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 $\mathcal{B}( D_s^+ \to a_0(980)^+ f_0(500), a_0(980)^+ \to \pi^+\eta, f_0(500)\to \pi^0\pi^0) = (0.98 \pm 0.16_{\rm{stat.}} \pm 0.22_{\rm{syst.}})\%$ 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 $(1.77 \pm 0.21_{\rm stat.} \pm 0.12_{\rm syst.})\%$. 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 $\mathcal{B}(D_s^+\to \pi^+\pi^0\pi^0\eta|_{\rm{non}-\eta^\prime})=(2.97 \pm 0.23_{\rm stat.} \pm 0.14_{\rm sys.})$ reduces the undetected $D_s^+ \to \eta X$ decay branching fractions to (0.1 $\pm$ 3.1)\%.