${{\boldsymbol \eta}}$ $\boldsymbol CP$-NONCONSERVING DECAY PARAMETER

${{\boldsymbol \pi}^{+}}{{\boldsymbol \pi}^{-}}{{\boldsymbol e}^{+}}{{\boldsymbol e}^{-}}$ DECAY-PLANE ASYMMETRY PARAMETER ${{\boldsymbol A}_{{\phi}}}$ INSPIRE search

In the ${{\mathit \eta}}$ rest frame, the total momentum of the ${{\mathit e}^{+}}{{\mathit e}^{-}}$ pair is equal and opposite to that of the ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ pair. Let $\hat{{\mathit z}}$ be the unit vector along the momentum of the ${{\mathit e}^{+}}{{\mathit e}^{-}}$ pair; let $\hat{{\mathit n}}_{ee}$ and $\hat{{\mathit n}}_{ {{\mathit \pi}} {{\mathit \pi}} }$ be the unit vectors normal to the ${{\mathit e}^{+}}{{\mathit e}^{-}}$ and ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ planes; and let $\phi $ be the angle between the two normals. Then
 sin$\phi $ cos $\phi $ = [($\hat{{\mathit n}}_{ee}{\times }\hat{{\mathit n}}_{ {{\mathit \pi}} {{\mathit \pi}} }$) $\cdot{}$ $\hat{{\mathit z}}$] ($\hat{{\mathit n}}_{ee}\cdot{}\hat{{\mathit n}}_{ {{\mathit \pi}} {{\mathit \pi}} }$) ,
and
  ${{\mathit A}_{{\phi}}}{}\equiv$ ${{{\mathit N}_{{{sin{{\mathit \phi}}~cos{{\mathit \phi}}>0}}}}~−~{{\mathit N}_{{{sin{{\mathit \phi}}~cos{{\mathit \phi}}<0}}}}\over {{\mathit N}_{{{sin{{\mathit \phi}}~cos{{\mathit \phi}}>0}}}}~+~{{\mathit N}_{{{sin{{\mathit \phi}}~cos{{\mathit \phi}}<0}}}} }$ .


VALUE ($ 10^{-2} $) EVTS DOCUMENT ID TECN  COMMENT
$-0.6$ $\pm2.5$ $\pm1.8$ $1555$ $\pm52$
AMBROSINO
2009B
KLOE ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \phi}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \gamma}}$
  Conservation Laws:
$\mathit CP$ INVARIANCE
  References:
AMBROSINO 2009B
PL B675 283 Measurement of the Branching Ratio and Search for a $\mathit CP$ Violating Asymmetry in the ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit e}^{+}}{{\mathit e}^{-}}$( ${{\mathit \gamma}}$) Decay at KLOE