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Can the nature of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>980</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> be tested in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msubsup><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></…
From the amplitude analysis of the ${D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{0}\ensuremath{\eta}$ decay, the BESIII Collaboration first observed the ${D}_{s}^{+}\ensuremath{\rightarrow}{a}_{0}(980{)}^{+}{\ensuremath{\pi}}^{0}$ and ${D}_{s}^{+}\ensuremath{\rightarrow}{a}_{0}(980{)}^{0}{\ensuremath{\pi}}^{+}$ decay modes, which are expected to occur through the pure $W$-annihilation processes. The measured branching fraction $\mathcal{B}[{D}_{s}^{+}\ensuremath{\rightarrow}{a}_{0}(980{)}^{+(0)}{\ensuremath{\pi}}^{0(+)},{a}_{0}(980{)}^{+(0)}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+(0)}\ensuremath{\eta}]$ is, however, found to be larger than those of known $W$-annihilation decays by 1 order of …