Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Study of the Decay $D^{+}_{s}\rightarrow \pi^{+}\pi^{+}\pi^{-}\eta$ and
  Observation of the W-annihilation Decay $D^{+}_{s}\rightarrow
  a_0(980)^+\rho^0$   The decay $D^{+}_{s}\rightarrow \pi^{+}\pi^{+}\pi^{-}\eta$ is observed for
the first time, using $e^+e^-$ collision data corresponding to an integrated
luminosity of 6.32 fb$^{-1}$, collected by the BESIII detector at
center-of-mass energies between 4.178 and 4.226 GeV. The absolute branching
fraction for this decay is measured to be $\mathcal{B}(D^+_s \to \pi^+ \pi^+
\pi^- \eta) = (3.12\pm0.13_{\rm stat.}\pm0.09_{\rm syst.})$%. The first
amplitude analysis of this decay reveals the sub-structures in
$D^{+}_{s}\rightarrow \pi^{+}\pi^{+}\pi^{-}\eta$ and determines the relative
fractions and the phases among these sub-structures. The dominant intermediate
process is $D^{+}_{s}\rightarrow a_1(1260)^+ \eta, a_1(1260)^+ \rightarrow
\rho(770)^0\pi^+$ with a branching fraction of $(1.73 \pm 0.14_{\rm stat.} \pm
0.08_{\rm syst.})$%. We also observe the W-annihilation process
$D^{+}_{s}\rightarrow a_0(980)^+\rho(770)^0$, $a_0(980)^+ \to \pi^+ \eta$ with
a branching fraction of $(0.21\pm0.08_{\rm stat.}\pm0.05_{\rm syst.})$%, which
is larger than the branching fractions of other measured pure W-annihilation
decays by one order of magnitude.

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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: cs
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The categories of this paper are: chao-dyn