$\boldsymbol CPT$-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

$-2.9$ $\pm2.0$

AMBROSINO

2006

KLOE

• • • We do not use the following data for averages, fits, limits, etc. • • •

$-0.8$ $\pm2.5$

13k

AMBROSINO

2006

KLOE

$-0.5$ $\pm3.0$

APOSTOLAKIS

1999

CPLR

Strangeness tagged

$2$ $\pm13$ $\pm3$

650k

ANGELOPOULOS

1998

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