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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 $\mathit v$ = ($\mathit s_{2}$ $−$ $\mathit s_{1}$) $/$ ${{\mathit m}^{2}}_{{{\mathit \pi}}}$

($\mathit g_{+}$ $–$ $\mathit g_{-}$) $/$ ($\mathit g_{+}$ + $\mathit g_{-}$) FOR ${{\mathit K}^{\pm}}$ $\rightarrow$ ${{\mathit \pi}^{\pm}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$

INSPIRE   PDGID:

S010DG0

A nonzero value for this quantity indicates $\mathit CP$ violation.

VALUE ($ 10^{-4} $) EVTS DOCUMENT ID TECN $\bf{ 1.8 \pm1.8}$ OUR AVERAGE $1.8$ $\pm1.7$ $\pm0.6$ 91.3M 1 BATLEY 2007 E NA48 $2$ $\pm18$ $\pm5$ 619k 2 AKOPDZHANOV 2005 TNF • • We do not use the following data for averages, fits, limits, etc. • • $1.8$ $\pm2.2$ $\pm1.3$ 47M 3 BATLEY 2006 A NA48 1  BATLEY 2007E includes data from BATLEY 2006A. Uses quadratic parametrization and PDG 2006 value $\mathit g$ = $0.626$ $\pm0.007$ to obtain ${{\mathit g}_{{+}}}$ ${{\mathit g}_{{-}}}$ = ($2.2$ $\pm2.1$ $\pm0.7$) $ \times 10^{-4}$. Neglects any possible charge asymmetries in higher order slope parameters ${{\mathit h}}$ or ${{\mathit k}}$. 2  Asymmetry obtained assuming that ${{\mathit g}_{{+}}}+{{\mathit g}_{{-}}}$ = 2${\times }$0.652 (PDG 2002 ) and that asymmetries in ${{\mathit h}}$ and ${{\mathit k}}$ are zero. 3  Linear and quadratic slopes from PDG 2004 are used. Any possible charge asymmetries in higher order slope parameters ${{\mathit h}}$ or ${{\mathit k}}$ are neglected.

Conservation Laws:

$\mathit CP$ INVARIANCE

References:

BATLEY 2007E EPJ C52 875 Search for Direct $\mathit CP$ Violating Charge Asymmetries in ${{\mathit K}^{\pm}}$ $\rightarrow$ ${{\mathit \pi}^{\pm}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ and ${{\mathit K}^{\pm}}$ $\rightarrow$ ${{\mathit \pi}^{\pm}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ Decays BATLEY 2006A PL B638 22 Search for Direct $\mathit CP$-Violation in ${{\mathit K}^{\pm}}$ $\rightarrow$ ${{\mathit \pi}^{\pm}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ Decays Also PL B640 297 (errat.) Erratum to BATLEY 2006A/ Search for Direct $\mathit CP$-Violation in ${{\mathit K}^{\pm}}$ $\rightarrow$ ${{\mathit \pi}^{\pm}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ Decays AKOPDZHANOV 2005 EPJ C40 343 Measurements of the Charge Asymmetry of the Dalitz Plot Parameters for ${{\mathit K}^{\pm}}$ $\rightarrow$ ${{\mathit \pi}^{\pm}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ Decays Also PAN 68 948 Measurement of the Charge Asymmetry of the Dalitz Plot Parameters for ${{\mathit K}^{\pm}}$ $\rightarrow$ ${{\mathit \pi}^{\pm}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ Decays

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