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

INSPIRE   JSON  (beta) PDGID:
S010GTP
Unless otherwise stated, all experiments include terms quadratic in ($\mathit s_{3}$ $−$ $\mathit s_{0}$) $/$ ${{\mathit m}^{2}}_{{{\mathit \pi}^{+}}}$. See note above on “Dalitz Plot Parameters for ${{\mathit K}}$ $\rightarrow$ 3 ${{\mathit \pi}}$ Decays.”

See BATUSOV 1998 for a discussion of the discrepancy between their result and others, especially BOLOTOV 1986. At this time we have no way to resolve the discrepancy so we depend on the large scale factor as a warning.
VALUE EVTS DOCUMENT ID TECN CHG  COMMENT
$\bf{ 0.626 \pm0.007}$ OUR AVERAGE
$0.6259$ $\pm0.0043$ $\pm0.0093$ 493k
AKOPDZHANOV
2005B
 TNF $\pm{}$
$0.627$ $\pm0.004$ $\pm0.010$ 252k 1, 2
AJINENKO
2003B
 ISTR -
• • We do not use the following data for averages, fits, limits, etc. • •
$0.736$ $\pm0.014$ $\pm0.012$ 33k
BATUSOV
1998
SPEC +
$0.582$ $\pm0.021$ 43k
BOLOTOV
1986
CALO -
$0.670$ $\pm0.054$ 3263
BRAUN
1976B
 HLBC +
$0.630$ $\pm0.038$ 5635
SHEAFF
1975
HLBC +
$0.510$ $\pm0.060$ 27k
SMITH
1975
WIRE +
$0.67$ $\pm0.06$ 1365
AUBERT
1972
HLBC +
$0.544$ $\pm0.048$ 4048
DAVISON
1969
HLBC + Also emulsion
1  Measured using in-flight decays of the 25 GeV negative secondary beam.
2  They form new world averages ${{\mathit g}}_{-}$ = ($0.617$ $\pm0.018$) and ${{\mathit g}}_{+}$ = ($0.684$ $\pm0.033$) which give $\Delta {{\mathit g}}_{\tau '}$ = $0.051$ $\pm0.028$.
References