Observation of $D_s^{+}\to a_0(980{)}^{+}{f}_0(500)$ in the Amplitude Analysis of $D_s^{+}\to {\pi }^{+}{\pi }^0{\pi }^0\eta$

Abstract

We report the first observation of the decay $D_s^{+}\to {\pi }^{+}{\pi }^0{\pi }^0\eta$ in a data set corresponding to an integrated luminosity of 7.33 fb${}^{-1}$, collected in $e^{+}{e}^{-}$ collisions by the BESIII detector at center-of-mass energies between 4.128 and 4.226 GeV. An unexpectedly large branching fraction $\mathcal{B}(D_s^{+}\to a_0(980{)}^{+}{f}_0(500),a_0(980{)}^{+}\to {\pi }^{+}\eta ,f_0(500)\to {\pi }^0{\pi }^0)=(0.98\pm 0.16_{stat.}\pm 0.22_{syst.})\%$ is measured with a significance exceeding $10\sigma$, offering new constraints on the internal structure of light scalar mesons. The dominant intermediate process is $D_s^{+}\to a_1(1260{)}^{+}\eta ,a_1(1260{)}^{+}\to \rho (770{)}^{+}{\pi }^0$ with a branching fraction of $(1.77\pm 0.21_{stat.}\pm 0.12_{syst.})\%$. The isospin symmetry has been validated to the decays of $a_1(1260{)}^{+}\to \rho (770{)}^0{\pi }^{+}$ and $a_1(1260{)}^{+}\to \rho (770{)}^{+}{\pi }^0$. Moreover, the measured $\mathcal{B}(D_s^{+}\to {\pi }^{+}{\pi }^0{\pi }^0\eta {|}_{\mathrm{non}-{\eta }^{\prime }})=(2.97\pm 0.23_{stat.}\pm 0.14_{sys.})$ reduces the undetected $D_s^{+}\to \eta X$ decay branching fractions to (0.1 $\pm$ 3.1)\%.