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 “$\mathit{C}P$ violation in ${\mathit{K}}_L$ decays” in the ${\mathit{K}}_L^0$ Particle Listings. The result labeled “OUR FIT Assuming $\mathit{C}PT$” [``OUR FIT Not assuming $\mathit{C}PT$''] includes all measurements except those with the comment “Not assuming $\mathit{C}PT$” [``Assuming $\mathit{C}P{T}^{″}$]. Measurements with neither comment do not assume $\mathit{C}PT$ and enter both fits.

VALUE (${10}^{10}$ $\hslash$ s${}^{-1}$) DOCUMENT ID TECN  COMMENT $\mathbf{0.5289}\pm \mathbf{0.0010}$ OUR FIT  Not assuming $\mathit{C}PT$ $\mathbf{0.5293}\pm \mathbf{0.0009}$ OUR FIT  Error includes scale factor of 1.3.  Assuming $\mathit{C}PT$ $0.52797$ $\pm 0.00195$ 1, 2 ABOUZAID 2011 KTEV Not assuming $\mathit{C}PT$ $0.52699$ $\pm 0.00123$ 1, 3 ABOUZAID 2011 KTEV Assuming $\mathit{C}PT$ $0.5240$ $\pm 0.0044$ $\pm 0.0033$ APOSTOLAKIS 1999 C CPLR ${\mathit{K}}^0-{\bar{\mathit{K}}}^0$ to ${\pi }^{+}{\pi }^{-}$ $0.5297$ $\pm 0.0030$ $\pm 0.0022$ 4 SCHWINGENHEUE.. 1995 E773 $20-160$ GeV $\mathit{K}$ beams $0.5286$ $\pm 0.0028$ 5 GIBBONS 1993 E731 Assuming $\mathit{C}PT$ $0.5257$ $\pm 0.0049$ $\pm 0.0021$ 4 GIBBONS 1993 C E731 Not assuming $\mathit{C}PT$ $0.5340$ $\pm 0.00255$ $\pm 0.0015$ 6 GEWENIGER 1974 C SPEC Gap method $0.5334$ $\pm 0.0040$ $\pm 0.0015$ 6, 7 GJESDAL 1974 SPEC Assuming $\mathit{C}PT$ • • We do not use the following data for averages, fits, limits, etc. • • $0.5261$ $\pm 0.0015$ 8 ALAVI-HARATI 2003 KTEV Assuming $\mathit{C}PT$ $0.5288$ $\pm 0.0043$ 9 ALAVI-HARATI 2003 KTEV Not assuming $\mathit{C}PT$ $0.5343$ $\pm 0.0063$ $\pm 0.0025$ 10 ANGELOPOULOS 2001 CPLR $0.5295$ $\pm 0.0020$ $\pm 0.0003$ 11 ANGELOPOULOS 1998 D CPLR Assuming $\mathit{C}PT$ $0.5307$ $\pm 0.0013$ 12 ADLER 1996 C RVUE $0.5274$ $\pm 0.0029$ $\pm 0.0005$ 11 ADLER 1995 CPLR Sup. by ANGELOPOULOS 1998D $0.482$ $\pm 0.014$ 13 ARONSON 1982 B SPEC $\mathit{E}=30-$110 GeV $0.534$ $\pm 0.007$ 14 CARNEGIE 1971 ASPK Gap method $0.542$ $\pm 0.006$ 14 ARONSON 1970 ASPK Gap method $0.542$ $\pm 0.006$ CULLEN 1970 CNTR 1  The two ABOUZAID 2011 values use the same data. The first enters the ''assuming $\mathit{C}PT$'' fit and the second enters the ''not assuming $\mathit{C}PT$'' fit. 2  ABOUZAID 2011 fit has $\mathrm{\Delta }\mathit{m}$, ${\tau }_s$, ${\varphi }_{ϵ}$, Re(${ϵ}^{{}^{\prime }}/ϵ$), and Im(${ϵ}^{{}^{\prime }}/ϵ$) as free parameters. See Im(${ϵ}^{{}^{\prime }}/ϵ$) in the ''${\mathit{K}}_L^0$ $\mathit{C}P$ violation'' section for correlation information. 3  ABOUZAID 2011 fit has $\mathrm{\Delta }\mathit{m}$ and ${\tau }_s$ free but constrains ${\varphi }_{ϵ}$ to the Superweak value, i.e. assumes $\mathit{C}PT$. See ''${\mathit{K}}_S^0$ Mean Life'' section for correlation information. 4  Fits $\mathrm{\Delta }\mathit{m}$ and ${\varphi }_{+-}$ simultaneously. GIBBONS 1993C systematic error is from B.$$Winstein via private communication. $20-160$ GeV $\mathit{K}$ beams. 5  GIBBONS 1993 value assume ${\varphi }_{+-}$ = ${\varphi }_{00}$ = ${\varphi }_{\mathrm{SW}}$ = ($43.7$ $\pm 0.2{)}^{\circ }$, i.e. assumes $\mathit{C}PT$. $20-160$ GeV $\mathit{K}$ beams. 6  These two experiments have a common systematic error due to the uncertainty in the momentum scale, as pointed out in WAHL 1989. 7  GJESDAL 1974 uses charge asymmetry in ${\mathit{K}}_{\ell 3}^0$ decays. 8  ALAVI-HARATI 2003 fit $\mathrm{\Delta }\mathit{m}$ and ${\tau }_{{\mathit{K}}_S^0}$ simultaneously. ${\varphi }_{+-}$ is constrained to the Superweak value, i.e. $\mathit{C}PT$ is assumed. See ``${\mathit{K}}_S^0$ Mean Life'' section for correlation information. Superseded by ABOUZAID 2011. 9  ALAVI-HARATI 2003 fit $\mathrm{\Delta }\mathit{m}$, ${\varphi }_{+-}$, and ${\tau }_{{\mathit{K}}_S}$ simultaneously. See ${\varphi }_{+-}$ in the ``${\mathit{K}}_L$ $\mathit{C}P$ violation'' section for correlation information. Superseded by ABOUZAID 2011. 10  ANGELOPOULOS 2001 uses strong interactions strangeness tagging at two different times. 11  Uses ${\bar{\mathit{K}}}_{e3}^0$ and ${\mathit{K}}_{e3}^0$ strangeness tagging at production and decay. Assumes $\mathit{C}PT$ conservation on $\mathrm{\Delta }\mathit{S}=-\mathrm{\Delta }\mathit{Q}$ transitions. 12  ADLER 1996C is the result of a fit which includes nearly the same data as entered into the ``OUR$$FIT'' value above. 13  ARONSON 1982 find that $\mathrm{\Delta }\mathit{m}$ may depend on the kaon energy. 14  ARONSON 1970 and CARNEGIE 1971 use ${\mathit{K}}_S^0$ mean life = ($0.862$ $\pm 0.006$) $\times {10}^{-10}$ 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:

$\mathrm{\Delta }\mathit{S}$ = 2 VIA MIXING

References

ABOUZAID 2011 PR D83 092001 Precise Measurements of Direct $\mathit{C}P$ Violation, $\mathit{C}PT$ Symmetry, and other Parameters in the Neutral Kaon System ALAVI-HARATI 2003 PR D67 012005 Measurements of Direct $\mathit{C}P$ Violation, $\mathit{C}PT$ Symmetry, and other Parameters in the Neutral Kaon System Also PR D70 079904 (errat.) Erratum to ALAVI-HARATI 2003: “Measurements of Direct $\mathit{C}P$-Violation, $\mathit{C}PT$ Symmetry, and other Parameters in the Neutral Kaon System'' ANGELOPOULOS 2001 PL B503 49 ${\mathit{K}}^0$ $\leftrightarrow$ ${\bar{\mathit{K}}}^0$ 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 $\mathit{C}P$ 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 ${\pi }^{+}{\pi }^{-}$ 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 $\mathit{C}PT$-Invariance Measurements in the CPLEAR Experiment: a Detailed Description of the Analysis of Neutral-Kaon Decays to $\mathit{e}\pi \nu$ ADLER 1996C PL B369 367 Evaluation of the Phase of the $\mathit{C}P$ 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 $\mathit{C}PT$ Tests in the Neutral Kaon System GIBBONS 1993 PRL 70 1199 New Measurements of the Neutral Kaon Parameters ${\mathrm{\Delta }}_m$, ${\tau }_S$, ${\mathrm{\Phi }}_{00}$ $-$ ${\mathrm{\Phi }}_{+-}$, and ${\mathrm{\Phi }}_{+-}$ Also PR D55 6625 $\mathit{C}P$ and $\mathit{C}PT$ 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 $\mathit{C}P$ Violation Parameter Re(${ϵ}^{{}^{\prime }}/ϵ$) and other Kaon Decay Parameters Also PR D55 6625 $\mathit{C}P$ and $\mathit{C}PT$ 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 ${\mathit{K}}^0{\bar{\mathit{K}}}^0$ System in the Energy Range 30-110 GeV Also PL 116B 73 Interaction of the ${\mathit{K}}^0{\bar{\mathit{K}}}^0$ System with External Fields Also PR D28 476 Energy Dependence of the Fundamental Parameters of the ${\mathit{K}}^0{\bar{\mathit{K}}}^0$ System. 1. Experimental Analysis Also PR D28 495 Energy Dependence of the Fundamental Parameters of the ${\mathit{K}}^0{\bar{\mathit{K}}}^0$ 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