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

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

INSPIRE   PDGID:
S034TV0
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 ${{\mathit D}_{{s}}^{+}}$. $\bar C_{T}{}\equiv$ $\vec {{\mathit p}}_{{{\mathit K}^{-}}}\cdot{}$ ($\vec {{\mathit p}}_{{{\mathit \pi}^{-}}}{\times }\vec {{\mathit p}}_{{{\mathit \pi}^{+}}}$) is the corresponding quantity for the ${{\mathit D}_{{s}}^{-}}$. 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 ${{\mathit K}_S^0}$ ${{\mathit K}^{\pm}}$ ${{\mathit \pi}^{+}}$ ${{\mathit \pi}^{-}}$ $\rightarrow$ ${{\mathit D}_{{s}}^{\pm}}$ is not accessible, while the $\mathit P$-conjugate process is.
VALUE ($ 10^{-3} $) EVTS DOCUMENT ID TECN  COMMENT
$-13.6$ $\pm7.7$ $\pm3.4$ $29.8$ $\pm0.3$k
LEES
2011E
 BABR ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $\approx{}{{\mathit \Upsilon}{(4S)}}$
• • We do not use the following data for averages, fits, limits, etc. • •
$-36$ $\pm67$ $\pm23$ $508$ $\pm34$
LINK
2005E
 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
LINK 2005E
PL B622 239 Search for $\mathit T$ Violation in Charm Meson Decays