#### ${\boldsymbol m}_{{{\boldsymbol K}_L^0} }–{\boldsymbol m}_{{{\boldsymbol K}_S^0} }$

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
 2011
KTEV Not assuming $\mathit CPT$
$0.52699$ $\pm0.00123$ 1, 3
 2011
KTEV Assuming $\mathit CPT$
$0.5240$ $\pm0.0044$ $\pm0.0033$
 1999 C
CPLR ${{\mathit K}^{0}}-{{\overline{\mathit K}}^{0}}$ to ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$
$0.5297$ $\pm0.0030$ $\pm0.0022$ 4
 1995
E773 $20 - 160$ GeV ${{\mathit K}}$ beams
$0.5286$ $\pm0.0028$ 5
 1993
E731 Assuming $\mathit CPT$
$0.5257$ $\pm0.0049$ $\pm0.0021$ 4
 1993 C
E731 Not assuming $\mathit CPT$
$0.5340$ $\pm0.00255$ $\pm0.0015$ 6
 1974 C
SPEC Gap method
$0.5334$ $\pm0.0040$ $\pm0.0015$ 6, 7
 1974
SPEC Assuming $\mathit CPT$
• • We do not use the following data for averages, fits, limits, etc. • •
$0.5261$ $\pm0.0015$ 8
 2003
KTEV Assuming $\mathit CPT$
$0.5288$ $\pm0.0043$ 9
 2003
KTEV Not assuming $\mathit CPT$
$0.5343$ $\pm0.0063$ $\pm0.0025$ 10
 2001
CPLR
$0.5295$ $\pm0.0020$ $\pm0.0003$ 11
 1998 D
CPLR Assuming $\mathit CPT$
$0.5307$ $\pm0.0013$ 12
 1996 C
RVUE
$0.5274$ $\pm0.0029$ $\pm0.0005$ 11
 1995
CPLR Sup. by ANGELOPOULOS 1998D
$0.482$ $\pm0.014$ 13
 1982 B
SPEC $\mathit E=30-$110 GeV
$0.534$ $\pm0.007$ 14
 1971
ASPK Gap method
$0.542$ $\pm0.006$ 14
 1970
ASPK Gap method
$0.542$ $\pm0.006$
 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
 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
 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
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
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 $\Phi _{+-}$
 GIBBONS 1993C
Thesis RX-1487 A Precise Measurement of the $\mathit CP$ Violation Parameter Re(${{\mathit \epsilon}^{\,'}}/{{\mathit \epsilon}}$) and other Kaon Decay Parameters
 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
 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