For earlier measurements, beginning with GOOD 1961 and FITCH 1961 , see our 1986 edition, Physics Letters 170B 132 (1986).

OUR FIT is described in the note on “$\mathit CP$ violation in ${{\mathit K}_{{L}}}$ decays” in the ${{\mathit K}_L^0}$ Particle Listings. The result labeled “OUR FIT Assuming $\mathit CPT$” [``OUR FIT Not assuming $\mathit CPT$''] includes all measurements except those with the comment “Not assuming $\mathit CPT$” [``Assuming $\mathit CPT''$]. Measurements with neither comment do not assume $\mathit CPT$ and enter both fits.

VALUE ($ 10^{10} $ $\hbar{}$ s${}^{-1}$) DOCUMENT ID TECN  COMMENT $\bf{ 0.5289 \pm0.0010}$ OUR FIT  Not assuming $\mathit CPT$ $\bf{ 0.5293 \pm0.0009}$ OUR FIT  Error includes scale factor of 1.3.  Assuming $\mathit CPT$ $0.52797$ $\pm0.00195$ 1, 2 ABOUZAID 2011 KTEV Not assuming $\mathit CPT$ $0.52699$ $\pm0.00123$ 1, 3 ABOUZAID 2011 KTEV Assuming $\mathit CPT$ $0.5240$ $\pm0.0044$ $\pm0.0033$ APOSTOLAKIS 1999 C CPLR ${{\mathit K}^{0}}-{{\overline{\mathit K}}^{0}}$ to ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ $0.5297$ $\pm0.0030$ $\pm0.0022$ 4 SCHWINGENHEUE.. 1995 E773 $20 - 160$ GeV ${{\mathit K}}$ beams $0.5286$ $\pm0.0028$ 5 GIBBONS 1993 E731 Assuming $\mathit CPT$ $0.5257$ $\pm0.0049$ $\pm0.0021$ 4 GIBBONS 1993 C E731 Not assuming $\mathit CPT$ $0.5340$ $\pm0.00255$ $\pm0.0015$ 6 GEWENIGER 1974 C SPEC Gap method $0.5334$ $\pm0.0040$ $\pm0.0015$ 6, 7 GJESDAL 1974 SPEC Assuming $\mathit CPT$ • • We do not use the following data for averages, fits, limits, etc. • • $0.5261$ $\pm0.0015$ 8 ALAVI-HARATI 2003 KTEV Assuming $\mathit CPT$ $0.5288$ $\pm0.0043$ 9 ALAVI-HARATI 2003 KTEV Not assuming $\mathit CPT$ $0.5343$ $\pm0.0063$ $\pm0.0025$ 10 ANGELOPOULOS 2001 CPLR $0.5295$ $\pm0.0020$ $\pm0.0003$ 11 ANGELOPOULOS 1998 D CPLR Assuming $\mathit CPT$ $0.5307$ $\pm0.0013$ 12 ADLER 1996 C RVUE $0.5274$ $\pm0.0029$ $\pm0.0005$ 11 ADLER 1995 CPLR Sup. by ANGELOPOULOS 1998D $0.482$ $\pm0.014$ 13 ARONSON 1982 B SPEC $\mathit E=30-$110 GeV $0.534$ $\pm0.007$ 14 CARNEGIE 1971 ASPK Gap method $0.542$ $\pm0.006$ 14 ARONSON 1970 ASPK Gap method $0.542$ $\pm0.006$ CULLEN 1970 CNTR 1  The two ABOUZAID 2011 values use the same data. The first enters the ''assuming $\mathit CPT$'' fit and the second enters the ''not assuming $\mathit CPT$'' fit. 2  ABOUZAID 2011 fit has $\Delta \mathit m$, ${{\mathit \tau}_{{s}}}$, ${{\mathit \phi}_{{\epsilon}}}$, Re(${{\mathit \epsilon}^{\,'}}/{{\mathit \epsilon}}$), and Im(${{\mathit \epsilon}^{\,'}}/{{\mathit \epsilon}}$) as free parameters. See Im(${{\mathit \epsilon}^{\,'}}/{{\mathit \epsilon}}$) in the ''${{\mathit K}_L^0}$ $\mathit CP$ violation'' section for correlation information. 3  ABOUZAID 2011 fit has $\Delta \mathit m$ and ${{\mathit \tau}_{{s}}}$ free but constrains ${{\mathit \phi}_{{\epsilon}}}$ to the Superweak value, i.e. assumes $\mathit CPT$. See ''${{\mathit K}_S^0}$ Mean Life'' section for correlation information. 4  Fits $\Delta \mathit m$ and $\phi _{+−}$ simultaneously. GIBBONS 1993C systematic error is from B.$~$Winstein via private communication. $20 - 160$ GeV ${{\mathit K}}$ beams. 5  GIBBONS 1993 value assume $\phi _{+−}$ = $\phi _{00}$ = $\phi _{{\mathrm {SW}}}$ = ($43.7$ $\pm0.2)^\circ{}$, i.e. assumes $\mathit CPT$. $20 - 160$ GeV ${{\mathit K}}$ beams. 6  These two experiments have a common systematic error due to the uncertainty in the momentum scale, as pointed out in WAHL 1989 . 7  GJESDAL 1974 uses charge asymmetry in ${{\mathit K}_{{{{\mathit \ell}}3}}^{0}}$ decays. 8  ALAVI-HARATI 2003 fit $\Delta \mathit m$ and ${\mathit \tau}_{{{\mathit K}_S^0} }$ simultaneously. $\phi _{+−}$ is constrained to the Superweak value, i.e. $\mathit CPT$ is assumed. See ``${{\mathit K}_S^0}$ Mean Life'' section for correlation information. Superseded by ABOUZAID 2011 . 9  ALAVI-HARATI 2003 fit $\Delta \mathit m$, $\phi _{+−}$, and $\tau _{{{\mathit K}_{{S}}}}$ simultaneously. See $\phi _{+−}$ in the ``${{\mathit K}_{{L}}}$ $\mathit CP$ violation'' section for correlation information. Superseded by ABOUZAID 2011 . 10  ANGELOPOULOS 2001 uses strong interactions strangeness tagging at two different times. 11  Uses ${{\overline{\mathit K}}_{{e3}}^{0}}$ and ${{\mathit K}_{{e3}}^{0}}$ strangeness tagging at production and decay. Assumes $\mathit CPT$ conservation on $\Delta \mathit S=−\Delta \mathit Q$ transitions. 12  ADLER 1996C is the result of a fit which includes nearly the same data as entered into the ``OUR$~$FIT'' value above. 13  ARONSON 1982 find that $\Delta \mathit m$ may depend on the kaon energy. 14  ARONSON 1970 and CARNEGIE 1971 use ${{\mathit K}_S^0}$ mean life = ($0.862$ $\pm0.006$) $ \times 10^{-10}$ s. We have not attempted to adjust these values for the subsequent change in the ${{\mathit K}_S^0}$ mean life or in $\eta _{+−}$.

Conservation Laws:

$\Delta \mathit S$ = 2 VIA MIXING

References:

ABOUZAID 2011 PR D83 092001 Precise Measurements of Direct $\mathit CP$ Violation, $\mathit CPT$ Symmetry, and other Parameters in the Neutral Kaon System ALAVI-HARATI 2003 PR D67 012005 Measurements of Direct $\mathit CP$ Violation, $\mathit CPT$ Symmetry, and other Parameters in the Neutral Kaon System Also PR D70 079904 (errat.) Erratum to ALAVI-HARATI 2003 : “Measurements of Direct $\mathit CP$-Violation, $\mathit CPT$ Symmetry, and other Parameters in the Neutral Kaon System'' ANGELOPOULOS 2001 PL B503 49 ${{\mathit K}^{0}}$ $\leftrightarrow$ ${{\overline{\mathit K}}^{0}}$ Transitions Monitored by Strong Interactions: a New Determination of the ${{\mathit K}_L^0}$ $−$ ${{\mathit K}_S^0}$ Mass Difference APOSTOLAKIS 1999C PL B458 545 A Determination of the $\mathit CP$ Violation Parameter $\eta _{+−}$ from the Decay of Strangeness Tagged Neutral Kaons Also EPJ C18 41 A Detailed Description of the Analysis of the Decay of Neutral Kaons to ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ in the CPLEAR Experiment ANGELOPOULOS 1998D PL B444 38 Measurement of the ${{\mathit K}_L^0}$ $−$ ${{\mathit K}_S^0}$ Mass Difference using Semileptonic Decays of 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 ${{\mathit e}}{{\mathit \pi}}{{\mathit \nu}}$ ADLER 1996C PL B369 367 Evaluation of the Phase of the $\mathit CP$ Violation Parameter $\eta _{+−}$ and ${{\mathit K}_L^0}$ $−$ ${{\mathit K}_S^0}$ Mass Difference from a Correlation Analysis of Different Experiments ADLER 1995 PL B363 237 Measurement of ${{\mathit K}_L^0}$ $−$ ${{\mathit K}_S^0}$ Mass Difference using Semileptonic Decays of Tagged Neutral Kaons SCHWINGENHEUER 1995 PRL 74 4376 $\mathit CPT$ Tests in the Neutral Kaon System GIBBONS 1993 PRL 70 1199 New Measurements of the Neutral Kaon Parameters $\Delta _{m}$, $\tau _{S}$, $\Phi _{00}$ $−$ $\Phi _{+-}$, and $\Phi _{+-}$ Also PR D55 6625 $\mathit CP$ and $\mathit CPT$ Symmetry Test from the Two Pion Decays of the Neutral Kaon with the FNAL E731 Detector GIBBONS 1993C Thesis RX-1487 A Precise Measurement of the $\mathit CP$ Violation Parameter Re(${{\mathit \epsilon}^{\,'}}/{{\mathit \epsilon}}$) and other Kaon Decay Parameters Also PR D55 6625 $\mathit CP$ and $\mathit CPT$ Symmetry Test from the Two Pion Decays of the Neutral Kaon with the FNAL E731 Detector ARONSON 1982B PRL 48 1306 Determination of the Fundamental Parameters of the ${{\mathit K}^{0}}{{\overline{\mathit K}}^{0}}$ System in the Energy Range 30-110 GeV Also PL 116B 73 Interaction of the ${{\mathit K}^{0}}{{\overline{\mathit K}}^{0}}$ System with External Fields Also PR D28 476 Energy Dependence of the Fundamental Parameters of the ${{\mathit K}^{0}}{{\overline{\mathit K}}^{0}}$ System. 1. Experimental Analysis Also PR D28 495 Energy Dependence of the Fundamental Parameters of the ${{\mathit K}^{0}}{{\overline{\mathit K}}^{0}}$ System. 2. Theoretical Formalism GEWENIGER 1974C PL 52B 108 Measurement of the Kaon Mass Difference ${\mathit m}_{{{\mathit K}_L^0} }–{\mathit m}_{{{\mathit K}_S^0} }$ by the Two Regenerator Method GJESDAL 1974 PL 52B 113 A Measurement of the ${\mathit m}_{{{\mathit K}_L^0} }–{\mathit m}_{{{\mathit K}_S^0} }$ from the Charge Asymmetry in Semileptonic Kaon Decays CARNEGIE 1971 PR D4 1 ${{\mathit K}_{{1}}^{0}}$ $−$ ${{\mathit K}_{{2}}^{0}}$ Mass Difference ARONSON 1970 PRL 25 1057 Precise Determination of the ${{\mathit K}_L^0}$ $−{{\mathit K}_S^0}$ Mass Difference by the Gap Method CULLEN 1970 PL 32B 523 Precision Determination of the ${{\mathit K}_L^0}$ ${{\mathit K}_S^0}$ Mass Difference