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 $\mathit h$ FOR ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$

INSPIRE   PDGID:
S013HT0
See notes in section “LINEAR COEFFICIENT $\mathit g$ FOR ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ $\vert $MATRIX ELEMENT$\vert ^2$” above.
VALUE EVTS DOCUMENT ID TECN
$\bf{ 0.076 \pm0.006}$ OUR AVERAGE
$0.061$ $\pm0.004$ $\pm0.015$ 500k
ANGELOPOULOS
1998C
 CPLR
$0.095$ $\pm0.032$ 6499
CHO
1977
HBC
$0.048$ $\pm0.036$ 4709
PEACH
1977
HBC
$0.079$ $\pm0.007$ 509k
MESSNER
1974
ASPK
• • We do not use the following data for averages, fits, limits, etc. • •
$-0.011$ $\pm0.018$ 29k 1
ALBROW
1970
ASPK
$0.043$ $\pm0.052$ 4400 1
SMITH
1970
OSPK
1  Quadratic coefficients $\mathit h$ and $\mathit k$ required by some experiments. (See section on ``QUADRATIC COEFFICIENT $\mathit k$'' below.) Correlations prevent us from averaging results of fits not including $\mathit g$, $\mathit h$, and $\mathit k$ terms.
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
ALBROW 1970
PL 33B 516 An Experimental Study of the Decay ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ ${{\mathit \pi}^{0}}$
SMITH 1970
PL 32B 133 Experimental Study of the Decay Spectrum of ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$