# DECAY-PLANE ASYMMETRY IN ${{\boldsymbol \pi}^{+}}{{\boldsymbol \pi}^{-}}{{\boldsymbol e}^{+}}{{\boldsymbol e}^{-}}$ DECAYS

This is the $\mathit CP$-violating asymmetry
$\mathit A$= ${\mathit N_{{\mathrm {sin\phi }}{\mathrm {cos \phi }}>0.0}−\mathit N_{{\mathrm {sin\phi }}{\mathrm {cos \phi }}<0.0}\over \mathit N_{{\mathrm {sin\phi }}{\mathrm {cos \phi }}>0.0}+\mathit N_{{\mathrm {sin\phi }}{\mathrm {cos \phi }}<0.0}}$
where $\phi$ is the angle between the ${{\mathit e}^{+}}{{\mathit e}^{-}}$ and ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ planes in the ${{\mathit K}_S^0}$ rest frame.

# $\boldsymbol CP$ asymmetry $\boldsymbol A$ in ${{\boldsymbol K}_S^0}$ $\rightarrow$ ${{\boldsymbol \pi}^{+}}{{\boldsymbol \pi}^{-}}{{\boldsymbol e}^{+}}{{\boldsymbol e}^{-}}$ INSPIRE search

VALUE (%) DOCUMENT ID TECN  COMMENT
$\bf{ -0.4 \pm0.8 }$ OUR AVERAGE
$-0.4$ $\pm0.8$ 1
 2011
NA48 2002 data
$-1.1$ $\pm4.1$
 2003 C
NA48 1998+1999 data
• • • We do not use the following data for averages, fits, limits, etc. • • •
$0.5$ $\pm4.0$ $\pm1.6$
 2003 C
NA48 1999 data
1  The result is used to set the limit $\mathit A$ $<$ 1.5$\%$ at 90$\%$ C.L.
Conservation Laws:
 $\mathit CP$ INVARIANCE
References:
 BATLEY 2011
PL B694 301 Precision Measurement of the Ratio B( ${{\mathit K}_S^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit e}^{+}}{{\mathit e}^{-}}$ )/B( ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ )
 LAI 2003C
EPJ C30 33 Investigation of ${{\mathit K}_{{L,S}}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit e}^{+}}{{\mathit e}^{-}}$ Decays