Observation of the $ W$-Annihilation Process $ {D}_{s}^{+}\to \omega {\rho }^{+}$ and Measurement of $ {D}_{s}^{+}\to \varphi {\rho }^{+}$ in $ {D}_{s}^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}{\pi }^{0}{\pi }^{0}$ Decays

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\text{}\text{}{\mathrm{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\pm 0.0{8}_{\mathrm{stat}}{{\text{}}_{-0.07}^{+0.05}}_{\mathrm{syst}})\%$. In comparison to the low significance of the $ \mathcal{D}$ wave in the decay $ {D}_{s}^{+}\to \varphi {\rho }^{+}$, the dominance of the $ \mathcal{D}$ wave over the $ \mathcal{S}$ and $ \mathcal{P}$ waves, with a fraction of $ (51.85\pm 7.2{8}_{\mathrm{stat}}{{\text{}}_{-7.90}^{+4.83}}_{\mathrm{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\pm 0.1{5}_{\mathrm{stat}}\pm 0.1{3}_{\mathrm{syst}})\%$. Moreover, the branching fraction of $ {D}_{s}^{+}\to \varphi {\rho }^{+}$ is measured to be $ (3.98\pm 0.3{3}_{\mathrm{stat}}{{\text{}}_{-0.19}^{+0.21}}_{\mathrm{syst}})\%$, and the $ {R}_{\varphi }=\mathcal{B}(\varphi \to {\pi }^{+}{\pi }^{-}{\pi }^{0})/\mathcal{B}(\varphi \to {K}^{+}{K}^{-})$ is determined to be ($ 0.222\pm 0.01{9}_{\mathrm{stat}}{{\text{}}_{-0.016}^{+0.016}}_{\mathrm{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 $.