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

TL;DR

This paper reports the first observation of a specific decay mode of the $D_s^+$ meson involving scalar mesons, with a large branching fraction, providing insights into light scalar meson structures through amplitude analysis.

Contribution

It presents the first observation and measurement of the decay $D_s^+ o a_0(980)^+f_0(500)$, offering new constraints on light scalar mesons and validating isospin symmetry in related decays.

Findings

Branching fraction of $D_s^+ o a_0(980)^+f_0(500)$ measured as (0.98 ± 0.16 ± 0.22)%

Dominant process is $D_s^+ o a_1(1260)^+ o ho(770)^+ o o ext{pi}^0$ with a branching fraction of (1.77 ± 0.21 ± 0.12)%

Reduced the upper limit on $D_s^+ o ext{eta} X$ decay branching fractions to about 0.1%.

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)\%.