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 2009 B KLOE ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \phi}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \gamma}}$

Conservation Laws:

$\mathit CP$ INVARIANCE

References