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 ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$

INSPIRE   PDGID:
S013HTZ
We do not average measurements that do not account for the effect of final state rescattering.
VALUE ($ 10^{-3} $) EVTS DOCUMENT ID TECN
$+0.59$ $\pm0.20$ $\pm1.16$ 68M 1
ABOUZAID
2008A
KTEV
• • We do not use the following data for averages, fits, limits, etc. • •
$-6.1$ $\pm0.9$ $\pm0.5$ 14.7M 2
LAI
2001B
NA48
$-3.3$ $\pm1.1$ $\pm0.7$ 5M 3, 2
SOMALWAR
1992
E731
1  Result obtained using CI3pI model of CABIBBO 2005 to include ${{\mathit \pi}}{{\mathit \pi}}$ rescattering effects. The systematic error includes an external error of $1.06 \times 10^{-3}$ from the parametrization input of (a$_{0}−$a$_{2}$) ${\mathit m}_{{{\mathit \pi}^{+}}}$ = $0.268$ $\pm0.017$ from BATLEY 2006B.
2  LAI 2001B and SOMALWAR 1992 results do not include ${{\mathit \pi}}{{\mathit \pi}}$ final state rescattering effects.
3  SOMALWAR 1992 chose ${\mathit m}_{{{\mathit \pi}^{+}}}$ as normalization to make it compatible with the Particle Data Group ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ definitions.
References:
ABOUZAID 2008A
PR D78 032009 Detailed Study of the ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ Dalitz Plot
LAI 2001B
PL B515 261 Measurement of the Quadratic Slope Parameter in the ${{\mathit K}_L^0}$ $\rightarrow$ 3 ${{\mathit \pi}^{0}}$ Decay Dalitz Plot
SOMALWAR 1992
PRL 68 2580 Measurement of the Quadratic Slope Parameter in the ${{\mathit K}_L^0}$ $\rightarrow$ 3 ${{\mathit \pi}^{0}}$ Decay Dalitz Plot