pi^{0}\eta\eta$ decay can be described well. We also make the predictions for
the $\pi^{0}\pi^{0}$ invariant mass spectrum of the $D^{0} \rightarrow
\pi^{0}\pi^{0}\pi^{0}$, where the $f_{0}(980)$ can be found, and for the
$\pi^{0}\pi^{0}$, $\pi^{0}\eta$ invariant mass spectrum of the $D^{0}
\rightarrow \pi^{0}\pi^{0}\eta$, where the $f_{0}(500)$, $f_{0}(980)$ and
$a_{0}(980)$ appear. Furthermore, the branching ratios of each decay channel
are predicted. We expect more accurate measurements of these decays to better
understand the nature of the states $f_{0}(500)$, $f_{0}(980)$ and
$a_{0}(980)$.

25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn