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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   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 2005 B TNF $\pm{}$ $0.627$ $\pm0.004$ $\pm0.010$ 252k 1, 2 AJINENKO 2003 B 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 1976 B 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:

AKOPDZHANOV 2005B JETPL 82 675 Measurements of the Dalitz Plot Parameters for ${{\mathit K}^{\pm}}$ $\rightarrow$ ${{\mathit \pi}^{\pm}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ Decays AJINENKO 2003B PL B567 159 Measurement of the Dalitz Plot Slope Parameters for ${{\mathit K}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \pi}^{-}}$ Decay using ISTRA+ Detector BATUSOV 1998 NP B516 3 Measurement of Dalitz Plot Slope Parameters for ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ Decay BOLOTOV 1986 SJNP 44 73 Investigation of ${{\mathit K}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ Decay BRAUN 1976B LNC 17 521 An Experimental Determination of the Parameters Describing the ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ Decay Matrix Element SHEAFF 1975 PR D12 2570 Experimental Study of the Energy Spectrum of the ${{\mathit \pi}^{+}}$ in ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ Decay SMITH 1975 NP B91 45 An Experimental Investigation of the Decays ${{\mathit K}^{\pm}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \pi}^{\pm}}$ . The Slope Parameter and its Charge Asymmetry AUBERT 1972 NC 12A 509 Experimental Study of the Matrix Element in the ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ Decay DAVISON 1969 PR 180 1333 Energy Spectrum of the ${{\mathit \pi}^{+}}$ in ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$

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