ENERGY DEPENDENCE OF ${{\mathit K}_L^0}$ DALITZ PLOT

For discussion, see note on Dalitz plot parameters in the ${{\mathit K}^{\pm}}$ section of the Particle Listings above. For definitions of $\mathit a_{\mathit v}$, $\mathit a_{\mathit t}$, $\mathit a_{\mathit u}$, and $\mathit a_{\mathit y}$, see the earlier version of the same note in the 1982 edition of this $\mathit Review$ published in Physics Letters 111B 70 (1982).
$\vert $matrix element$\vert ^2$ = 1 + $\mathit g{}\mathit u$ + $\mathit h{}\mathit u{}^{2}$ + $\mathit j{}\mathit v$ + $\mathit k{}\mathit v{}^{2}$ + $\mathit f{}\mathit u{}\mathit v$ where $\mathit u$ = ($\mathit s_{3}$ $−$ $\mathit s_{0}$) $/$ ${{\mathit m}^{2}}_{{{\mathit \pi}}}$ and $\mathit v$ = ($\mathit s_{2}$ $−$ $\mathit s_{1}$) $/$ ${{\mathit m}^{2}}_{{{\mathit \pi}}}$

QUADRATIC COEFFICIENT $\mathit k$ FOR ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$

INSPIRE   PDGID:
S013KT0
VALUE EVTS DOCUMENT ID TECN
$\bf{ 0.0099 \pm0.0015}$ OUR AVERAGE
$0.0104$ $\pm0.0017$ $\pm0.0024$ 500k
ANGELOPOULOS
1998C
CPLR
$0.024$ $\pm0.010$ 6499
CHO
1977
HBC
$-0.008$ $\pm0.012$ 4709
PEACH
1977
HBC
$0.0097$ $\pm0.0018$ 509k
MESSNER
1974
ASPK
References:
ANGELOPOULOS 1998C
EPJ C5 389 The Neutral Kaon Decays to ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$: a Detailed Analysis of the CPLEAR Data
CHO 1977
PR D15 587 A Measurement of ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ Decay Parameters
PEACH 1977
NP B127 399 A Study of the Dalitz Plot in the Decay ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$
MESSNER 1974
PRL 33 1458 Measurement of the ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ Dalitz Plot