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   JSON PDGID:
S013E+-
VALUE ($ 10^{-3} $) EVTS DOCUMENT ID TECN  COMMENT
$\bf{ 2.233 \pm0.012}$ OUR FIT  Error includes scale factor of 1.7.
($222.6$ $\pm0.8$) $ \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