STRANGE MESONS($\boldsymbol S$ = $\pm1$, $\boldsymbol C$ = $\boldsymbol B$ = 0) ${{\mathit K}^{+}}$ = ${\mathit {\mathit u}}$ ${\mathit {\overline{\mathit s}}}$, ${{\mathit K}^{0}}$ = ${\mathit {\mathit d}}$ ${\mathit {\overline{\mathit s}}}$, ${{\overline{\mathit K}}^{0}}$ = ${\mathit {\overline{\mathit d}}}$ ${\mathit {\mathit s}}$, ${{\mathit K}^{-}}$ = ${\mathit {\overline{\mathit u}}}$ ${\mathit {\mathit s}}$, similarly for ${{\mathit K}^{*}}$'s INSPIRE search

# ${{\boldsymbol K}_L^0}$ $I(J^P)$ = $1/2(0^{-})$

 ${\mathit m}_{{{\mathit K}_L^0} }–{\mathit m}_{{{\mathit K}_S^0} }$ $(52.93 \pm0.09) \times 10^{8}$ $\hbar{}$ s${}^{-1}$ (S = 1.3)
 ${{\mathit K}_L^0}$ MEAN LIFE $(5.116 \pm0.021) \times 10^{-8}$ s (S = 1.1)
ENERGY DEPENDENCE OF ${{\boldsymbol K}_L^0}$ DALITZ PLOT
 LINEAR COEFFICIENT $\mathit g$ FOR ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ $0.678 \pm0.008$  (S = 1.5)
 QUADRATIC COEFFICIENT $\mathit h$ FOR ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ $0.076 \pm0.006$
 QUADRATIC COEFFICIENT $\mathit k$ FOR ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ $0.0099 \pm0.0015$
 LINEAR COEFFICIENT $\mathit j$ FOR ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ ($\mathit CP$-VIOLATING TERM)
 QUADRATIC COEFFICIENT $\mathit f$ FOR ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ ($\mathit CP$-VIOLATING TERM)
 QUADRATIC COEFFICIENT $\mathit h$ FOR ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ $0.0006 \pm0.0012$
${{\boldsymbol K}_L^0}$ FORM FACTORS
 $\lambda _{+}$ (LINEAR ENERGY DEPENDENCE OF $\mathit f_{+}$ IN ${{\mathit K}_{{e3}}^{0}}$ DECAY) $0.0282 \pm0.0004$  (S = 1.1)
 $\lambda _{+}$ (LINEAR ENERGY DEPENDENCE OF $\mathit f_{+}$ IN ${{\mathit K}_{{\mu3}}^{0}}$ DECAY) $0.0271 \pm0.0010$  (S = 1.4)
 $\lambda _{0}$ (LINEAR ENERGY DEPENDENCE OF $\mathit f_{0}$ IN ${{\mathit K}_{{\mu3}}^{0}}$ DECAY) $0.0142 \pm0.0023$  (S = 2.8)
 $\lambda$'$_{+}$(LINEAR ${{\mathit K}_{{e3}}^{0}}$ FORM FACTOR FROM QUADRATIC FIT) $0.0240 \pm0.0012$  (S = 1.2)
 $\lambda$'$_{+}$(QUADRATIC ${{\mathit K}_{{e3}}^{0}}$ FORM FACTOR) $0.0020 \pm0.0005$  (S = 1.2)
 $\lambda$'$_{+}$(LINEAR ${{\mathit K}_{{\mu3}}^{0}}$ FORM FACTOR FROM QUADRATIC FIT) $0.0189 \pm0.0024$    ...
 $\lambda$'$_{+}$(QUADRATIC ${{\mathit K}_{{\mu3}}^{0}}$ FORM FACTOR) $0.0037 \pm0.0012$  (S = 1.3)  ...
 $\lambda _{0}$(LINEAR $\mathit f_{0}{{\mathit K}_{{\mu3}}^{0}}$ FORM FACTOR FROM QUADRATIC FIT) $0.0107 \pm0.0014$  (S = 1.3)  ...
 $M{}^{{{\mathit e}}}_{V}$ (POLE MASS FOR ${{\mathit K}_{{e3}}^{0}}$ DECAY) $878 \pm6$ MeV (S = 1.1)
 $M{}^{{{\mathit \mu}}}_{V}$ (POLE MASS FOR ${{\mathit K}_{{\mu3}}^{0}}$ DECAY) $900 \pm21$ MeV (S = 1.7)  ...
 $M{}^{{{\mathit \mu}}}_{S}$ (POLE MASS FOR ${{\mathit K}_{{\mu3}}^{0}}$ DECAY) $1222 \pm80$ MeV (S = 2.3)  ...
 ${{\mathit \Lambda}_{{+}}}$ (DISPERSIVE VECTOR FORM FACTOR FOR ${{\mathit K}_{{\mu3}}^{0}}$ DECAY) $0.0251 \pm0.0006$  (S = 1.5)
 ln$\mathit (C)$ (DISPERSIVE SCALAR FORM FACTOR FOR ${{\mathit K}_{{\mu3}}^{0}}$ DECAY) $0.175 \pm0.018$  (S = 2.0)
 $\mathit a_{1}(\mathit t_{0}$, $\mathit Q{}^{2}$) FORM FACTOR PARAMETER $1.02 \pm0.04$
 $\mathit a_{2}(\mathit t_{0}$, $\mathit Q{}^{2}$) FORM FACTOR PARAMETER $0.8 \pm2.2$
 $\vert \mathit f_{\mathit S}/\mathit f_{+}\vert$ FOR ${{\mathit K}_{{e3}}^{0}}$ DECAY $0.015 {}^{+0.014}_{-0.016}$
 $\vert \mathit f_{\mathit T}/\mathit f_{+}\vert$ FOR ${{\mathit K}_{{e3}}^{0}}$ DECAY $0.05 {}^{+0.04}_{-0.05}$
 $\vert \mathit f_{\mathit T}/\mathit f_{+}\vert$ FOR ${{\mathit K}_{{\mu3}}^{0}}$ DECAY $0.12 \pm0.12$
 $\alpha _{{{\mathit K}^{*}}}$ DECAY FORM FACTOR FOR ${{\mathit K}_{{L}}}$ $\rightarrow$ ${{\mathit \ell}^{+}}{{\mathit \ell}^{-}}{{\mathit \gamma}}$ , ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \ell}^{+}}{{\mathit \ell}^{-}}{{\mathit \ell}^{'+}}{{\mathit \ell}^{'-}}$ $-0.205 \pm0.022$  (S = 1.8)
 $\alpha _{{{\mathit K}^{*}}}$ DECAY FORM FACTOR FOR ${{\mathit K}_{{L}}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit \gamma}}$ $-0.217 \pm0.034$  (S = 2.4)
 $\alpha _{{{\mathit K}^{*}}}$ DECAY FORM FACTOR FOR ${{\mathit K}_{{L}}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}{{\mathit \gamma}}$ $-0.158 \pm0.027$
 $\alpha {}^{{\mathrm {eff}}}_{{{\mathit K}^{*}}}$ DECAY FORM FACTOR FOR ${{\mathit K}_{{L}}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit e}^{+}}{{\mathit e}^{-}}$ $-0.14 \pm0.22$
 $\alpha _{DIP}$ DECAY FORM FACTOR FOR ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \ell}^{+}}{{\mathit \ell}^{-}}{{\mathit \gamma}}$ , ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \ell}^{+}}{{\mathit \ell}^{-}}{{\mathit \ell}^{'+}}{{\mathit \ell}^{'-}}$ $-1.69 \pm0.08$  (S = 1.7)
 $\alpha _{DIP}$ DECAY FORM FACTOR FOR ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit \gamma}}$ $-1.73 \pm0.05$
 $\alpha _{DIP}$ DECAY FORM FACTOR FOR ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}{{\mathit \gamma}}$ $-1.54 \pm0.10$
 $\alpha _{DIP}$ DECAY FORM FACTOR FOR ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ $-1.6 \pm0.4$
 a$_{1}$/a$_{2}$ FORM FACTOR FOR M1 DIRECT EMISSION AMPLITUDE $-0.737 \pm0.014$ GeV${}^{2}$
 $\bar f_{S}$ DECAY FORM FACTOR FOR ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{\pm}}{{\mathit \pi}^{0}}{{\mathit e}^{\mp}}{{\mathit \nu}_{{e}}}$ $0.049 \pm0.011$  (S = 1.7)
 $\bar f_{P}$ DECAY FORM FACTOR FOR ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{\pm}}{{\mathit \pi}^{0}}{{\mathit e}^{\mp}}{{\mathit \nu}_{{e}}}$ $-0.052 \pm0.012$
 $\lambda _{g}$ DECAY FORM FACTOR FOR ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{\pm}}{{\mathit \pi}^{0}}{{\mathit e}^{\mp}}{{\mathit \nu}_{{e}}}$ $0.085 \pm0.020$
 $\bar h$ DECAY FORM FACTOR FOR ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{\pm}}{{\mathit \pi}^{0}}{{\mathit e}^{\mp}}{{\mathit \nu}_{{e}}}$ $-0.30 \pm0.13$
 $\mathit L_{3}$ CHIRAL PERT. THEO. PARAM. FOR ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{\pm}}{{\mathit \pi}^{0}}{{\mathit e}^{\mp}}{{\mathit \nu}_{{e}}}$ $-0.00396 \pm0.00028$  (S = 1.6)
 $\mathit a_{\mathit V}$, VECTOR MESON EXCHANGE CONTRIBUTION $-0.43 \pm0.06$  (S = 1.5)
$\boldsymbol CP$-VIOLATION PARAMETERS IN ${{\boldsymbol K}_L^0}$ DECAYS
CHARGE ASYMMETRY IN ${{\boldsymbol K}_{{\ell3}}^{0}}$ DECAYS
 $\mathit A_{\mathit L}$ = weighted average of $\mathit A_{\mathit L}({{\mathit \mu}}$) and $\mathit A_{\mathit L}({{\mathit e}}$) $0.00332 \pm0.00006$
 $\mathit A_{\mathit L}({{\mathit \mu}}$) = [$\Gamma\mathrm {( {{\mathit \pi}^{-}} {{\mathit \mu}^{+}} {{\mathit \nu}_{{\mu}}} )}$ $−$ $\Gamma\mathrm {( {{\mathit \pi}^{+}} {{\mathit \mu}^{-}} {{\overline{\mathit \nu}}_{{\mu}}} )}$]/SUM $0.00304 \pm0.00025$
 $\mathit A_{\mathit L}({{\mathit e}}$) = [$\Gamma\mathrm {( {{\mathit \pi}^{-}} {{\mathit e}^{+}} {{\mathit \nu}_{{e}}} )}$ $−$ $\Gamma\mathrm {( {{\mathit \pi}^{+}} {{\mathit e}^{-}} {{\overline{\mathit \nu}}_{{e}}} )}$]/SUM $0.00334 \pm0.00007$
PARAMETERS FOR ${{\boldsymbol K}_L^0}$ $\rightarrow$ 2 ${{\boldsymbol \pi}}$ DECAY
 $\vert \eta _{00}\vert$ = $\vert$A( ${{\mathit K}_L^0}$ $\rightarrow$ 2 ${{\mathit \pi}^{0}}$ ) / A( ${{\mathit K}_S^0}$ $\rightarrow$ 2 ${{\mathit \pi}^{0}}$ )$\vert$ $0.002220 \pm0.000011$  (S = 1.8)
 $\vert \eta _{+−}\vert$ = $\vert$A( ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ ) $/$ A( ${{\mathit K}_S^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ )$\vert$ $0.002232 \pm0.000011$  (S = 1.8)
 $\vert \epsilon \vert$ = (2$\vert \eta _{+−}\vert$ + $\vert \eta _{00}\vert$)/3 $0.002228 \pm0.000011$  (S = 1.8)
 $\vert \eta _{00}/\eta _{+−}\vert$ $0.9950 \pm0.0007$  (S = 1.6)
 Re($\epsilon {{}^\prime}/\epsilon$) = (1$−\vert \eta _{00}/\eta _{+−}\vert$)/3 $0.00166 \pm0.00023$  (S = 1.6)
 $\phi _{+−}$, PHASE of $\eta _{+−}$ $43.51 \pm0.05$ $^\circ{}$ (S = 1.2)  ...
 $\phi _{00}$, PHASE OF $\eta _{00}$ $43.52 \pm0.05$ $^\circ{}$ (S = 1.3)  ...
 $\phi _{\epsilon }$ = (2$\phi _{+−}+\phi _{00}$)/3 $43.52 \pm0.05$ $^\circ{}$ (S = 1.2)  ...
 Im($\epsilon {{}^\prime}/\epsilon$) = $−(\phi _{00}$ $−$ $\phi _{+−}$)/3 $-0.002 \pm0.005$ $^\circ{}$ (S = 1.7)
DECAY-PLANE ASYMMETRY IN ${{\boldsymbol \pi}^{+}}{{\boldsymbol \pi}^{-}}{{\boldsymbol e}^{+}}{{\boldsymbol e}^{-}}$ DECAYS
 $\mathit CP$ ASYMMETRY $\mathit A$ in ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit e}^{+}}{{\mathit e}^{-}}$ $0.137 \pm0.015$
PARAMETERS FOR ${{\boldsymbol e}^{+}}{{\boldsymbol e}^{-}}{{\boldsymbol e}^{+}}{{\boldsymbol e}^{-}}$ DECAYS
 $\beta _{\mathit CP}$ from ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit e}^{+}}{{\mathit e}^{-}}$ $-0.19 \pm0.07$
 $\gamma _{\mathit CP}$ from ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit e}^{+}}{{\mathit e}^{-}}$ $0.01 \pm0.11$  (S = 1.6)
CHARGE ASYMMETRY IN ${{\boldsymbol \pi}^{+}}{{\boldsymbol \pi}^{-}}{{\boldsymbol \pi}^{0}}$ DECAYS
 LINEAR COEFFICIENT $\mathit j$ FOR ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ $0.0012 \pm0.0008$
 QUADRATIC COEFFICIENT $\mathit f$ FOR ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ $0.004 \pm0.006$
PARAMETERS for ${{\boldsymbol K}_L^0}$ $\rightarrow$ ${{\boldsymbol \pi}^{+}}{{\boldsymbol \pi}^{-}}{{\boldsymbol \gamma}}$ DECAY
 $\vert \eta _{+−{{\mathit \gamma}}}\vert$ = $\vert$A( ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \gamma}}$ , $\mathit CP$ violating)/A( ${{\mathit K}_S^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \gamma}}$ )$\vert$ $0.00235 \pm0.00007$
 $\phi _{+−{{\mathit \gamma}}}$ = phase of $\eta _{+−{{\mathit \gamma}}}$ $44 \pm4$ $^\circ{}$
 $\vert \epsilon {}^{'}_{+−{{\mathit \gamma}}}\vert /\epsilon$ for ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \gamma}}$ $<0.3$   CL=90.0%
 $\vert$g$_{E1}\vert$ for ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \gamma}}$ $<0.21$   CL=90.0%
$\boldsymbol T$ VIOLATION TESTS IN ${{\boldsymbol K}_L^0}$ DECAYS
 Im($\xi$) in ${{\mathit K}_{{\mu3}}^{0}}$ DECAY (from transverse ${{\mathit \mu}}$ pol.) $-0.007 \pm0.026$
$\boldsymbol CPT$-INVARIANCE TESTS IN ${{\boldsymbol K}_L^0}$ DECAYS
 PHASE DIFFERENCE $\phi _{00}$ $−$ $\phi _{+−}$ $0.006 \pm0.014$ $^\circ{}$ (S = 1.7)  ...
 PHASE DIFFERENCE $\phi _{+−}$ $−$ $\phi _{{\mathrm {SW}}}$ $0.6 \pm1.2$ $^\circ{}$
 Re(${2\over 3}\eta _{+−}$ $+$ ${1\over 3}\eta _{00})−{\mathit A_{L}\over 2}$ $(-0.3 \pm3.5) \times 10^{-5}$
$\boldsymbol x$ = A( ${{\overline{\boldsymbol K}}^{0}}$ $\rightarrow$ ${{\boldsymbol \pi}^{-}}{{\boldsymbol \ell}^{+}}{{\boldsymbol \nu}}$ )/A( ${{\boldsymbol K}^{0}}$ $\rightarrow$ ${{\boldsymbol \pi}^{-}}{{\boldsymbol \ell}^{+}}{{\boldsymbol \nu}}$ ) = A($\Delta \boldsymbol S=−\Delta \boldsymbol Q)/A(\Delta \boldsymbol S=\Delta \boldsymbol Q$)
 REAL PART OF $\mathit x$ $-0.002 \pm0.006$
 IMAGINARY PART OF $\mathit x$ $0.0012 \pm0.0021$
 constrained fit information