# Im($\eta _{000}$) = Im($\boldsymbol A$( ${{\boldsymbol K}_S^0}$ $\rightarrow$ ${{\boldsymbol \pi}^{0}}{{\boldsymbol \pi}^{0}}{{\boldsymbol \pi}^{0}}$ )/$\boldsymbol A$( ${{\boldsymbol K}_L^0}$ $\rightarrow$ ${{\boldsymbol \pi}^{0}}{{\boldsymbol \pi}^{0}}{{\boldsymbol \pi}^{0}}$ )) INSPIRE search

${{\mathit K}_S^0}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ violates $\mathit CP$ conservation, in contrast to ${{\mathit K}_S^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ which has a $\mathit CP$-conserving part.
VALUE EVTS DOCUMENT ID TECN  COMMENT
$\bf{ -0.001 \pm0.016}$ OUR AVERAGE
$0.000$ $\pm0.009$ $\pm0.013$ 4.9M 1
 2005 A
NA48 Assumes $\mathit CPT$
$-0.05$ $\pm0.12$ $\pm0.05$ 17300 2
 1998 B
CPLR Assumes $\mathit CPT$
1  LAI 2005A assumes Re($\eta _{000}$)=Re($\epsilon )=1.66 \times 10^{-3}$. The equivalent limit is $\vert \eta _{000}\vert {}_{CPT}<$0.025 at 90$\%$ CL Without assuming $\mathit CPT$ invariance, they obtain Re($\eta _{000})=-0.002$ $\pm0.011$ $\pm0.015$ and Im($\eta _{000})=-0.003$ $\pm0.013$ $\pm0.017$ with a statistical correlation coefficient of 0.77 and an overall correlation coefficient of 0.57 between imaginary and real part. The equivalent limit is $\vert \eta _{000}\vert <$0.045 at 90$\%$ CL
2  ANGELOPOULOS 1998B assumes Re($\eta _{000}$) = Re($\epsilon$) = $1.635 \times 10^{-3}$. Without assuming $\mathit CPT$ invariance, they obtain Re($\eta _{000}$) = $0.18$ $\pm0.14$ $\pm0.06$ and Im($\eta _{000}$) = $0.15$ $\pm0.20$ $\pm0.03$.
Conservation Laws:
 $\mathit CP$ INVARIANCE
References:
 LAI 2005A
PL B610 165 Search for $\mathit CP$ Violation in ${{\mathit K}^{0}}$ $\rightarrow$ 3 ${{\mathit \pi}^{0}}$ Decays
 ANGELOPOULOS 1998B
PL B425 391 Search for $\mathit CP$ Violation in the Decay of Tagged ${{\mathit K}^{0}}$ and ${{\overline{\mathit K}}^{0}}$ to ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$