Observation of the $W$-annihilation process $D_s^+ \to \omega\rho^+$ and measurement of $D_s^+ \to \phi\rho^+$ in $D^+_s\to \pi^+\pi^+\pi^-\pi^0\pi^0$ decays

TL;DR

This paper reports the first amplitude analysis and branching fraction measurements of specific charm meson decays, including the first observation of the $W$-annihilation decay $D_s^+ o ext{omega} ho^+$, providing insights into decay dynamics and polarization puzzles.

Contribution

It presents the first amplitude analysis and measurements of $D_s^+$ decays, notably observing the pure $W$-annihilation decay $D_s^+ o ext{omega} ho^+$ and analyzing polarization effects.

Findings

First observation of $D_s^+ o ext{omega} ho^+$ with a branching fraction of ~1%.

Measured branching fraction of $D_s^+ o au^+ au^-$ decay as 4.41%.

Determined the ratio $R_{ ext{phi}}$ consistent with previous charm decay measurements but deviating from other experiments.

Abstract

We present the first amplitude analysis and branching fraction measurement of the decay $D^+_s\to \pi^+\pi^+\pi^-\pi^0\pi^0$, using $e^+e^-$ collision data collected 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$^{-1}$, and report the first observation of the pure $W$-annihilation decay $D_s^+ \to \omega\rho^+$ with a branching fraction of $(0.99\pm0.08_{\rm stat}{\ ^{+0.05}_{-0.07}}_{\rm syst})\%$. %The absolute branching fraction is measured to be $(0.99\pm0.08_{\rm stat}\pm0.07_{\rm syst})\%$. In comparison to the low significance of the $\mathcal{D}$ wave in the decay $D_s^+ \to \phi\rho^+$, the dominance of the $\mathcal{D}$ wave over the $\mathcal{S}$ and $\mathcal{P}$ waves, with a fraction of $(51.85\pm7.28_{\rm stat}{\ ^{+4.83}_{-7.90}}_{\rm syst})\%$ observed in the decay $D_s^+ \to \omega\rho^+$, provides crucial information for the``polarization puzzle", as well as for the understanding of charm meson decays. The branching fraction of $D^+_s\to \pi^+\pi^+\pi^-\pi^0\pi^0$ is measured to be ($4.41\pm0.15_{\rm stat}\pm0.13_{\rm syst}$)\%. Moreover, the branching fraction of $D_s^+ \to \phi\rho^+$ is measured to be $(3.98\pm0.33_{\rm stat}{\ ^{+0.21}_{-0.19}}_{\rm syst})\%$, and the $R_{\phi}= {\mathcal{B}(\phi\to\pi^+\pi^-\pi^0)}/{\mathcal{B}(\phi\to K^+K^-)}$ is determined to be $(0.222\pm0.019_{\rm stat}{\ ^{+0.016}_{-0.016}}_{\rm syst}$), which is consistent with the previous measurement based on charm meson decays, but deviates from the results from $e^+e^-$ annihilation and $K$-$N$ scattering experiments by more than 3$\sigma$.