# $\boldsymbol CPT$-VIOLATION PARAMETERS

In ${{\mathit K}^{0}}-{{\overline{\mathit K}}^{0}}$ mixing, if $\mathit CP$-violating interactions include a $\mathit T$ conserving part then
$|{{\mathit K}_{{S}}}\rangle{}$ = [$|{{\mathit K}_{{1}}}\rangle{}+(\epsilon +\delta )|{{\mathit K}_{{2}}}\rangle{}]/\sqrt {1+\vert \epsilon +\delta \vert ^2 }$  $|{{\mathit K}_{{L}}}\rangle{}$ = [$|{{\mathit K}_{{2}}}\rangle{}+(\epsilon −\delta )|{{\mathit K}_{{1}}}\rangle{}]/\sqrt {1+\vert \epsilon −\delta \vert ^2 }$ where  $|{{\mathit K}_{{1}}}\rangle{}$ = [$|{{\mathit K}^{0}}\rangle{}+|{{\overline{\mathit K}}^{0}}\rangle{}]/\sqrt {2 }$  $|{{\mathit K}_{{2}}}\rangle{}$ = [$|{{\mathit K}^{0}}\rangle{}−|{{\overline{\mathit K}}^{0}}\rangle{}]/\sqrt {2 }$ and  $|{{\overline{\mathit K}}^{0}}\rangle{}$ = $\mathit CP|{{\mathit K}^{0}}\rangle{}$.
The parameter $\delta$ specifies the $\mathit CPT$-violating part.
Estimates of $\delta$ are given below assuming the validity of the $\Delta \mathit S=\Delta \mathit Q$ rule. See also THOMSON 1995 for a test of $\mathit CPT$-symmetry conservation in ${{\mathit K}^{0}}$ decays using the Bell-Steinberger relation.

# Re(y) INSPIRE search

A non-zero value would violate $\mathit CPT$ invariance in $\Delta \mathit S$ = $\Delta \mathit Q$ amplitude. Re(y) is the following combination of ${{\mathit K}_{{{e3}}}}$ decay amplitudes: Re(y) = Re ${A( {{\overline{\mathit K}}^{0}} \rightarrow {{\mathit e}^{-}} {{\mathit \pi}^{+}} {{\overline{\mathit \nu}}_{{e}}} ){}^{*} - A( {{\mathit K}^{0}} \rightarrow {{\mathit e}^{+}} {{\mathit \pi}^{-}} {{\mathit \nu}_{{e}}} )\over A( {{\overline{\mathit K}}^{0}} \rightarrow {{\mathit e}^{-}} {{\mathit \pi}^{+}} {{\overline{\mathit \nu}}_{{e}}} ){}^{*} + A( {{\mathit K}^{0}} \rightarrow {{\mathit e}^{+}} {{\mathit \pi}^{-}} {{\mathit \nu}_{{e}}} )}$

VALUE ($10^{-3}$) EVTS DOCUMENT ID TECN
$0.4$ $\pm2.5$ 13k 1
 2006 E
KLOE
• • • We do not use the following data for averages, fits, limits, etc. • • •
$0.3$ $\pm3.1$ 2
 1999 B
CPLR
1  They use the PDG 2004 for the ${{\mathit K}_L^0}$ semileptonic charge asymmetry and PDG 2004 ($\mathit CP$ review, $\mathit CPT$ NOT ASSUMED) for Re($\epsilon$).
2  Constrained by Bell-Steinberger (or unitarity) relation.
Conservation Laws:
 $\mathit CPT$ INVARIANCE
References:
 AMBROSINO 2006E
PL B636 173 Study of the Branching Ratio and Charge Asymmetry for the Decay ${{\mathit K}_S^0}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit e}}{{\mathit \nu}}$ with the KLOE Detector
 APOSTOLAKIS 1999B
PL B456 297 Determination of the $\mathit T$- and $\mathit CPT$ Violation Parameters in the Neutral Kaon System using the Bell Steinberger Relation and Data from CPLEAR