PARAMETERS FOR ${{\mathit K}_L^0}$ $\rightarrow$ 2 ${{\mathit \pi}}$ DECAY

$\eta _{+−}$ = A( ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ ) $/$ A( ${{\mathit K}_S^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ ) $\eta _{00}$ = A( ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ ) $/$ A( ${{\mathit K}_S^0}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ )
The fitted values of $\vert \eta _{+−}\vert $ and $\vert \eta _{00}\vert $ given below are the results of a fit to $\vert \eta _{+−}\vert $, $\vert \eta _{00}\vert $, $\vert \eta _{00}/\eta _{+−}\vert $, and Re($\epsilon {{}^\prime}/\epsilon $). Independent information on $\vert \eta _{+−}\vert $ and $\vert \eta _{00}\vert $ can be obtained from the fitted values of the ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ and ${{\mathit K}_S^0}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ branching ratios and the ${{\mathit K}_L^0}$ and ${{\mathit K}_S^0}$ lifetimes. This information is included as data in the $\vert \eta _{+−}\vert $ and $\vert \eta _{00}\vert $ sections with a Document ID “BRFIT.” See the note “$\mathit CP$ violation in ${{\mathit K}_{{L}}}$ decays” above for details.

$\phi _{00}$, PHASE OF $\eta _{00}$

INSPIRE   PDGID:
S013FOO
See comment in $\phi _{+−}$ header above for treatment of $\Delta \mathit m$ and ${{\mathit \tau}_{{s}}}$ dependence, as well as for the inclusion of data in both the “Assuming $\mathit CPT$” and “Not Assuming $\mathit CPT$” fits.

OUR FIT is described in the note on “$\mathit CP$ violation in ${{\mathit K}_{{L}}}$ decays” in the ${{\mathit K}_L^0}$ Particle Listings.
VALUE ($^\circ{}$) DOCUMENT ID TECN  COMMENT
$\bf{ 43.7 \pm0.6}$ OUR FIT  Error includes scale factor of 1.2.  Not assuming $\mathit CPT$
$\bf{ 43.52 \pm0.05}$ OUR FIT  Error includes scale factor of 1.3.  Assuming $\mathit CPT$
$44.5 \pm2.3 \pm0.5$ 1
CAROSI
1990
NA31
• • We do not use the following data for averages, fits, limits, etc. • •
$44.06$ $\pm0.68$ 2
ABOUZAID
2011
KTEV Not assuming $\mathit CPT$
$41.7 \pm5.9 \pm0.2$ 3
ANGELOPOULOS
1998
CPLR
$50.8$ $\pm7.1$ $\pm1.7$ 4
ADLER
1996B
CPLR Sup. by ANGELOPOULOS 1998
$47.4$ $\pm1.4$ $\pm0.9$ 5
KARLSSON
1990
E731
1  CAROSI 1990 measures $\phi _{00}$ = ( $47.1$ $\pm2.1$ $\pm1.0$ ) + $579$ [ $\Delta \mathit m$$–$ $0.5351$ ] + $252$ [ ${{\mathit \tau}_{{s}}}$$–$ $0.8922$ ] ($^\circ{}$) . We have adjusted the measurement to use our best values of ( $\Delta \mathit m$ = $0.5293$ $\pm0.0009$ ) , ( ${{\mathit \tau}_{{s}}}$ = $0.8954$ $\pm0.0004$ ) . Our first error is their experiment's error and our second error is the systematic error from using our best values.
2  Not independent of other phase parameters reported in ABOUZAID 2011 .
3  ANGELOPOULOS 1998 measures $\phi _{00}$ = ( $42.0$ $\pm5.6$ $\pm1.9$ ) + $240$ [ $\Delta \mathit m$$–$ $0.5307$ ] ($^\circ{}$) . We have adjusted the measurement to use our best values of ( $\Delta \mathit m$ = $0.5293$ $\pm0.0009$ ) . Our first error is their experiment's error and our second error is the systematic error from using our best values. The $\tau _{{{\mathit s}}}$ dependence is negligible.
4  ADLER 1996B identified initial neutral kaon individually as being a ${{\mathit K}^{0}}$ or a ${{\overline{\mathit K}}^{0}}$. The systematic uncertainty is $\pm1.5^\circ{}$ combined in quadrature with $\pm0.8^\circ{}$ due to $\Delta \mathit m$.
5  KARLSSON 1990 systematic error does not include regeneration phase uncertainty.
Conservation Laws:
$\mathit CP$ VIOLATION OBSERVED
References:
ABOUZAID 2011
PR D83 092001 Precise Measurements of Direct $\mathit CP$ Violation, $\mathit CPT$ Symmetry, and other Parameters in the Neutral Kaon System
ANGELOPOULOS 1998
PL B420 191 Measurement of the $\mathit CP$ Violation Parameter $\eta _{00}$ using Tagged ${{\overline{\mathit K}}^{0}}$ and ${{\mathit K}^{0}}$
ADLER 1996B
ZPHY C70 211 First Observation of a Particle Antiparticle Asymmetry in the Decay of Neutral Kaons into ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$
CAROSI 1990
PL B237 303 A Measurement of the Phases of the $\mathit CP$ Violating Amplitudes in ${{\mathit K}^{0}}$ $\rightarrow$ 2 ${{\mathit \pi}}$ Decays and a Test of $\mathit CPT$ Invariance
KARLSSON 1990
PRL 64 2976 A Test of $\mathit CPT$ Symmetry Through a Determination of the Difference in the Phases of $\eta _{00}$ and $\eta _{+−}$ in ${{\mathit K}}$ $\rightarrow$ 2 ${{\mathit \pi}}$ Decays