PARAMETERS FOR ${{\mathit K}_S^0}$ $\rightarrow$ 3 ${{\mathit \pi}}$ DECAY

Im($\eta _{000}){}^{2}$ = $\Gamma\mathrm {( {{\mathit K}_S^0} \rightarrow 3 {{\mathit \pi}^{0}} )}$ / $\Gamma\mathrm {( {{\mathit K}_L^0} \rightarrow 3 {{\mathit \pi}^{0}} )}$

INSPIRE   PDGID:
S012ET0
$\mathit CPT$ assumed valid (i.e. Re($\eta _{000}$) $\simeq{}$ 0). This limit determines branching ratio $\Gamma($ ${{\mathit K}_S^0}$ $\rightarrow$ 3 ${{\mathit \pi}^{0}}$ $)/\Gamma_{\text{total}}$ above.
VALUE CL% EVTS DOCUMENT ID TECN  COMMENT
• • We do not use the following data for averages, fits, limits, etc. • •
$<0.1$ 90 632 1
BARMIN
1983
HLBC
$<0.28$ 90 2
GJESDAL
1974B
 SPEC Indirect meas.
1  BARMIN 1983 find Re($\eta _{000}$) = ($-0.08$ $\pm0.18$) and Im($\eta _{000}$) = ($-0.05$ $\pm0.27$). Assuming $\mathit CPT$ invariance they obtain the limit quoted above.
2  GJESDAL 1974B uses ${{\mathit K}}2{{\mathit \pi}}$, ${{\mathit K}_{{\mu3}}}$, and ${{\mathit K}_{{e3}}}$ decay results, unitarity, and $\mathit CPT$. Calculates $\vert (\eta _{000})\vert $ = $0.26$ $\pm0.20$. We convert to upper limit.
References:
BARMIN 1983
PL 128B 129 Search for $\mathit CP$ Violation in the ${{\mathit K}^{0}}$ $\rightarrow$ 3 ${{\mathit \pi}^{0}}$ Decay
Also
SJNP 39 269 Search for $\mathit CP$ Violation in the ${{\mathit K}^{0}}$ $\rightarrow$ 3 ${{\mathit \pi}^{0}}$ Decay
GJESDAL 1974B
PL 52B 119 The Phase $\phi _{+−}$ of $\mathit CP$ Violation in the ${{\mathit K}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ Decay