First measurement of $\mathbf{T}$-odd moments in ${\mathbf{D}}^0\to {\mathbf{K}}_{\mathbf{S}}^0{\mathbf{\pi }}^{+}{\mathbf{\pi }}^{-}{\mathbf{\pi }}^0$ decays

Abstract

We report the first measurement of the $T$-odd moments in the decay $D^0\to K_S^0{\pi }^{+}{\pi }^{-}{\pi }^0$ from a data sample corresponding to an integrated luminosity of $966{\mathrm{fb}}^{-1}$ collected by the Belle experiment at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. From these moments we determine the $CP$-violation-sensitive asymmetry $a_{CP}^{T\text{-odd}}=\left[-0.28\pm 1.38(stat.{)}_{-0.76}^{+0.23}(syst.)\right]\times 10^{-3}$, which is consistent with no $CP$ violation. In addition, we perform $a_{CP}^{T\text{-odd}}$ measurements in different regions of the $D^0\to K_S^0{\pi }^{+}{\pi }^{-}{\pi }^0$ phase space; these are also consistent with no $CP$ violation.

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