$\mathit CP$ VIOLATING ASYMMETRIES OF $\mathit P$-ODD ($\mathit T$-ODD) MOMENTS

The $\mathit CP$-sensitive $\mathit P$-odd ($\mathit T$-odd) correlation in ${{\mathit D}^{0}}$, ${{\overline{\mathit D}}^{0}}$ decays. The ${{\mathit D}^{0}}$ and ${{\overline{\mathit D}}^{0}}$ are distinguished by the charge of the parent ${{\mathit D}^{*}}$: ${{\mathit D}^{*+}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\mathit \pi}^{+}}$ and ${{\mathit D}^{*-}}$ $\rightarrow$ ${{\overline{\mathit D}}^{0}}{{\mathit \pi}^{-}}$.

$\mathit A_{{\mathrm {Tviol}}}({{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$) in ${{\mathit D}^{0}}$, ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$

INSPIRE   PDGID:
S032C76
C$_{T}{}\equiv$ $\vec {{\mathit p}}_{{{\mathit K}_S^0} }\cdot{}$ ($\vec {{\mathit p}}_{{{\mathit \pi}^{+}}}{\times }\vec {{\mathit p}}_{{{\mathit \pi}^{-}}}$) is a parity-odd correlation evaluated in the ${{\mathit D}^{0}}$ rest frame. $\bar C_{T}$ is defined as the $\mathit CP$-conjugate observable with ${{\overline{\mathit D}}^{0}}$ daughter particles. Then A$_{T}{}\equiv$ [$\Gamma (C_{T}>$ 0)$−$ $\Gamma (C_{T}<$ 0)] $/$ [$\Gamma (C_{T}>$ 0)$+$ $\Gamma (C_{T}<$ 0)], and $\bar A_{T}{}\equiv$ [$\Gamma (−\bar C_{T}>$ 0)$−$ $\Gamma (−\bar C_{T}<$ 0)] $/$ [$\Gamma (−\bar C_{T}>$ 0)$+$ $\Gamma (−\bar C_{T}<$ 0)], and A$_{Tviol}{}\equiv$ ${1\over 2}(A_{T}$ $−$ $\bar A_{T}$). C$_{T}$ and $\bar C_{T}$ are commonly referred to as $\mathit T$-odd moments, because they are odd under $\mathit T$ reversal. However, the $\mathit T$-conjugate process ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}$ ${{\mathit \pi}^{-}}$ ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit D}^{0}}$ is not accessible, while the $\mathit CP$-conjugate process is.
VALUE ($ 10^{-3} $) EVTS DOCUMENT ID TECN  COMMENT
$-0.28$ $\pm1.38$ ${}^{+0.23}_{-0.76}$ 745k 1
PRASANTH
2017
BELL ${{\mathit e}^{+}}{{\mathit e}^{-}}$ at ${{\mathit \Upsilon}{(nS)}}$'s
1  PRASANTH 2017 also measures $\mathit A_{{\mathrm {Tviol}}}$ in sub-regions of the ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ phase-space. No evidence of $\mathit T$ violation is found.
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