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

INSPIRE   PDGID:

S010DG

This is a $\mathit CP$ violating asymmetry between linear coefficients ${{\mathit g}_{{+}}}$ for ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ decay and ${{\mathit g}_{{-}}}$ for ${{\mathit K}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ decay.

VALUE ($ 10^{-4} $) EVTS DOCUMENT ID TECN $-1.5$ $\pm1.5$ $\pm1.6$ 3.1G 1 BATLEY 2007 E NA48 • • We do not use the following data for averages, fits, limits, etc. • • $1.7$ $\pm2.1$ $\pm2.0$ 1.7G 2 BATLEY 2006 NA48 $-70.0$ $\pm53$ 3.2M FORD 1970 ASPK 1  BATLEY 2007E includes data from BATLEY 2006 . Uses quadratic parametrization and value ${{\mathit g}_{{+}}}$+ ${{\mathit g}_{{-}}}$ = 2${{\mathit g}}$ from BATLEY 2007B. This measurement neglects any possible charge asymmetries in higher order slope parameters ${{\mathit h}}$ or ${{\mathit k}}$. 2  This measurement neglects any possible charge asymmetries in higher order slope parameters ${{\mathit h}}$ or ${{\mathit k}}$.

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 2006 PL B634 474 Search for Direct $\mathit CP$ Violation in the Decays ${{\mathit K}^{\pm}}$ $\rightarrow$ 3 ${{\mathit \pi}^{\pm}}$ FORD 1970 PRL 25 1370 Search for Violation of $\mathit CP$ Invariance in ${{\mathit \tau}^{\pm}}$ Decay

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