We perform for the first time an amplitude analysis of the decay $D^{+}\to K_S^0{\pi }^{+}\eta$ and report the observation of the decay $D^{+}\to K_S^0{a}_0(980{)}^{+}$ using $2.93{\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}$ collision data taken at a center-of-mass energy of 3.773 GeV with the BESIII detector. As the only $W$-annihilation-free decay among $D$ to $a_0(980)$ pseudoscalar, $D^{+}\to K_S^0{a}_0(980{)}^{+}$ is the ideal decay in extracting the contributions of the $W$-emission amplitudes involving $a_0(980)$ and to study the final-state interactions. The absolute branching fraction of $D^{+}\to K_S^0{\pi }^{+}\eta$ is measured to be $(1.27\pm 0.04_{\mathrm{stat}}\pm 0.03_{\mathrm{syst}})\%$. The branching fractions of intermediate processes $D^{+}\to K_S^0{a}_0(980{)}^{+}$ with $a_0(980{)}^{+}\to {\pi }^{+}\eta$ and $D^{+}\to {\pi }^{+}{\overline{K}}_0^{*}(1430{)}^0$ with ${\overline{K}}_0^{*}(1430{)}^0\to K_S^0\eta$ are measured to be $(1.33\pm 0.05_{\mathrm{stat}}\pm 0.04_{\mathrm{syst}})\%$ and $(0.14\pm 0.03_{\mathrm{stat}}\pm 0.01_{\mathrm{syst}})\%$, respectively.

• Received 23 September 2023
• Revised 10 January 2024
• Accepted 14 February 2024

DOI:https://doi.org/10.1103/PhysRevLett.132.131903

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Published by the American Physical Society