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

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

INSPIRE   JSON PDGID:
S031A35
C$_{T}{}\equiv$ $\vec {{\mathit p}}_{{{\mathit K}_S^0} }\cdot{}$ ($\vec {{\mathit p}}_{{{\mathit K}^{-}}}{\times }\vec {{\mathit p}}_{{{\mathit \pi}^{+}}}$) is a parity-odd correlation of the momenta of the ${{\mathit K}_S^0}$ , ${{\mathit K}^{-}}$, and highest-momenta ${{\mathit \pi}^{+}}$ for the ${{\mathit D}^{+}}.\bar C_{T}{}\equiv$ $\vec {{\mathit p}}_{{{\mathit K}_S^0} }\cdot{}$ ($\vec {{\mathit p}}_{{{\mathit K}^{+}}}{\times }\vec {{\mathit p}}_{{{\mathit \pi}^{-}}}$) 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
$-2.3$ $\pm4.5$ $\pm1.5$ 70.8k 1
AGGARWAL
2025
 
BEL2 ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $\approx{}{{\mathit \Upsilon}{(4S)}}$
1  AGGARWAL 2025 measures C$_{T}{}\equiv$ $\vec {{\mathit p}}_{{{\mathit K}_S^0} }$ $\cdot{}$ ($\vec {{\mathit p}}_{{{\mathit K}^{-}}}{\times }\vec {{\mathit p}}_{{{\mathit \pi}^{+}}}$) and other T-odd observables, all compatible with T-conservation, using Belle and Belle II data.
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