# $\boldsymbol CPT$-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(x$_{-}$) INSPIRE search

A non-zero value would violate $\mathit CPT$ invariance in decay amplitudes with $\Delta \mathit S$ ${}\not=$ $\Delta \mathit Q$. x$_{-}$, used here to define Re(x$_{-}$), and x$_{+}$, used below in the $\Delta \mathit S$ = $\Delta \mathit Q$ section are the following combinations of ${{\mathit K}_{{e3}}}$ decay amplitudes: x$_{\pm{}}$ = ${1\over 2}{ A( {{\overline{\mathit K}}^{0}} \rightarrow {{\mathit \pi}^{-}} {{\mathit e}^{+}} {{\mathit \nu}_{{e}}} )\over A( {{\mathit K}^{0}} \rightarrow {{\mathit \pi}^{-}} {{\mathit e}^{+}} {{\mathit \nu}_{{e}}} )}$ $\pm{}$ ${ A( {{\mathit K}^{0}} \rightarrow {{\mathit \pi}^{+}} {{\mathit e}^{-}} {{\overline{\mathit \nu}}_{{e}}} ){}^{*}\over A( {{\overline{\mathit K}}^{0}} \rightarrow {{\mathit \pi}^{+}} {{\mathit e}^{-}} {{\overline{\mathit \nu}}_{{e}}} ){}^{*}}$ .

VALUE ($10^{-3}$) EVTS DOCUMENT ID TECN  COMMENT
$-2.9$ $\pm2.0$ 1
 2006 H
KLOE
• • • We do not use the following data for averages, fits, limits, etc. • • •
$-0.8$ $\pm2.5$ 13k 2
 2006 E
KLOE
$-0.5$ $\pm3.0$ 3
 1999 B
CPLR Strangeness tagged
$2$ $\pm13$ $\pm3$ 650k
 1998 F
CPLR Strangeness tagged
1  AMBROSINO 2006H uses Bell-Steinberger relations with the following measurements: B( ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ ) in AMBROSINO 2006F, B( ${{\mathit K}_S^0}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ ) in AMBROSINO 2005B, the ${{\mathit K}_S^0}$ -semileptonic charge asymmetry in AMBROSINO 2006E, and ${{\mathit K}^{0}}$-semileptonic results in ANGELOPOULOS 1998F.
2  Uses PDG 2004 for the ${{\mathit K}_L^0}$ semileptonic charge asymmetry and Re($\delta$) from CPLEAR, ANGELOPOULOS 1998F.
3  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
 AMBROSINO 2006H
JHEP 0612 011 Determination of $\mathit CP$ and $\mathit CPT$ Violation Parameters in the Neutral Kaon System using the Bell-Steinberger Relation and Data from the KLOE Experiment
 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
 ANGELOPOULOS 1998F
PL B444 52 A Determination of the $\mathit CPT$ Violation Parameter Re($\delta$) from the Semileptonic Decay of Strangeness Tagged Neutral Kaons