# $\boldsymbol CPT$-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.

# IMAGINARY PART OF $\delta$ INSPIRE search

A nonzero value violates $\mathit CPT$ invariance.
VALUE ($10^{-5}$) EVTS DOCUMENT ID TECN  COMMENT
$-1.5$ $\pm1.6$ 1
 2011
KTEV
• • • We do not use the following data for averages, fits, limits, etc. • • •
$0.4$ $\pm2.1$ 2
 2006 H
KLOE
$-0.2$ $\pm2.0$ 3
 2005 A
NA48
$2.4$ $\pm5.0$ 4
 1999 B
RVUE
$-90$ $\pm290$ $\pm100$ 1.3M 5
 1998 F
CPLR
$2100$ $\pm3700$ 6481 6
 1995
${{\mathit K}_{{{{\mathit \ell}}3}}}$ reanalysis
1  ABOUZAID 2011 uses Bell-Steinberger relations.
2  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.
3  LAI 2005A values are obtained through unitarity (Bell-Steinberger relations), improving determination of $\eta _{000}$ and combining other data from PDG 2004 and APOSTOLAKIS 1999B.
4  APOSTOLAKIS 1999B assumes only unitarity and combines CPLEAR and other results.
5  If $\Delta \mathit S=\Delta \mathit Q$ is not assumed, ANGELOPOULOS 1998F finds Im$\delta =(-15$ $\pm23$ $\pm3){\times }10^{-3}$.
6  DEMIDOV 1995 reanalyzes data from HART 1973 and NIEBERGALL 1974 .
Conservation Laws:
 $\mathit CPT$ INVARIANCE
References:
 ABOUZAID 2011
PR D83 092001 Precise Measurements of Direct $\mathit CP$ Violation, $\mathit CPT$ Symmetry, and other Parameters in the Neutral Kaon System
 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
 LAI 2005A
PL B610 165 Search for $\mathit CP$ Violation in ${{\mathit K}^{0}}$ $\rightarrow$ 3 ${{\mathit \pi}^{0}}$ Decays
 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
 DEMIDOV 1995
PAN 58 968 The Limits on $\mathit CPT$ Odd Part of $\mathit CP$ Violation from ${{\mathit K}^{0}}$ (${{\overline{\mathit K}}^{0}}$) Semileptonic Decays