First measurement of $\mathit{T}$-odd moments in decays

We report the first measurement of the $T$-odd moments in the decay $D^{0} \rightarrow K_{S}^{0} \pi^{+} \pi^{-} \pi^{0}$ from a data sample corresponding to an integrated luminosity of $966{\mathrm{f}\mathrm{b}}^{-1}$ collected by the Belle experiment at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. From these moments we determine the $CP$-violation-sensitive asymmetry $a_{CP}^{T$\text{-odd}$} = \left[-0.28 \pm 1.38 ~(\rm{stat.}) ^{+0.23}{-0.76} ~(\rm{syst.})\right] \times 10^{-3}$,whichisconsistentwithno$CP$violation\mathrm{.}Inaddition,weperform$a{CP}^{T$\text{-odd}$}$measurementsindifferentregionsofthe$D^{0} \rightarrow K_{S}^{0} \pi^{+} \pi^{-} \pi^{0}$ phase space; these are also consistent with no $CP$ violation.