$\mathit CPT$-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   PDGID:
S011XRM
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
AMBROSINO
2006H
 KLOE
• • We do not use the following data for averages, fits, limits, etc. • •
$-0.8$ $\pm2.5$ 13k 2
AMBROSINO
2006E
 KLOE
$-0.5$ $\pm3.0$ 3
APOSTOLAKIS
1999B
 CPLR Strangeness tagged
$2$ $\pm13$ $\pm3$ 650k
ANGELOPOULOS
1998F
 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
Also
EPJ C22 55 $\mathit T$-Violation and $\mathit CPT$-Invariance Measurements in the CPLEAR Experiment: a Detailed Description of the Analysis of Neutral-Kaon Decays to ${{\mathit e}}{{\mathit \pi}}{{\mathit \nu}}$