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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 ${{\mathit K}^{\pm}}$ $\rightarrow$ ${{\mathit \pi}^{\pm}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$

INSPIRE   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 2007 B 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:

BATLEY 2007B PL B649 349 Measurement of the Dalitz Plot Slope Parameters of the ${{\mathit K}^{\pm}}$ $\rightarrow$ ${{\mathit \pi}^{\pm}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ Decay DEVAUX 1977 NP B126 11 A Study of 225000 ${{\mathit \tau}^{+}}$ Decays LUCAS 1973 PR D8 719 New Determination of the Dalitz Plot Distribution for ${{\mathit \tau}^{-}}$ Decays FORD 1972 PL 38B 335 Experimental Study on the ${{\mathit \tau}^{\pm}}$ Decay Matrix Element HOFFMASTER 1972 NP B36 1 Analysis of the Pion Spectrum of 39819 ${{\mathit \tau}^{+}}$ Decays at Rest GRAUMAN 1970 PR D1 1277 Analysis of 17898 ${{\mathit \tau}^{+}}$ Decays at Rest Also PRL 23 737 Evidence for Violation of the $\Delta \mathit I={1\over 2}$ Rule in ${{\mathit K}^{+}}$ $\rightarrow$ 3 ${{\mathit \pi}}$ Decay MAST 1969 PR 183 1200 51000 ${{\mathit \tau}^{-}}$ Decays BUTLER 1968 UCRL 18420 A Study of 10,000 ${{\mathit \tau}^{+}}$ Decays MOSCOSO 1968 Thesis Thesis ZINCHENKO 1967 Thesis Rutgers Study of ${{\mathit K}^{+}}$ Decays into Three Pions FERRO-LUZZI 1961 NC 22 1087 Analysis of 1347 ${{\mathit \tau}^{-}}$ Decays

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