#### $\mathit A_{\mathit Tviol}$( ${{\mathit K}_S^0}$ ${{\mathit K}^{\pm}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ ) in ${{\mathit D}^{\pm}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit K}^{\pm}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$

C$_{T}{}\equiv$ $\vec {{\mathit p}}_{{{\mathit K}^{+}} }\cdot{}$ ($\vec {{\mathit p}}_{{{\mathit \pi}^{+}} }{\times }\vec {{\mathit p}}_{{{\mathit \pi}^{-}} }$) is a parity-odd correlation of the ${{\mathit K}^{+}}$ , ${{\mathit \pi}^{+}}$ , and ${{\mathit \pi}^{-}}$ momenta for the ${{\mathit D}^{+}}$ . $\bar C_{T}{}\equiv$ $\vec {{\mathit p}}_{{{\mathit K}^{-}} }\cdot{}$ ($\vec {{\mathit p}}_{{{\mathit \pi}^{-}} }{\times }\vec {{\mathit p}}_{{{\mathit \pi}^{+}} }$) is the corresponding quantity for the ${{\mathit D}^{-}}$ . 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 ${{\mathit K}_S^0}$ ${{\mathit K}^{\pm}}$ ${{\mathit \pi}^{+}}$ ${{\mathit \pi}^{-}}$ $\rightarrow$ ${{\mathit D}^{\pm}}$ is not accessible, while the $\mathit P$-conjugate process is.
VALUE ($10^{-3}$) EVTS DOCUMENT ID TECN  COMMENT
$-12.0$ $\pm10.0$ $\pm4.6$ $21.2$ $\pm0.4$k
 2011 E
BABR ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $\approx{}{{\mathit \Upsilon}{(4S)}}$
• • We do not use the following data for averages, fits, limits, etc. • •
$+23$ $\pm62$ $\pm22$ $523$ $\pm32$
 2005 E
FOCS ${{\mathit \gamma}}$ A, ${{\overline{\mathit E}}}_{\gamma }{}\approx{}$180 GeV
Conservation Laws:
TIME REVERSAL ($\mathit T$) INVARIANCE
References:
 LEES 2011E
PR D84 031103 Search for $\mathit CP$ Violation using $\mathit T$-odd Correlations in ${{\mathit D}^{+}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ and ${{\mathit D}_{{s}}^{+}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ Decays
PL B622 239 Search for $\mathit T$ Violation in Charm Meson Decays