${\mathit m}_{{{\mathit K}_L^0} }–{\mathit m}_{{{\mathit K}_S^0} }$ INSPIRE search

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.

S013D
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
1999C
 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
1993C
 E731 Not assuming $\mathit CPT$
$0.5340$ $\pm0.00255$ $\pm0.0015$ 6
GEWENIGER
1974C
 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
1998D
 CPLR Assuming $\mathit CPT$
$0.5307$ $\pm0.0013$ 12
ADLER
1996C
 RVUE
$0.5274$ $\pm0.0029$ $\pm0.0005$ 11
ADLER
1995
CPLR Sup. by ANGELOPOULOS 1998D
$0.482$ $\pm0.014$ 13
ARONSON
1982B
 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