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.

$\vert \eta _{+−}\vert $ = $\vert $A( ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ ) $/$ A( ${{\mathit K}_S^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ )$\vert $

INSPIRE   PDGID:
S013E+-
VALUE ($ 10^{-3} $) EVTS DOCUMENT ID TECN  COMMENT
$\bf{ 2.232 \pm0.011}$ OUR FIT  Error includes scale factor of 1.8.
($222.6$ $\pm0.7$) $ \times 10^{-2}$
BRFIT
2016
• • We do not use the following data for averages, fits, limits, etc. • •
$2.223$ $\pm0.012$ 1
LAI
2007
NA48
$2.219$ $\pm0.013$ 2
AMBROSINO
2006F
 KLOE
$2.228$ $\pm0.010$ 3
ALEXOPOULOS
2004
KTEV
$2.286$ $\pm0.023$ $\pm0.026$ 70M 4
APOSTOLAKIS
1999C
 CPLR ${{\mathit K}^{0}}-{{\overline{\mathit K}}^{0}}$ asymmetry
$2.310$ $\pm0.043$ $\pm0.031$ 5
ADLER
1995B
 CPLR ${{\mathit K}^{0}}-{{\overline{\mathit K}}^{0}}$ asymmetry
$2.32$ $\pm0.14$ $\pm0.03$ $10^{5}$
ADLER
1992B
 CPLR ${{\mathit K}^{0}}-{{\overline{\mathit K}}^{0}}$ asymmetry
$2.30$ $\pm0.035$
GEWENIGER
1974B
 ASPK
1  Value obtained from the NA48 measurements of $\Gamma\mathrm {( {{\mathit K}_L^0} \rightarrow {{\mathit \pi}^{+}} {{\mathit \pi}^{-}} )}/\Gamma\mathrm {( {{\mathit K}_L^0} \rightarrow {{\mathit \pi}} {{\mathit e}} {{\mathit \nu}_{{e}}} )}$ and ${\mathit \tau}_{{{\mathit K}_S^0} }$ and KLOE measurements of B( ${{\mathit K}_S^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ ) and ${\mathit \tau}_{{{\mathit K}_L^0} }$. $\Gamma\mathrm {( {{\mathit K}_L^0} \rightarrow {{\mathit \pi}^{+}} {{\mathit \pi}^{-}} )}$ is defined to include the inner bremsstrahlung component $\Gamma\mathrm {( {{\mathit K}_L^0} \rightarrow {{\mathit \pi}^{+}} {{\mathit \pi}^{-}} {{\mathit \gamma}} (IB))}$ but exclude the direct emission component B( ${{\mathit K}_S^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ (DE)). Their $\vert {{\mathit \eta}_{{+-}}}\vert $ value is not directly used in our fit, but enters the fit via their branching ratio and lifetime measurements.
2  AMBROSINO 2006F uses KLOE branching ratios and ${\mathit \tau}_{{{\mathit L}}}$ together with ${\mathit \tau}_{{{\mathit S}}}$ from PDG 2004 . Their $\vert \eta _{+−}\vert $ value is not directly used in our fit, but enters the fit via their branching ratio and lifetime measurements.
3  ALEXOPOULOS 2004 $\vert \eta _{+−}\vert $ uses their ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ branching fractions, ${{\mathit \tau}_{{S}}}$ = ($0.8963$ $\pm0.0005$) $ \times 10^{-10}~$s from the average of KTeV and NA48 ${{\mathit \tau}_{{S}}}$ measurements, and assumes that $\Gamma\mathrm {( {{\mathit K}_S^0} \rightarrow {{\mathit \pi}} {{\mathit \ell}} {{\mathit \nu}_{{{{\mathit \ell}}}}} )}$ = $\Gamma\mathrm {( {{\mathit K}_L^0} \rightarrow {{\mathit \pi}} {{\mathit \ell}} {{\mathit \nu}_{{{{\mathit \ell}}}}} )}$ giving B( ${{\mathit K}_S^0}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \ell}}{{\mathit \nu}_{{{{\mathit \ell}}}}}$ ) = 0.118$\%$. Their $\eta _{+−}$ is not directly used in our fit, but enters our fit via their branching ratio measurements.
4  APOSTOLAKIS 1999C report ($2.264$ $\pm0.023$ $\pm0.026+9.1[\tau _{{{\mathit s}}}−0.8934]){\times }10^{-3}$. We evaluate for our 2006 best value $\tau _{{{\mathit s}}}$= ($0.8958$ $\pm0.0005$) $ \times 10^{-10}~$s.
5  ADLER 1995B report ($2.312$ $\pm0.043$ $\pm0.030$ $-1[\Delta \mathit m-0.5274$] $+9.1[{{\mathit \tau}_{{s}}}-0.8926]){\times }10^{-3}$. We evaluate for our 1996 best values $\Delta \mathit m$ = ($0.5304$ $\pm0.0014$) $ \times 10^{-10}~\hbar{}$s${}^{-1}$ and ${{\mathit \tau}_{{s}}}$ = ($0.8927$ $\pm0.0009$) $ \times 10^{-10}~$s. Superseded by APOSTOLAKIS 1999C.
Conservation Laws:
$\mathit CP$ VIOLATION OBSERVED
References:
BRFIT 2016
RPP 2016 edition Review of Particle Physics 2016
LAI 2007
PL B645 26 Measurement of the Ratio $\gamma\mathrm {( {{\mathit K}_L^0} \rightarrow {{\mathit \pi}^{+}} {{\mathit \pi}^{-}} )}/\Gamma\mathrm {( {{\mathit K}_L^0} \rightarrow {{\mathit \pi}^{\pm}} {{\mathit e}^{\mp}} {{\mathit \nu}} )}$ and Extraction of the $\mathit CP$ Violation Parameter $\vert \eta _{+−}\vert $
AMBROSINO 2006F
PL B638 140 Measurement of the Branching Ratio of the ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ Decay with the KLOE Detector
ALEXOPOULOS 2004
PR D70 092006 Measurements of ${{\mathit K}_L^0}$ Branching Fractions and the $\mathit CP$ Violation Parameter $\vert {{\mathit \eta}^{\pm}}\vert $
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
ADLER 1995B
PL B363 243 Measurement of the $\mathit CP$ Violation Parameter $\eta _{+−}$ using Tagged ${{\mathit K}^{0}}$ and ${{\overline{\mathit K}}^{0}}$
ADLER 1992B
PL B286 180 First Determination of $\mathit CP$ Violation Parameter from ${{\mathit K}^{0}}$ $−$ ${{\overline{\mathit K}}^{0}}$ Decay Asymmetry
Also
SJNP 55 840 First Results of the CPLEAR Experiment at CERN: Study of $\mathit CP$ Violation and $\mathit CPT$ Test using ${{\mathit K}^{0}}$ $−$ ${{\overline{\mathit K}}^{0}}$ Interferometry
GEWENIGER 1974B
PL 48B 487 A New Determination of the ${{\mathit K}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ Decay Parameters
Also
PL 52B 119 The Phase $\phi _{+−}$ of $\mathit CP$ Violation in the ${{\mathit K}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ Decay