The decay $D_s^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}\eta$ is observed for the first time, using $e^{+}{e}^{-}$ collision data corresponding to an integrated luminosity of $6.32{\mathrm{fb}}^{-1}$, 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 $\mathcal{B}(D_s^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}\eta )=(3.12\pm 0.13_{\mathrm{stat}}\pm 0.09_{\mathrm{syst}})\%$. The first amplitude analysis of this decay reveals the substructures in $D_s^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}\eta$ and determines the relative fractions and the phases among these substructures. The dominant intermediate process is $D_s^{+}\to a_1(1260{)}^{+}\eta ,a_1(1260{)}^{+}\to \rho (770{)}^0{\pi }^{+}$ with a branching fraction of $(1.73\pm 0.14_{\mathrm{stat}}\pm 0.08_{\mathrm{syst}})\%$. We also observe the $W$-annihilation process $D_s^{+}\to a_0(980{)}^{+}\rho (770{)}^0$, $a_0(980{)}^{+}\to {\pi }^{+}\eta$ with a branching fraction of $(0.21\pm 0.08_{\mathrm{stat}}\pm 0.05_{\mathrm{syst}})\%$, which is larger than the branching fractions of other measured pure $W$-annihilation decays by 1 order of magnitude.

• Received 1 July 2021
• Accepted 27 September 2021

DOI:https://doi.org/10.1103/PhysRevD.104.L071101

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Published by the American Physical Society