$\mathit CP$ 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 ${{\mathit D}^{*-}}$ $\rightarrow$ ${{\overline{\mathit D}}^{0}}{{\mathit \pi}^{-}}$.

$\mathit A_{\mathit Tviol}$(2 ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$) in ${{\mathit D}^{0}}$, ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ 2 ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$

INSPIRE   JSON  (beta) PDGID:
S032D55
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 of the ${{\mathit K}_S^0}$ (with higher momentum), ${{\mathit \pi}^{+}}$, and ${{\mathit \pi}^{-}}$ momenta (evaluated in the ${{\mathit D}^{0}}$ rest frame) for the ${{\mathit D}^{0}}$. $\bar C_{T}{}\equiv$ $\vec {{\mathit p}}_{{{\mathit K}_S^0} }\cdot{}$ ($\vec {{\mathit p}}_{{{\mathit \pi}^{-}}}{\times }\vec {{\mathit p}}_{{{\mathit \pi}^{+}}}$) is the corresponding quantity for the ${{\overline{\mathit D}}^{0}}$. 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 ${{\mathit K}_S^0}$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}$ ${{\mathit \pi}^{-}}$ $\rightarrow$ ${{\mathit D}^{0}}$ is not accessible, while the $\mathit CP$-conjugate process is.
VALUE ($ 10^{-2} $) EVTS DOCUMENT ID TECN  COMMENT
$-1.95$ $\pm1.42$ ${}^{+0.14}_{-0.12}$ 6095
SANGAL
2023
BELL ${{\mathit e}^{+}}{{\mathit e}}$ at ${{\mathit \Upsilon}{(4S,5S)}}$, 10.520 GeV
References