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.

Re($\epsilon {{}^\prime}/\epsilon $) = (1$−\vert \eta _{00}/\eta _{+−}\vert $)/3

INSPIRE   PDGID:
S013EPS
We have neglected terms of order $\omega \cdot{}$Re($\epsilon {{}^\prime}/\epsilon $), where $\omega $ = Re(A$_{2}$)/Re(A$_{0}$) $\simeq{}$ 1/22. If included, this correction would lower Re($\epsilon {{}^\prime}/\epsilon $) by about $0.04 \times 10^{-3}$. See SOZZI 2004 .
VALUE ($ 10^{-3} $) DOCUMENT ID TECN  COMMENT
$\bf{ 1.66 \pm0.23}$ OUR FIT  Error includes scale factor of 1.6.
$\bf{ 1.68 \pm0.20}$ OUR AVERAGE  Error includes scale factor of 1.4.  See the ideogram below.
$1.92$ $\pm0.21$ 1
ABOUZAID
2011
KTEV Assuming $\mathit CPT$
$1.47$ $\pm0.22$
BATLEY
2002
NA48
$0.74$ $\pm0.52$ $\pm0.29$
GIBBONS
1993B
E731
• • • We use the following data for averages but not for fits. • • •
$2.3$ $\pm0.65$ 2, 3
BARR
1993D
NA31
• • We do not use the following data for averages, fits, limits, etc. • •
$2.110$ $\pm0.343$ 1, 4
ABOUZAID
2011
KTEV Not assuming $\mathit CPT$
$2.07$ $\pm0.28$
ALAVI-HARATI
2003
KTEV In ABOUZAID 2011
$1.53$ $\pm0.26$
LAI
2001C
NA48 Incl. in BATLEY 2002
$2.80$ $\pm0.30$ $\pm0.28$
ALAVI-HARATI
1999D
KTEV In ALAVI-HARATI 2003
$1.85$ $\pm0.45$ $\pm0.58$
FANTI
1999C
NA48 In LAI 2001C
$2.0$ $\pm0.7$ 5
BARR
1993D
NA31
$-0.4$ $\pm1.4$ $\pm0.6$
PATTERSON
1990
E731 in GIBBONS 1993B
$3.3$ $\pm1.1$ 5
BURKHARDT
1988
NA31
$3.2$ $\pm2.8$ $\pm1.2$ 2
WOODS
1988
E731
1  The two ABOUZAID 2011 values use the same data. The fits are performed with and without $\mathit CPT$ invariance requirement.
2  These values are derived from $\vert \eta _{00}/\eta _{+−}\vert $ measurements. They enter the average in this section but enter the fit via the $\vert \eta _{00}/\eta _{+−}\vert $ only.
3  This is the combined results from BARR 1993D and BURKHARDT 1988 , taking into account their common systematic uncertainty.
4  We use ABOUZAID 2011 Re(${{\mathit \epsilon}^{\,'}}/{{\mathit \epsilon}}$) value with $\mathit CPT$ assumption in our fits for $\vert \eta _{+−}\vert $, $\vert \eta _{00}\vert $, and Re(${{\mathit \epsilon}^{\,'}}/{{\mathit \epsilon}}$).
5  These values are derived from $\vert \eta _{00}/\eta _{+−}\vert $ measurements.

           Re($\epsilon {{}^\prime}/\epsilon $) = (1$−\vert \eta _{00}/\eta _{+−}\vert $)/3
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
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''
BATLEY 2002
PL B544 97 A Precision Measurement of Direct $\mathit CP$ Violation in the Decay of Neutral Kaons into Two Pions
LAI 2001C
EPJ C22 231 A Precise Measurement of the Direct $\mathit CP$ Violation Parameter Re(${{\mathit \epsilon}^{\,'}}/{{\mathit \epsilon}}$)
ALAVI-HARATI 1999D
PRL 83 22 Observation of Direct $\mathit CP$ Violation in K$_{S,L}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ Decays
FANTI 1999C
PL B465 335 A New Measurement of Direct $\mathit CP$ Violation in Two Pion Decays of the Neutral Kaon
BARR 1993D
PL B317 233 A New Measurement of Direct $\mathit CP$ Violation in the Neutral Kaon System
GIBBONS 1993B
PRL 70 1203 Measurements of the $\mathit CP$ Violation Parameter Re(${{\mathit \epsilon}^{\,'}}/{{\mathit \epsilon}}$)
PATTERSON 1990
PRL 64 1491 Determination of Re(${{\mathit \epsilon}^{\,'}}/{{\mathit \epsilon}}$) by the Simultaneous Detection of the Four ${{\mathit K}}_{L,S}\rightarrow{{\mathit \pi}}{{\mathit \pi}}$ Decay Modes
BURKHARDT 1988
PL B206 169 First Evidence for Direct $\mathit CP$ Violation
WOODS 1988
PRL 60 1695 First Result on a New Measurement of ${{\mathit \epsilon}^{\,'}}/{{\mathit \epsilon}}$ in the Neutral Kaon System