${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$   Decay Mode Summary INSPIRE   PDGID:
S032.143
Mode (*) Fraction ($\Gamma_i$ / $\Gamma$) Scale Factor/
Conf. Level		 P(MeV/c)  
$\Gamma_{88}$ ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ $0.052$ $\pm0.006$ S=1.0  813
Category: Hadronic modes with one ${{\overline{\mathit K}}}$
Note: Submodes of the ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ mode with a ${{\mathit K}^{*}}$ and/or ${{\mathit \rho}}$ were studied by COFFMAN 1992B, but with only 140 events. With nothing new for 18 years, we refer to our 2008 edition, Physics Letters B667 1 (2008), for those results.
The following data is related to the above value:
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$\Gamma($ ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ $)/\Gamma($ ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ $)$
$\Gamma_{88}/\Gamma_{43}$
$\Gamma($ ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \omega}}$ $)/\Gamma($ ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ $)$
$\Gamma_{118}/\Gamma_{88}$
$\Gamma($ ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ $)/\Gamma_{\text{total}}$
$\Gamma_{88}/\Gamma$