Study of $D_{s}^{+} \rightarrow f_{0}(980)\rho^+$ and $\phi \pi^+$ decays through $D_{s}^{+}\rightarrow \pi^{+}\pi^{+}\pi^{-}\pi^{0}$

TL;DR

This paper presents the first amplitude analysis of specific $D_s^+$ decays, revealing a significant $f_0(980) ho^+$ decay mode, precise branching fractions, and a notable deviation in $ ho$ decay ratios from the world average.

Contribution

It provides the first detailed amplitude analysis of $D_s^+$ decays into four pions, measuring branching fractions and discovering a significant decay mode with implications for meson decay dynamics.

Findings

Observation of $D_s^+ o f_0(980) ho^+$ with >10$\sigma$ significance.

Measured branching fractions for $D_s^+$ decays to $ ho^+ ho^- ext{ and } ext{eta} ext{ modes}.

Found a $ ho$ decay ratio deviating from the world average by over 4$\sigma$.

Abstract

We perform the first amplitude analysis of $D^+_s \to \pi^+\pi^+\pi^-\pi^0$ decays, based on data samples of electron-positron collisions recorded with the BESIII detector at center-of-mass energies between 4.128 and 4.226~GeV, corresponding to an integrated luminosity of 7.33~fb$^{-1}$. We report the observation of $D_{s}^{+} \to f_0(980)\rho(770)^{+}$ with a statistical significance greater than 10$\sigma$ and determine the branching fractions $\mathcal{B}(D_s^+\to\pi^+\pi^+\pi^-\pi^0|_{{\rm non}-\eta})=(2.04\pm0.08_{\rm stat.}\pm0.05_{\rm syst.})\%$ and $\mathcal{B}(D_s^+\to\eta\pi^+)=(1.56\pm0.09_{\rm stat.}\pm0.04_{\rm syst.})\%$. Moreover, we measure the relative branching fraction between $\phi\to\pi^+\pi^-\pi^0$ and $\phi\to K^+K^-$ to be $\frac{\mathcal{B}(\phi(1020) \to \pi^+\pi^-\pi^0)}{\mathcal{B}(\phi(1020) \to K^+K^-)}=0.230 \pm 0.014_{\rm stat.} \pm 0.010_{\rm syst.}$, which deviates from the world average value by more than $4\sigma$.