Observation of $D_s^+ \to a_0(980)^+f_0(500)$ in the Amplitude Analysis of $D_s^+ \to π^+ π^0 π^0 η$

Abstract

We report the first observation of the decay $D_s^+ \to π^+π^0π^0η$ 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 $\mathcal{B}( D_s^+ \to a_0(980)^+ f_0(500), a_0(980)^+ \to π^+η, f_0(500)\to π^0π^0) = (0.98 \pm 0.16_{\rm{stat.}} \pm 0.22_{\rm{syst.}})\%$ is measured with a significance exceeding $10σ$, offering new constraints on the internal structure of light scalar mesons. The dominant intermediate process is $D_s^+ \to a_1(1260)^+η, a_1(1260)^+\to ρ(770)^+π^0$ 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 $a_1(1260)^+\to ρ(770)^0π^+$ and $a_1(1260)^+\to ρ(770)^+π^0$. Moreover, the measured $\mathcal{B}(D_s^+\to π^+π^0π^0η|_{\rm{non}-η^\prime})=(2.97 \pm 0.23_{\rm stat.} \pm 0.14_{\rm sys.})$ reduces the undetected $D_s^+ \to ηX$ decay branching fractions to (0.1 $\pm$ 3.1)\%.

Figures (3)

• Figure 1: Topological diagrams of the decay $D_s^+ \to a_0(980)^+ f_0(500)$, where the $a_0(980)^+$ and $f_0(500)$ are represented in (a-b) as a two-quark state and in (c-d) as a tetraquark state.
• Figure 2: The projections of the fit are shown on (a) $M_{\pi^+\eta}$, (b) $M_{\pi^0\pi^0}$, (c) $M_{\pi^+\pi^0\pi^0}$, (d) $M_{\eta\pi^0}$, (e) $M_{\pi^+\pi^0}$, (f) $M_{\eta\pi^0\pi^+}$ and (g) $M_{\eta\pi^0\pi^0}$. The combinations of the two identical $\pi^0$s are added in (d), and (e), because of the exchange symmetry.
• Figure 3: Fits to the $M_{\rm sig}$ distributions of DT candidates for (a) all events and (b) $\pi^+\eta^\prime$. The data samples are represented by points with error bars, the total fit by the red line, and the fitted signal and background by the blue dotted and black dashed lines, respectively.