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.

中文翻译：

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衰变Ds+→π+π+π−η的研究和W-湮灭衰变的观察Ds+→a0(980)+ρ0

衰败 $D_{秒}^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}\eta$ 首次观察到，使用 ${\mathrm{电子}}^{+}{\mathrm{电子}}^{-}$ 对应于积分光度的碰撞数据 $6.32{\mathrm{脸书}}^{-1}$，由 BESIII 探测器在 4.178 和 4.226 GeV 之间的质心能量处收集。这种衰变的绝对支化分数被测量为$\mathcal{乙}(D_{秒}^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}\eta )=(3.12\pm 0.13_{\mathrm{状态}}\pm 0.09_{\mathrm{系统}})\%$. 这种衰减的第一次振幅分析揭示了$D_{秒}^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}\eta$并确定这些子结构之间的相对分数和相。占主导地位的中间过程是$D_{秒}^{+}\to {\mathrm{一种}}_1(1260{)}^{+}\eta ,{\mathrm{一种}}_1(1260{)}^{+}\to \rho (770{)}^0{\pi }^{+}$ 支化分数为 $(1.73\pm 0.14_{\mathrm{状态}}\pm 0.08_{\mathrm{系统}})\%$. 我们还观察到$宽$-歼灭过程 $D_{秒}^{+}\to {\mathrm{一种}}_0(980{)}^{+}\rho (770{)}^0$, ${\mathrm{一种}}_0(980{)}^{+}\to {\pi }^{+}\eta$ 支化分数为 $(0.21\pm 0.08_{\mathrm{状态}}\pm 0.05_{\mathrm{系统}})\%$，这大于其他测量纯的支化分数 $宽$-湮灭衰减1个数量级。