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$\mathit CPT$-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.

IMAGINARY PART OF $\delta $

INSPIRE   PDGID:

S011DIM

A nonzero value violates $\mathit CPT$ invariance.

VALUE ($ 10^{-5} $) EVTS DOCUMENT ID TECN  COMMENT $-1.5$ $\pm1.6$ 1 ABOUZAID 2011 KTEV • • We do not use the following data for averages, fits, limits, etc. • • $0.4$ $\pm2.1$ 2 AMBROSINO 2006 H KLOE $-0.2$ $\pm2.0$ 3 LAI 2005 A NA48 $2.4$ $\pm5.0$ 4 APOSTOLAKIS 1999 B RVUE $-90$ $\pm290$ $\pm100$ 1.3M 5 ANGELOPOULOS 1998 F CPLR $2100$ $\pm3700$ 6481 6 DEMIDOV 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 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 ${{\mathit e}}{{\mathit \pi}}{{\mathit \nu}}$ 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

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