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

$\vert $matrix element$\vert ^2$ = 1 + $\mathit g{}\mathit u$ + $\mathit h{}\mathit u{}^{2}$ + $\mathit k{}\mathit v{}^{2}$ where $\mathit u$ = ($\mathit s_{3}$ $−$ $\mathit s_{0}$) $/$ ${{\mathit m}^{2}}_{{{\mathit \pi}}}$ and $\mathit v$ = ($\mathit s_{2}$ $−$ $\mathit s_{1}$) $/$ ${{\mathit m}^{2}}_{{{\mathit \pi}}}$

LINEAR COEFFICIENT $\mathit g$ FOR ${{\mathit K}^{\pm}}$ $\rightarrow$ ${{\mathit \pi}^{\pm}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$

INSPIRE   JSON  (beta) PDGID:
S010GT
Some experiments use Dalitz variables $\mathit x$ and $\mathit y$. In the comments we give $\mathit a_{\mathit y}$ = coefficient of $\mathit y$ term. See note above on “Dalitz Plot Parameters for ${{\mathit K}}$ $\rightarrow$ 3 ${{\mathit \pi}}$ Decays.” For discussion of the conversion of $\mathit a_{\mathit y}$ to $\mathit g$, see the earlier version of the same note in the $\mathit Review$ published in Physics Letters 111B 70 (1982).
VALUE EVTS DOCUMENT ID TECN CHG  COMMENT
$-0.21134$ $\pm0.00017$ 471M 1
BATLEY
2007B
NA48 $\pm{}$
• • We do not use the following data for averages, fits, limits, etc. • •
$-0.2221$ $\pm0.0065$ 225k
DEVAUX
1977
SPEC + $\mathit a_{\mathit y}=0.2814$ $\pm0.0082$
$-0.199$ $\pm0.008$ 81k 2
LUCAS
1973
HBC - $\mathit a_{\mathit y}=0.252$ $\pm0.011$
$-0.2157$ $\pm0.0028$ 750k
FORD
1972
ASPK + $\mathit a_{\mathit y}=0.2734$ $\pm0.0035$
$-0.2186$ $\pm0.0028$ 750k
FORD
1972
ASPK - $\mathit a_{\mathit y}=0.2770$ $\pm0.0035$
$-0.200$ $\pm0.009$ 39819 3
HOFFMASTER
1972
HLBC +
$-0.196$ $\pm0.012$ 17898 4
GRAUMAN
1970
HLBC + $\mathit a_{\mathit y}=0.228$ $\pm0.030$
$-0.193$ $\pm0.010$ 50919
MAST
1969
HBC - $\mathit a_{\mathit y}=0.244$ $\pm0.013$
$-0.218$ $\pm0.016$ 9994 5
BUTLER
1968
HBC + $\mathit a_{\mathit y}=0.277$ $\pm0.020$
$-0.190$ $\pm0.023$ 5778 5, 6
MOSCOSO
1968
HBC - $\mathit a_{\mathit y}=0.242$ $\pm0.029$
$-0.22$ $\pm0.024$ 5428 5, 6
ZINCHENKO
1967
HBC + $\mathit a_{\mathit y}=0.28$ $\pm0.03$
$-0.220$ $\pm0.035$ 1347 7
FERRO-LUZZI
1961
HBC - $\mathit a_{\mathit y}=0.28$ $\pm0.045$
1  Final state strong interaction and radiative corrections not included in the fit.
2  Quadratic dependence is required by ${{\mathit K}_L^0}$ experiments.
3  HOFFMASTER 1972 includes GRAUMAN 1970 data.
4  Emulsion data added $-$ all events included by HOFFMASTER 1972.
5  Experiments with large errors not included in average.
6  Also includes DBC events.
7  No radiative corrections included.
References