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.

$\phi _{\epsilon }$ = (2$\phi _{+−}+\phi _{00}$)/3

INSPIRE   PDGID:
S013EPH
This expression is a very good approximation, good to about $10^{-3}$ degrees because of the small measured values of $\phi _{00}−\phi _{+−}$ and Re $\epsilon $'/$\epsilon $, and small theoretical ambiguities.
VALUE ($^\circ{}$) DOCUMENT ID TECN  COMMENT
$\bf{ 43.5 \pm0.5}$ OUR FIT  Error includes scale factor of 1.3.  Not assuming $\mathit CPT$
$\bf{ 43.52 \pm0.05}$ OUR FIT  Error includes scale factor of 1.2.  Assuming $\mathit CPT$
$43.5164 \pm0.0002 \pm0.0518$ 1
SUPERWEAK
2016
Assuming $\mathit CPT$
$43.86$ $\pm0.63$ 2
ABOUZAID
2011
KTEV Not assuming $\mathit CPT$
1  SUPERWEAK 2016 is a fake measurement used to impose the $\mathit CPT$ or Superweak constraint $\phi _{+-}$= $\phi _{{\mathrm {SW}}}$ = tan${}^{-1}$[2 ${\Delta \mathit m\over \hbar{}}$ (${ {{\mathit \tau}_{{S}}} {{\mathit \tau}_{{L}}}\over {{\mathit \tau}_{{L}}} − {{\mathit \tau}_{{S}}} }$)]. This ``measurement'' is linearized using values near the PDG 2004 edition values of $\Delta \mathit m$, ${{\mathit \tau}_{{S}}}$ and ${{\mathit \tau}_{{L}}}$, and then adjusted to our current values as described in the following ``measurement''. SUPERWEAK 2016 measures $\phi _{\epsilon }$ = ( $43.50258$ $\pm0.00021$ ) + $54.1$ [ $\Delta \mathit m$$–$ $0.5289$ ] + $32.0$ [ ${{\mathit \tau}_{{s}}}$$–$ $0.89564$ ] ($^\circ{}$) . 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  ABOUZAID 2011 uses the full KTeV dataset collected in 1996, 1997, and 1999. See Im(${{\mathit \epsilon}^{\,'}}/{{\mathit \epsilon}}$) section for correlation information.
Conservation Laws:
$\mathit CP$ VIOLATION OBSERVED
References:
SUPERWEAK 2016
RPP 2016 edition Review of Particle Physics 2016
ABOUZAID 2011
PR D83 092001 Precise Measurements of Direct $\mathit CP$ Violation, $\mathit CPT$ Symmetry, and other Parameters in the Neutral Kaon System